Macroeconomics

National Income Accounting

Gross Domestic Product (GDP)

GDP measures the total monetary value of all final goods and services produced within a country's borders in a given time period. Only final goods are counted to avoid double counting; intermediate goods are excluded because their value is already embedded in the final product.

Three methods of measuring GDP:

1. Expenditure method: $GDP = C + I + G + (X - M)$

   • $C$ = household consumption (the largest component in most economies, typically 60--70% of GDP)
   • $I$ = investment (gross fixed capital formation + changes in inventories)
   • $G$ = government spending on goods and services (excludes transfer payments such as pensions and unemployment benefits, which are not payments for current production)
   • $X - M$ = net exports (exports minus imports)

2. Income method: sums all factor incomes earned by residents: $GDP = W + R + I + P + (\text{Mixed income}) + (\text{Taxes on production} - \text{Subsidies})$ Where $W$ = wages, $R$ = rent, $I$ = interest, $P$ = profit.

3. Output (value-added) method: sums the value added at each stage of production: $\text{Value added} = \text{Value of output} - \text{Value of intermediate inputs}$ This avoids double counting. Summing value added across all firms yields GDP.

Nominal vs. Real GDP

Nominal GDP is measured at current market prices. It changes due to both changes in output and changes in prices.

Real GDP adjusts for price level changes and is a better measure of actual output growth:

$\mathrm{Real\ GDP} = \frac{\mathrm{Nominal\ GDP}}{\mathrm{GDP\ Deflator}} \times 100$

The GDP deflator is a broad measure of the price level that includes all domestically produced goods and services:

$\mathrm{GDP\ Deflator} = \frac{\mathrm{Nominal\ GDP}}{\mathrm{Real\ GDP}} \times 100$

GNP and GNI

Gross National Product (GNP) measures the total output produced by a country's residents regardless of where it is produced:

$\mathrm{GNP} = \mathrm{GDP} + \text{Net factor income from abroad}$

Net factor income from abroad includes wages, profits, and rent earned by domestic residents from their foreign investments, minus the corresponding income earned by foreign residents within the domestic economy.

Gross National Income (GNI) is the preferred modern measure and is conceptually equivalent to GNP. It includes net primary income from abroad (compensation of employees, investment income):

$\mathrm{GNI} = \mathrm{GDP} + \text{Net primary income from abroad}$

GDP per Capita and Purchasing Power Parity

GDP per capita ($\mathrm{GDP} / \mathrm{Population}$) is used as a rough proxy for living standards but has significant limitations:

• Does not account for income distribution
• Excludes non-market activities (subsistence farming, unpaid domestic work, volunteer work)
• Does not reflect environmental degradation, resource depletion, or pollution
• Says nothing about health, education, political freedom, or leisure time
• Can be misleading in countries with large informal economies or high income inequality

Purchasing Power Parity (PPP) adjusts GDP for differences in the cost of living between countries, allowing more meaningful international comparisons. PPP GDP per capita reflects the actual volume of goods and services that the average income can buy in each country.

Limitations of GDP as a Measure of Welfare

• Non-market transactions: household production, volunteer work, and the informal economy are excluded
• Quality of life: GDP does not measure health, education, environmental quality, or political freedom
• Negative externalities: pollution, congestion, and resource depletion may increase GDP while reducing welfare
• Income distribution: a rising GDP per capita may coexist with widening inequality
• Sustainability: GDP does not distinguish between sustainable and unsustainable growth

Alternative measures include the Human Development Index (HDI), Genuine Progress Indicator (GPI), and the OECD Better Life Index.

Inflation

Measuring Inflation

Inflation is the sustained increase in the general price level over time. The primary measure is the Consumer Price Index (CPI), which tracks the price of a weighted basket of goods and services representative of household consumption.

$\mathrm{Inflation\ rate} = \frac{\mathrm{CPI}_t - \mathrm{CPI}_{t-1}}{\mathrm{CPI}_{t-1}} \times 100$

Constructing the CPI:

1. Select a representative basket of goods and services based on household expenditure surveys
2. Assign weights to each item based on its share of total household spending
3. Collect price data for each item at regular intervals
4. Calculate the weighted average price change relative to a base year

Limitations of CPI:

• Substitution bias: the basket is updated infrequently, so consumers who substitute away from goods that have become relatively more expensive are not properly accounted for
• New product bias: new goods and services (e.g., smartphones, streaming services) are not immediately included
• Quality change bias: improvements in quality that justify price increases are difficult to measure
• Outlet bias: consumers may switch to discount retailers, which is not captured
• Compositional bias: the basket may not reflect the spending patterns of all demographic groups

Types of Inflation

Demand-pull inflation occurs when aggregate demand exceeds aggregate supply at full employment, creating an inflationary gap:

$\mathrm{AD} > \mathrm{LRAS} \implies \mathrm{Price\ level\ rises}$

Causes include excessive growth in the money supply, large budget deficits, rising consumer confidence, or export booms.

Cost-push inflation occurs when costs of production increase, shifting SRAS leftward and raising prices while reducing output. Causes include:

• Rising wages (wage-push inflation)
• Higher raw material and energy prices (e.g., oil price shocks)
• Depreciation of the exchange rate (making imports more expensive)
• Indirect tax increases (e.g., VAT increases)

Built-in inflation (wage-price spiral): workers demand higher wages to keep up with rising prices, and firms pass these higher labour costs onto consumers as higher prices, creating a self-reinforcing cycle.

The Quantity Theory of Money

The Fisher equation of exchange:

$M \times V = P \times Y$

Where $M$ is the money supply, $V$ is the velocity of circulation (how many times each unit of money is spent per period), $P$ is the price level, and $Y$ is real output.

If $V$ and $Y$ are constant in the short run, then increases in $M$ lead to proportional increases in $P$:

$\%\Delta M + \%\Delta V = \%\Delta P + \%\Delta Y$

Monetarists, particularly Milton Friedman, argued that "inflation is always and everywhere a monetary phenomenon" -- sustained inflation cannot occur without excessive growth in the money supply.

Consequences of Inflation

• Redistribution: inflation redistributes income from lenders (creditors) to borrowers (debtors) because the real value of repayments falls. It also harms those on fixed incomes (pensioners)
• Uncertainty: high and unpredictable inflation discourages investment and long-term planning
• Menu costs: firms must frequently change prices, incurring administrative costs
• Shoe-leather costs: individuals spend time and resources managing cash holdings to minimise the inflation tax
• International competitiveness: if a country's inflation rate exceeds that of its trading partners, its exports become less competitive and imports become relatively cheaper, worsening the current account
• Tax distortions: if tax brackets are not indexed, inflation pushes taxpayers into higher brackets (fiscal drag)

Deflation (a sustained fall in the general price level) can be more damaging than moderate inflation:

• Increases the real burden of debt, potentially triggering defaults
• Discourages spending as consumers delay purchases expecting lower prices (deferred consumption)
• Can lead to a deflationary spiral: falling prices reduce firm revenues, leading to wage cuts and layoffs, further reducing demand and pushing prices down further
• Raises real interest rates, discouraging borrowing and investment

Disinflation is a reduction in the rate of inflation (prices are still rising, but more slowly). It is not the same as deflation.

The Phillips Curve

The short-run Phillips Curve (SRPC) depicts an inverse relationship between the rate of inflation and the rate of unemployment:

$\pi = \pi^e - \alpha(u - u_n) + \varepsilon$

Where $\pi$ is actual inflation, $\pi^e$ is expected inflation, $u$ is the unemployment rate, $u_n$ is the natural rate of unemployment (NAIRU), $\alpha$ is a parameter, and $\varepsilon$ is a supply shock term.

Short-run Phillips Curve: as unemployment falls below the natural rate, labour markets tighten, wages rise faster, and cost-push inflation increases. The curve is downward-sloping because lower unemployment is associated with higher wage demands and stronger aggregate demand.

Long-run Phillips Curve: is vertical at the natural rate of unemployment (NAIRU -- Non-Accelerating Inflation Rate of Unemployment). In the long run, there is no trade-off between inflation and unemployment. Any attempt to keep unemployment below the NAIRU through demand-side policies leads only to accelerating inflation, as workers adjust their expectations:

$\pi = \pi^e \quad \text{when } u = u_n$

The expectations-augmented Phillips curve (Friedman, Phelps): if the government tries to reduce unemployment below $u_n$, initial gains in employment are offset as workers demand higher wages in anticipation of higher inflation. The SRPC shifts upward, and unemployment returns to $u_n$ at a higher inflation rate.

Unemployment

Measuring Unemployment

The unemployment rate is the percentage of the labour force that is actively seeking work but unable to find it:

$\mathrm{Unemployment\ rate} = \frac{\mathrm{Number\ unemployed}}{\mathrm{Labour\ force}} \times 100$

The labour force includes all employed persons plus those actively seeking work. It excludes discouraged workers (those who have given up looking for work) and those not seeking work (students, retirees, homemakers).

Related measures:

• Participation rate $= \frac{\text{Labour force}}{\text{Working-age population}} \times 100$
• Employment rate $= \frac{\text{Number employed}}{\text{Working-age population}} \times 100$

Types of Unemployment

Structural unemployment is caused by a mismatch between workers' skills and the requirements of available jobs, or by geographical immobility. Examples include:

• Technological change (automation replacing jobs)
• Deindustrialisation (decline of manufacturing in advanced economies)
• Globalisation (offshoring of production to lower-cost countries)
• Skills obsolescence (workers trained for declining industries)

Structural unemployment is addressed by supply-side policies: retraining programmes, education investment, geographical mobility incentives, and labour market reforms.

Frictional unemployment is short-term unemployment that occurs when workers are between jobs, entering the labour force for the first time, or searching for better opportunities. It is always present in a dynamic economy and reflects normal turnover. Frictional unemployment is not necessarily undesirable -- it indicates that workers are searching for the best match for their skills.

Cyclical (demand-deficient) unemployment is caused by a deficiency in aggregate demand during a recession. Output falls below potential GDP, and firms lay off workers. It is addressed by demand-side policies (expansionary fiscal and monetary policy).

Seasonal unemployment occurs when workers are employed only during certain times of the year (e.g., agriculture, tourism, retail during holidays).

Real-wage unemployment is caused by wages being set above the equilibrium level (e.g., through minimum wage laws or strong trade unions), leading to an excess supply of labour. The quantity of labour supplied exceeds the quantity demanded at the artificially high wage.

The Natural Rate of Unemployment

The natural rate of unemployment ($u_n$, or NAIRU) is the rate of unemployment that prevails when the economy is at full employment. It equals the sum of frictional and structural unemployment.

$u_n = u_{\text{frictional}} + u_{\text{structural}}$

At the natural rate, cyclical unemployment is zero and the economy is operating at its potential output. The natural rate is not fixed; it can change due to:

• Changes in labour market flexibility (employment protection legislation, union power)
• Demographic changes (age distribution of the population)
• Changes in unemployment benefits and job search efficiency
• Technological change and the pace of structural adjustment

Costs of Unemployment

• Lost output: unemployment represents a waste of resources (the GDP gap). Okun's Law provides an empirical relationship: $\%\Delta Y = 3\% - 2\%\Delta u$ For every 1 percentage point increase in the unemployment rate above the natural rate, GDP falls by approximately 2% below potential
• Fiscal costs: lower tax revenues and higher government spending on unemployment benefits
• Social costs: increased poverty, crime, health problems, family breakdown, and loss of skills (hysteresis -- long-term unemployment can raise the natural rate by eroding skills and employability)
• Individual costs: loss of income, reduced self-esteem, and deterioration of mental and physical health

Aggregate Demand and Aggregate Supply

Aggregate Demand (AD)

AD is the total planned expenditure on goods and services at each price level:

$\mathrm{AD} = C + I + G + (X - M)$

The AD curve slopes downward due to:

1. Wealth effect (Pigou effect): as the price level rises, the real value of money balances falls, reducing consumption. Consumers feel less wealthy and spend less
2. Interest rate effect (Keynes effect): higher price levels increase the demand for money, raising interest rates, which reduces investment and consumption
3. Exchange rate effect (Mundell-Fleming effect): higher domestic price levels reduce export competitiveness and make imports relatively cheaper, reducing net exports

Shifts in AD

AD shifts rightward when:

• Consumer confidence rises (increasing $C$)
• Interest rates fall (increasing $I$ and $C$)
• Government spending increases (increasing $G$)
• Income taxes fall (increasing $C$ and $I$ via higher disposable income)
• The exchange rate depreciates (increasing $X$, reducing $M$)
• Foreign income rises (increasing $X$)
• Wealth increases (e.g., rising house prices, stock market gains)

AD shifts leftward when the reverse occurs.

Short-Run Aggregate Supply (SRAS)

The SRAS curve slopes upward because, in the short run, some input prices (particularly wages) are sticky. As the price level rises, firms find it profitable to increase output since revenues rise faster than costs.

SRAS shifts rightward when:

• Production costs fall (lower wages, cheaper raw materials, lower energy prices)
• Technology improves
• Productivity increases (more output per unit of input)
• Subsidies reduce costs
• The exchange rate depreciates (cheaper imported inputs)
• Favourable supply shocks (good harvests, falling oil prices)

SRAS shifts leftward when costs rise or negative supply shocks occur (e.g., natural disasters, geopolitical disruption of energy supplies).

Long-Run Aggregate Supply (LRAS)

The LRAS curve is vertical at the full employment level of output (potential GDP, $Y^*$). In the long run, all input prices are flexible, and output is determined by the economy's productive capacity (factors of production and technology). Changes in the price level do not affect long-run output.

Shifts in LRAS (representing economic growth) are caused by:

• Increases in the quantity or quality of factors of production (labour, capital, land)
• Technological progress
• Institutional improvements (better property rights, reduced corruption, more efficient legal systems)
• Education and training (improving human capital)
• Discovery of new natural resources

AD-AS Equilibrium

Short-run equilibrium is where AD intersects SRAS, determining the actual price level and output. This may differ from long-run equilibrium if the economy is operating above or below potential output.

• Recessionary gap: equilibrium output is below potential GDP. Cyclical unemployment exists.
• Inflationary gap: equilibrium output is above potential GDP. Overheating and demand-pull inflation result.

Long-run equilibrium occurs where AD intersects both SRAS and LRAS. The economy is at potential output, and cyclical unemployment is zero.

Self-correction mechanism: in the long run, a recessionary gap causes wages and other input prices to fall (downward flexibility), shifting SRAS rightward until the economy returns to potential output. An inflationary gap causes wages and prices to rise, shifting SRAS leftward until the economy returns to potential output.

Keynesians argue that wages are "sticky downward" (workers resist nominal wage cuts), so the self-correction mechanism may be slow and incomplete. This justifies active demand-side policy to close output gaps.

Fiscal Policy

Fiscal policy involves government decisions about taxation and spending to influence the economy.

Expansionary Fiscal Policy

Used during recessions to stimulate aggregate demand:

• Increase government spending ($G \uparrow$) -- direct injection into the economy
• Decrease taxes ($T \downarrow$) -- increases disposable income, boosting consumption ($C$) and investment ($I$)
• Increase transfer payments (unemployment benefits, welfare) -- supports household incomes

Contractionary Fiscal Policy

Used to reduce inflationary pressures:

• Decrease government spending ($G \downarrow$)
• Increase taxes ($T \uparrow$)
• Decrease transfer payments

The Multiplier Effect

The fiscal multiplier captures the idea that an initial change in spending generates a larger total change in national income through successive rounds of spending and re-spending.

Simple multiplier (no taxes, no imports):

$k = \frac{1}{1 - \mathrm{MPC}} = \frac{1}{\mathrm{MPS}}$

Where MPC is the marginal propensity to consume and MPS is the marginal propensity to save ($\mathrm{MPC} + \mathrm{MPS} = 1$).

An initial government spending increase of $\Delta G$ leads to a total change in output of:

$\Delta Y = k \times \Delta G = \frac{\Delta G}{1 - \mathrm{MPC}}$

The multiplier with proportional taxation:

$k_T = \frac{1}{1 - \mathrm{MPC}(1 - t)}$

Where $t$ is the marginal tax rate. Higher taxes reduce the multiplier because they leak spending power out of the circular flow at each round.

The multiplier with imports:

$k_{T,M} = \frac{1}{\mathrm{MPS} + t \times \mathrm{MPC} + \mathrm{MPM}}$

Where MPM is the marginal propensity to import. Imports are a leakage from the circular flow.

Worked example: if $\mathrm{MPC} = 0.75$, $t = 0.2$, and $\mathrm{MPM} = 0.1$:

$k = \frac{1}{0.25 + 0.2 \times 0.75 + 0.1} = \frac{1}{0.25 + 0.15 + 0.1} = \frac{1}{0.50} = 2$

A USD 100 billion increase in government spending would increase GDP by USD 200 billion.

The Balanced Budget Multiplier

If government spending and taxes increase by the same amount ($\Delta G = \Delta T$), the net effect on GDP is positive but smaller than the spending multiplier alone:

$k_B = \frac{\Delta Y}{\Delta G} = 1$

A USD 100 billion increase in both $G$ and $T$ increases GDP by USD 100 billion. The government spending injection has a direct multiplier effect, while the tax increase reduces disposable income by only the amount of the tax, and the induced reduction in consumption is MPC times the tax.

Budget Position

• Budget deficit: $G > T$ (government spending exceeds tax revenue)
• Budget surplus: $T > G$
• Balanced budget: $G = T$
• Public debt: the accumulated total of past budget deficits, representing total government borrowing obligations

Cyclical vs. structural budget balance:

• The cyclical deficit is the portion of the deficit attributable to the business cycle (lower tax revenues and higher transfer payments during recessions)
• The structural deficit is the deficit that would exist even at full employment, reflecting the underlying fiscal stance independent of the cycle

Limitations of Fiscal Policy

• Time lags: recognition lag (identifying the problem), decision lag (political process of approving spending or tax changes), implementation lag (projects take time to begin)
• Crowding out: increased government borrowing to finance a deficit may raise interest rates, reducing private investment. The extent of crowding out depends on the state of the economy (it is less significant during deep recessions when resources are idle)
• Size of the multiplier: if the multiplier is small (due to high MPS, high MPM, or high tax rates), fiscal policy has limited impact
• Political constraints: tax increases and spending cuts are politically unpopular; deficit spending may face opposition
• Inefficiency: government spending may not be directed to the most productive uses
• Ricardian equivalence: the proposition that households anticipate future tax liabilities from current deficit spending and therefore save rather than spend any tax cuts, neutralising the fiscal stimulus. Empirical support is limited but the concept highlights the importance of expectations

Monetary Policy

Monetary policy is conducted by a central bank and involves managing the money supply and interest rates to influence economic activity.

Functions of a Central Bank

1. Monetary policy: setting interest rates and managing the money supply to achieve price stability and support economic growth
2. Banker to the government: managing government accounts and issuing debt
3. Banker to commercial banks: holding reserves and providing liquidity (lender of last resort)
4. Issuer of currency: controlling the note issue
5. Financial stability: supervising and regulating the banking system

Expansionary Monetary Policy

• Lower the policy interest rate (e.g., the bank rate, federal funds rate, refinancing rate)
• Reduce reserve requirements for commercial banks
• Purchase government bonds (open market operations) to increase the money supply
• Quantitative easing (QE): large-scale purchases of government bonds and other assets when policy rates are already near zero (zero lower bound)

Lower interest rates reduce the cost of borrowing, encouraging consumption and investment. They also reduce the incentive to save and may depreciate the exchange rate, boosting net exports.

Contractionary Monetary Policy

• Raise the policy interest rate
• Increase reserve requirements
• Sell government bonds to reduce the money supply

Higher interest rates discourage borrowing and spending, reduce aggregate demand, and help control inflation.

Transmission Mechanism

The process by which monetary policy affects the real economy:

1. Interest rate channel: central bank changes the policy rate; commercial banks adjust their lending and deposit rates; changes in borrowing costs affect $C$ and $I$
2. Exchange rate channel: higher interest rates attract capital inflows, appreciating the exchange rate, reducing net exports ($X - M$)
3. Asset price channel: interest rate changes affect house prices and stock prices, altering household wealth and collateral values
4. Expectations channel: central bank forward guidance shapes expectations about future rates, influencing current spending and investment decisions
5. Credit channel: policy rates affect bank lending standards and the availability of credit

The Money Multiplier

In a fractional reserve banking system, commercial banks lend out a fraction of their deposits, creating new money:

$\text{Money multiplier} = \frac{1}{\text{Reserve ratio}} = \frac{1}{r}$

If the reserve ratio is $r = 0.1$, a deposit of USD 1000 can ultimately support USD 10000 in deposits through successive rounds of lending and re-depositing.

In practice, the money multiplier is less predictable because:

• Banks may hold excess reserves (above the required minimum)
• Not all loans are re-deposited (some are held as cash or used to purchase imports)
• The central bank can influence the money supply more directly through open market operations and quantitative easing

Inflation Targeting

Many central banks (e.g., the Bank of England, ECB, RBA) use inflation targeting: setting an explicit target for the inflation rate (typically 2%) and adjusting monetary policy to achieve it.

Advantages:

• Provides a clear nominal anchor for expectations
• Enhances central bank credibility and accountability
• Helps anchor inflation expectations, reducing the sacrifice ratio (the output loss required to reduce inflation)

Challenges:

• Supply-side shocks may create a conflict between inflation targeting and output stabilisation
• The transmission mechanism may be unpredictable
• Financial stability may be neglected in pursuit of price stability

Economic Growth

Short-Run vs. Long-Run Growth

Short-run growth is an increase in real GDP caused by shifts in AD or SRAS, moving the economy along its LRAS curve. It is associated with reductions in cyclical unemployment and utilisation of spare capacity. Short-run growth is not sustainable once the economy reaches full employment.

Long-run growth is an increase in the economy's productive capacity, represented by a rightward shift of the LRAS curve. It is the only sustainable source of rising living standards.

Sources of Long-Run Growth

Solow growth model: output depends on capital ($K$), labour ($L$), and technology ($A$):

$Y = A \cdot f(K, L)$

In per-worker terms:

$y = A \cdot f(k)$

Where $y = Y/L$ and $k = K/L$.

• Capital accumulation: increasing the stock of physical capital through investment. Subject to diminishing returns -- each additional unit of capital per worker produces smaller increases in output per worker
• Human capital: education, training, and health improvements that raise labour productivity
• Technological progress: innovation that increases total factor productivity (TFP). In the Solow model, technological progress is the only source of sustained long-run growth in output per worker, since capital accumulation alone is subject to diminishing returns
• Institutional quality: rule of law, property rights, political stability, and effective governance. North (1990) emphasised that institutions are the fundamental determinant of long-run economic performance
• Demographic factors: population growth increases total output but not necessarily output per capita. Age structure matters -- a high dependency ratio (many young or old relative to workers) reduces per capita growth

The Solow Model: Steady State

In the Solow model, the economy converges to a steady state where capital per worker is constant:

$s \cdot f(k^*) = (n + \delta) \cdot k^*$

Where $s$ is the savings rate, $n$ is the population growth rate, and $\delta$ is the depreciation rate. At the steady state:

• Investment per worker equals break-even investment (the amount needed to maintain the existing capital per worker)
• Output per worker is constant
• Growth in output per worker is zero (unless there is technological progress)

With exogenous technological progress at rate $g$, output per worker grows at rate $g$ in the steady state. Total output grows at rate $n + g$.

Endogenous Growth Theory

The Solow model treats technological progress as exogenous (determined outside the model). Endogenous growth theory (Romer, Lucas) explains technological progress as the result of deliberate economic decisions:

• R&D investment: firms invest in research and development, generating new knowledge and technology
• Human capital accumulation: individuals invest in education and skills
• Knowledge spillovers: new ideas benefit other firms and workers, creating positive externalities that can prevent diminishing returns

A simple endogenous growth model: $Y = A \cdot K$, where $A$ is a constant reflecting the productivity of capital. Here, there are no diminishing returns to capital, and the growth rate is:

$g_Y = s \cdot A - \delta$

Policies that increase the savings rate permanently increase the growth rate.

Convergence Debate

The absolute convergence hypothesis suggests that poorer countries will grow faster than richer ones and eventually catch up, since they have more scope for capital accumulation (diminishing returns set in later).

The conditional convergence hypothesis holds that convergence only occurs among countries with similar savings rates, population growth, institutional quality, and human capital. Empirical evidence broadly supports conditional convergence.

Supply-Side Policies

Supply-side policies aim to increase the economy's productive capacity (shift LRAS rightward) by improving the quantity, quality, and efficiency of factors of production.

Market-Oriented Supply-Side Policies

These policies aim to make markets work more efficiently by reducing government intervention:

• Privatisation: transferring state-owned enterprises to the private sector, motivated by the assumption that private ownership provides stronger incentives for efficiency, innovation, and responsiveness to consumers
• Deregulation: removing unnecessary government regulations that increase costs and stifle competition (e.g., removing barriers to entry, reducing licensing requirements)
• Tax reforms: reducing marginal tax rates to incentivise work, investment, and entrepreneurship. The Laffer curve illustrates the theoretical relationship between tax rates and tax revenue -- beyond some optimal rate, higher taxes discourage economic activity so much that revenue falls
• Labour market reforms: reducing trade union power, making it easier to hire and fire workers, reducing minimum wages, and cutting unemployment benefits to increase labour market flexibility
• Reducing welfare dependency: tightening eligibility for benefits and implementing workfare programmes
• Promoting competition: enforcing anti-trust laws to prevent monopolies and cartels

Interventionist Supply-Side Policies

These policies involve direct government action to improve the quality of factors of production:

• Investment in education and training: improving human capital through public spending on schools, universities, vocational training, and apprenticeship programmes
• Investment in infrastructure: transport networks (roads, railways, ports), energy systems, and digital infrastructure that reduce costs for firms and increase productivity
• Research and development subsidies: government funding for R&D in universities and firms to promote technological progress
• Industrial policy: government support for specific industries or technologies deemed strategically important (e.g., green technology, semiconductor manufacturing)
• Regional policy: government incentives to encourage firms to locate in depressed areas, reducing geographical inequalities

Evaluation of Supply-Side Policies

Advantages:

• Address the root causes of low growth (low productivity, insufficient capital) rather than merely managing demand
• Reduce inflationary pressure by increasing productive capacity
• Improve international competitiveness
• Can be complementary to demand-side policies

Disadvantages:

• Time lags: education, infrastructure, and R&D take years or decades to yield results
• High upfront costs (especially for interventionist policies)
• May increase inequality (e.g., reducing taxes on high earners, cutting welfare benefits)
• Market-oriented policies may sacrifice equity for efficiency
• The effectiveness of tax cuts in stimulating supply is debated (evidence on the Laffer curve is mixed)
• Deregulation may lead to negative externalities (e.g., financial deregulation contributing to the 2008 crisis)

Business Cycles

Phases of the Business Cycle

The business cycle refers to fluctuations in economic activity around the long-run trend:

1. Expansion (boom): rising GDP, falling unemployment, rising consumer and business confidence, upward pressure on prices. Interest rates may rise as the central bank combats inflation
2. Peak: the highest point of the cycle. The economy is at or above potential output. Inflation may be high; resource constraints emerge
3. Recession (contraction): falling GDP, rising unemployment, declining confidence, falling investment. A technical recession is commonly defined as two consecutive quarters of negative GDP growth
4. Trough: the lowest point of the cycle. The economy is below potential output. Unemployment is high; spare capacity exists

Causes of Business Cycles

• Demand-side shocks: changes in consumer confidence, government spending, monetary policy, or net exports
• Supply-side shocks: oil price shocks, natural disasters, technological disruptions, geopolitical events
• Financial cycles: credit booms and busts, asset price bubbles (housing, equities)
• Inventory cycles: firms overstock during booms and cut production during downturns (Kitchin cycle)
• Investment cycles: fluctuations in business investment driven by expectations and interest rates

Real Business Cycle Theory

A school of thought that attributes business cycles primarily to real (technology) shocks rather than monetary or demand-side factors. Proponents argue that fluctuations in GDP represent optimal responses to changes in productivity, and that government intervention to stabilise the cycle is unnecessary and potentially harmful.

Common Pitfalls

• Confusing nominal and real GDP. Always clarify which measure you are using, especially when comparing growth rates over time or across countries.
• Stating that "unemployment is caused by recession" without specifying cyclical unemployment. Structural and frictional unemployment exist even at full employment.
• Assuming that fiscal policy is always effective. Crowding out, time lags, and the size of the multiplier all limit its impact.
• Confusing a movement along the AD curve (caused by a change in the price level) with a shift of the AD curve (caused by changes in $C$, $I$, $G$, or $X - M$).
• Treating the Phillips Curve as a policy menu. The short-run trade-off does not exist in the long run.
• Forgetting that the LRAS curve is vertical. In the long run, demand-side policies only affect the price level, not output.
• Confusing disinflation with deflation. Disinflation means inflation is falling but still positive; deflation means prices are actually falling.
• Stating that the multiplier is always greater than 1. With high taxes and high imports, the multiplier can be very small or even less than 1 (if leakages are very large).
• Assuming that government debt is always undesirable. Borrowing to finance productive investment in infrastructure or education can boost long-run growth, making the debt sustainable.
• Confusing the budget deficit with the national debt. The deficit is the annual shortfall; the debt is the accumulated total of all past deficits.

Practice Problems

Problem 1: GDP Calculation with Multiple Components

An economy has the following expenditure components (in billions): Consumption = \4200$, Investment$= $1100$, Government spending$= $1500$, Exports$= $800$, Imports$= $950$.

(a) Calculate GDP and net exports.

(b) If the GDP deflator is 115 and the base year is 100, calculate real GDP.

(c) If the population is 50 million, calculate GDP per capita.

(a) $GDP = C + I + G + (X - M) = 4200 + 1100 + 1500 + (800 - 950)$

$GDP = 4200 + 1100 + 1500 + (-150) = \$6650 \text{ billion}$

Net exports = X - M = 800 - 950 = -\150$ billion (a trade deficit).

(b) \mathrm{Real\ GDP} = \frac{\mathrm{Nominal\ GDP}}{\mathrm{GDP\ Deflator}} \times 100 = \frac{6650}{115} \times 100 = \5782.6 \text\\{ billion\\}$

(c) GDP per capita = \frac{6650 \times 10^9}{50 \times 10^6} = \133,000$

Problem 2: Inflation Rate and Real Values

The CPI basket costs USD 240 in year 1 and USD 252 in year 2. A worker earned USD 50,000 in year 1 and USD 52,000 in year 2.

(a) Calculate the inflation rate between year 1 and year 2.

(b) Calculate the worker's real income in year 2 (in year 1 dollars).

(c) Has the worker's purchasing power increased or decreased?

(a) $\mathrm{Inflation\ rate} = \frac{252 - 240}{240} \times 100 = \frac{12}{240} \times 100 = 5\%$

(b) Real income in year 2 = \frac{52\,000}{252/240} = \frac{52\,000}{1.05} = \49,523.81$

(c) The worker's real income fell from USD 50,000 to approximately USD 49,524. Despite a nominal raise of USD 2,000, purchasing power decreased because the raise ($4\%$) was less than inflation ($5\%$).

Problem 3: Fiscal Multiplier with Taxes and Imports

The government increases spending by USD 50 billion. The marginal propensity to consume is $0.75$, the marginal tax rate is $0.2$, and the marginal propensity to import is $0.15$.

(a) Calculate the multiplier.

(b) Calculate the total change in national income.

(c) Explain why this multiplier is smaller than the simple multiplier.

(a) $\mathrm{MPS} = 1 - 0.75 = 0.25$

$k = \frac{1}{\mathrm{MPS} + t \times \mathrm{MPC} + \mathrm{MPM}} = \frac{1}{0.25 + 0.2 \times 0.75 + 0.15}$ $k = \frac{1}{0.25 + 0.15 + 0.15} = \frac{1}{0.55} = 1.818$

(b) \Delta Y = k \times \Delta G = 1.818 \times 50 = \90.9 \text\\{ billion\\}$

(c) The multiplier is smaller than the simple multiplier ($\frac{1}{0.25} = 4$) because taxes and imports are leakages from the circular flow. At each round of the multiplier process, some income is taxed (reducing disposable income) and some spending leaks abroad (on imports), reducing the amount re-spent in the domestic economy.

Problem 4: AD-AS Analysis of a Supply Shock

An economy is initially in long-run equilibrium at potential GDP. A sharp increase in world oil prices causes a negative supply shock.

(a) Explain the short-run effects on output, employment, and the price level.

(b) Explain the long-run self-correction process.

(c) Evaluate the use of demand-side policies in this situation.

(a) The negative supply shock shifts SRAS leftward. In the short run:

• Output falls below potential GDP (negative output gap)
• Unemployment rises (firms reduce production and lay off workers)
• The price level rises (cost-push inflation)

This combination of rising inflation and rising unemployment is called stagflation.

(b) In the long run, the recessionary gap puts downward pressure on wages and other input prices (as unemployment is high, workers have less bargaining power). Lower input costs shift SRAS back to the right, eventually restoring output to potential GDP and returning the price level to its original level. However, this adjustment process may be slow and painful.

(c) Expansionary fiscal or monetary policy could shift AD rightward to restore output more quickly, but at the cost of a permanently higher price level. This risks embedding higher inflation expectations. Contractionary policy would reduce inflation but worsen the recession. The dilemma illustrates the limitations of demand-side policy in response to supply shocks -- supply-side policies (e.g., investing in alternative energy, improving energy efficiency) are more appropriate for addressing the underlying cause.

Problem 5: Phillips Curve Analysis

An economy has a natural rate of unemployment of $5\%$. The current unemployment rate is $3\%$, and inflation is $4\%$. The expected inflation rate is $2\%$.

(a) Using the expectations-augmented Phillips curve, explain whether inflation is likely to accelerate.

(b) What would happen if the central bank attempted to maintain unemployment at $3\%$ permanently?

(c) How would a supply shock (e.g., rising oil prices) shift the Phillips curve?

(a) With unemployment at $3\%$, which is below the natural rate of $5\%$, the economy is overheating. The expectations-augmented Phillips curve predicts:

$\pi = \pi^e - \alpha(u - u_n)$

Since $u < u_n$, actual inflation exceeds expected inflation ($4\% > 2\%$). Workers will observe that inflation is higher than expected and will revise their expectations upward in the next period. As $\pi^e$ rises, the SRPC shifts upward, and at the same unemployment rate ($3\%$), inflation will be higher. This process continues -- inflation accelerates.

(b) To maintain unemployment at $3\%$ permanently, the central bank would need to accept ever-accelerating inflation, as each period of over-stimulation raises expected inflation and shifts the SRPC upward. This is unsustainable. In the long run, the economy returns to $u_n = 5\%$ with higher inflation.

(c) A negative supply shock (rising oil prices) shifts the SRPC upward and to the right. At any given unemployment rate, inflation is higher because of the cost-push effect. This creates a dilemma: the central bank must choose between accepting higher inflation (accommodating the shock) or accepting higher unemployment (tightening policy to prevent inflation from rising).

Problem 6: Money Multiplier and Open Market Operations

A central bank conducts open market operations by purchasing USD 200 million of government bonds. The reserve ratio is $0.1$ (10%), and the public holds no cash outside the banking system.

(a) Calculate the maximum possible increase in the money supply.

(b) List three reasons why the actual increase may be less than the theoretical maximum.

(a) Money multiplier $= \frac{1}{r} = \frac{1}{0.1} = 10$

Maximum increase in money supply = \200 \text\\{ million\\} \times 10 = $2,000 \text\\{ million\\}$

(b) The actual increase may be less because:

1. Banks may choose to hold excess reserves above the required minimum rather than lending them out
2. Not all loans are re-deposited in the banking system (some may be held as cash or used to purchase imports)
3. The public may choose to hold more cash outside banks, reducing the deposit base available for lending
4. Banks may be unwilling to lend during a recession due to increased credit risk (credit crunch)

Problem 7: Supply-Side Policy Evaluation

A government is considering two supply-side policies to promote long-run growth: (a) reducing the corporate tax rate from $30\%$ to $20\%$, and (b) increasing public spending on vocational training by USD 10 billion per year.

Evaluate both policies using economic theory.

(a) Reducing corporate tax:

• Market-oriented supply-side policy
• Likely to increase after-tax profitability, incentivising business investment ($I \uparrow$)
• May attract foreign direct investment
• Shifts LRAS rightward by increasing the capital stock
• Could increase inequality if the benefits accrue primarily to shareholders
• Effectiveness depends on the responsiveness of investment to tax changes (tax elasticity of investment)
• Short-term cost: reduced government tax revenue (may increase the budget deficit unless offset by spending cuts)

(b) Increasing vocational training spending:

• Interventionist supply-side policy
• Improves human capital, raising labour productivity
• Addresses structural unemployment by equipping workers with relevant skills
• Shifts LRAS rightward by improving the quality of the labour force
• Direct fiscal cost of USD 10 billion per year
• Time lag: benefits may not materialise for several years
• More equitable -- benefits workers directly, particularly those in lower-skilled occupations

Both policies shift LRAS rightward but through different channels (capital vs. labour). The optimal mix depends on the economy's specific constraints (e.g., a capital-scarce economy may benefit more from tax cuts; an economy with skill mismatches may benefit more from training).

National Income in Depth (HL Extension)

Real vs. Nominal GDP: Comprehensive Analysis

Nominal GDP values output at current market prices. Changes in nominal GDP reflect both changes in the quantities of goods and services produced and changes in their prices.

Real GDP values output at constant (base year) prices, isolating the effect of quantity changes from price changes.

$\text{Real GDP}_t = \sum_{i=1}^{n} P_{i,0} \cdot Q_{i,t}$

Where $P_{i,0}$ is the base-year price of good $i$ and $Q_{i,t}$ is the quantity produced in year $t$.

The GDP Deflator in Detail

The GDP deflator is the most comprehensive price index because it covers all domestically produced goods and services (consumption, investment, government spending, and net exports):

$\text{GDP Deflator}_t = \frac{\text{Nominal GDP}_t}{\text{Real GDP}_t} \times 100$

Unlike the CPI, the GDP deflator:

• Includes capital goods and government services (not just consumer goods)
• Excludes imported goods (the CPI includes imports if consumers buy them)
• Uses a Paasche-type index (current-period quantities as weights), which tends to understate inflation compared to the CPI (Laspeyres index)

GDP per Capita Calculations

$\text{GDP per capita} = \frac{\text{GDP}}{\text{Population}}$

$\text{Real GDP per capita} = \frac{\text{Real GDP}}{\text{Population}}$

Limitations as a welfare measure:

• Distribution-blind: GDP per capita of USD 50,000 is consistent with one person earning all income or with perfectly equal distribution
• Non-market activities excluded: subsistence farming, household production, volunteer work
• Environmental costs ignored: pollution and resource depletion may increase GDP
• Quality improvements difficult to capture: a smartphone today costs less (in real terms) than a basic mobile phone 20 years ago, yet delivers far more value
• Does not measure leisure: two countries with the same GDP per capita may have very different working hours
• Informal economy: countries with large informal sectors have GDP figures that significantly understate actual economic activity

Chain-Weighted Real GDP

Modern national accounts use chain-weighting to avoid the substitution bias of fixed-weight indices. Chain-weighted GDP uses a moving base year, averaging Laspeyres and Paasche measures:

$\text{Chain-weighted growth rate} = \sqrt{\text{Laspeyres growth rate} \times \text{Paasche growth rate}}$

This provides a more accurate measure of real growth, particularly when relative prices change significantly.

Common Pitfalls in National Income Accounting

• Comparing nominal GDP across years without adjusting for inflation. Always use real GDP for time-series comparisons.
• Using GDP per capita as a direct measure of individual income. GDP per capita is an average; median income provides a better picture of the typical person's experience.
• Double counting intermediate goods. Only final goods and services should be included in GDP.
• Confusing GDP with GNI. GDP measures output within borders; GNI measures income earned by residents regardless of location. For countries with large FDI inflows (e.g., Ireland), GDP significantly exceeds GNI.

AD/AS Model: Comprehensive Shifting Factors (HL Extension)

Comprehensive List of AD Shift Factors

Factor	Direction of AD Shift	Mechanism
Consumer confidence rises	Rightward	$C \uparrow$
Interest rates fall	Rightward	$C \uparrow, I \uparrow$
Income taxes cut	Rightward	$Y_d \uparrow \implies C \uparrow$
Government spending rises	Rightward	$G \uparrow$ directly
Wealth increases (house prices, stocks)	Rightward	$C \uparrow$ (wealth effect)
Exchange rate depreciates	Rightward	$X \uparrow, M \downarrow$
Foreign income rises	Rightward	$X \uparrow$
Population growth	Rightward	More consumers $\implies C \uparrow$
Consumer expectations of inflation rise	Rightward	$C \uparrow$ (buy now before prices rise)
Inflation expectations fall	Leftward	$C \downarrow$ (defer purchases)
Business confidence falls	Leftward	$I \downarrow$
Corporation tax rises	Leftward	$I \downarrow$ (lower after-tax returns)

Comprehensive List of SRAS Shift Factors

Factor	Direction of SRAS Shift	Mechanism
Wage rates fall	Rightward	Lower production costs
Raw material prices fall	Rightward	Lower production costs
Energy prices fall	Rightward	Lower production costs
Technology improves	Rightward	Higher productivity
Subsidies increase	Rightward	Lower effective costs
Exchange rate depreciates	Rightward (if imported inputs)	Cheaper inputs in domestic currency
Adverse supply shock (oil price spike)	Leftward	Higher production costs
Indirect tax (VAT) increases	Leftward	Higher costs passed to prices
Good harvest	Rightward	Lower food costs
Natural disaster	Leftward	Supply disruption

AD-AS Diagram Analysis Framework

For any AD/AS question, follow this systematic approach:

1. Identify the initial equilibrium (intersection of AD, SRAS, and ideally LRAS)
2. Identify which curve(s) shift and in which direction
3. Determine the short-run effects on price level, output, and employment
4. Identify the type of gap created (inflationary or recessionary)
5. Describe the long-run adjustment (if applicable) through wage and price flexibility
6. Evaluate the policy implications

Keynesian Multiplier Algebra (HL Extension)

Derivation of the Multiplier from the Consumption Function

Starting with the equilibrium condition in an open economy with government:

$Y = C + I + G + X - M$

Substituting the consumption function $C = a + b(Y - T)$ and the import function $M = mY$:

$Y = a + b(Y - T) + I + G + X - mY$

Assuming a proportional tax $T = tY$:

$Y = a + bY - btY + I + G + X - mY$

$Y - bY + btY + mY = a + I + G + X$

$Y(1 - b + bt + m) = a + I + G + X$

$Y = \frac{a + I + G + X}{1 - b(1 - t) + m}$

The denominator is the sum of all leakages:

$k = \frac{1}{1 - b(1 - t) + m} = \frac{1}{\text{MPS} + \text{MPT} + \text{MPM}}$

The Tax Multiplier

A change in autonomous taxes $\Delta T$ changes disposable income by $\Delta T$, which changes consumption by $b \cdot \Delta T$ (where $b$ is MPC):

$\Delta Y = \frac{-b}{1 - b(1 - t) + m} \cdot \Delta T$

The tax multiplier is:

$k_T = \frac{-b}{1 - b(1 - t) + m}$

The tax multiplier is always smaller in absolute value than the spending multiplier because a tax change affects only disposable income, not spending directly. Some of the tax change is absorbed by reduced saving.

Relationship:

$|k_G| = \frac{1}{1 - b(1 - t) + m} > |k_T| = \frac{b}{1 - b(1 - t) + m}$

Since $b < 1$, the spending multiplier always exceeds the absolute value of the tax multiplier.

Balanced Budget Multiplier: Proof

If $\Delta G = \Delta T$ (lump-sum taxes for simplicity):

$\Delta Y = k_G \cdot \Delta G + k_T \cdot \Delta T = \frac{1}{1-b}\Delta G + \frac{-b}{1-b}\Delta T$

$\Delta Y = \frac{\Delta G - b \cdot \Delta G}{1 - b} = \frac{\Delta G(1 - b)}{1 - b} = \Delta G$

The balanced budget multiplier equals 1, regardless of the MPC. An equal increase in government spending and taxes increases GDP by exactly the amount of the spending increase.

Worked Example: Full Multiplier Algebra

An economy has: $a = 300$, $b = 0.8$, $t = 0.25$, $m = 0.1$, $I = 500$, $G = 400$, $X = 200$.

$k = \frac{1}{1 - 0.8(1 - 0.25) + 0.1} = \frac{1}{1 - 0.6 + 0.1} = \frac{1}{0.5} = 2$

$Y^* = 2 \times (300 + 500 + 400 + 200) = 2 \times 1400 = 2800$

If $G$ increases by 50: $\Delta Y = 2 \times 50 = 100$. New $Y^* = 2900$.

If $T$ increases by 50 (lump sum): $k_T = \frac{-0.8}{0.5} = -1.6$. $\Delta Y = -1.6 \times 50 = -80$.

If both $G$ and $T$ increase by 50: $\Delta Y = 100 - 80 = 20 = \Delta G$. The balanced budget multiplier is confirmed.

Phillips Curve Analysis in Depth (HL Extension)

Short-Run Phillips Curve: Algebra

The expectations-augmented Phillips curve:

$\pi_t = \pi_t^e - \alpha(u_t - u_n) + \varepsilon_t$

Where:

• $\pi_t$ is the actual inflation rate in period $t$
• $\pi_t^e$ is the expected inflation rate
• $u_t$ is the actual unemployment rate
• $u_n$ is the natural rate of unemployment (NAIRU)
• $\alpha$ is the slope parameter (how quickly inflation responds to unemployment gaps)
• $\varepsilon_t$ is a supply shock term

Implications:

• When $u_t < u_n$: $\pi_t > \pi_t^e$ (inflation exceeds expectations; unemployment below natural rate)
• When $u_t = u_n$: $\pi_t = \pi_t^e$ (inflation equals expectations; economy at natural rate)
• When $u_t > u_n$: $\pi_t < \pi_t^e$ (inflation below expectations; unemployment above natural rate)

Adaptive Expectations and the Acceleration Hypothesis

Under adaptive expectations, agents form expectations based on past inflation:

$\pi_t^e = \pi_{t-1}$

If the government tries to maintain $u_t < u_n$ permanently:

Period 1: $\pi_1 = \pi_0 - \alpha(u_1 - u_n)$. Since $u_1 < u_n$, $\pi_1 > \pi_0$. Period 2: $\pi_2^e = \pi_1$. $\pi_2 = \pi_1 - \alpha(u_1 - u_n) > \pi_1$. Period 3: $\pi_3^e = \pi_2$. $\pi_3 = \pi_2 - \alpha(u_1 - u_n) > \pi_2$.

Inflation accelerates without bound. This is the accelerationist hypothesis (Friedman, 1968; Phelps, 1967).

Long-Run Phillips Curve

In the long run, expectations catch up to reality ($\pi_t^e = \pi_t$):

$\pi_t = \pi_t - \alpha(u_t - u_n) + \varepsilon_t$

$0 = -\alpha(u_t - u_n) + \varepsilon_t$

$u_t = u_n + \frac{\varepsilon_t}{\alpha}$

In the absence of supply shocks ($\varepsilon_t = 0$), $u_t = u_n$ regardless of the inflation rate. The LRPC is vertical at $u_n$.

The Sacrifice Ratio

The sacrifice ratio measures the cumulative loss in output (as a percentage of one year's GDP) required to reduce inflation by one percentage point:

$\text{Sacrifice ratio} = \frac{\text{Cumulative }\%\Delta Y \text{ below trend}}{\text{Reduction in inflation}}$

Typical estimates for advanced economies range from 1.5 to 3. A sacrifice ratio of 2 means that reducing inflation by 1 percentage point requires a cumulative output loss equal to 2% of annual GDP.

The NAIRU and Hysteresis

The NAIRU is not fixed. Hysteresis refers to the phenomenon where a prolonged period of high unemployment can raise the natural rate itself:

• Long-term unemployed workers lose skills and become detached from the labour force
• Discouraged workers stop searching and exit the labour force
• Capital stock depreciates during long recessions, reducing the economy's productive capacity
• Insider-outsider dynamics: employed workers (insiders) resist wage cuts, keeping wages above the level needed to employ the long-term unemployed (outsiders)

If hysteresis is significant, the LRPC may shift rightward after a deep recession, implying that the costs of unemployment are permanent rather than temporary.

Common Pitfalls in Phillips Curve Analysis

• Drawing the LRPC as downward-sloping. The LRPC is always vertical at the NAIRU.
• Assuming the short-run trade-off is a menu for policymakers. The trade-off exists only for unexpected inflation.
• Confusing adaptive and rational expectations. Adaptive expectations are backward-looking (based on past inflation); rational expectations use all available information and may predict policy correctly, rendering systematic demand management ineffective.

Monetary Policy Transmission Mechanism (HL Extension)

Interest Rate Channel

The traditional channel through which monetary policy affects the real economy:

1. Central bank changes the policy rate (e.g., bank rate)
2. Commercial banks adjust their lending and deposit rates
3. Changes in borrowing costs affect household consumption ($C$) and business investment ($I$)
4. Changes in $C$ and $I$ shift AD

Interest sensitivity of components:

• Investment: highly sensitive to interest rates. The present value of future cash flows falls when the discount rate rises. Projects that were profitable at lower rates may become unviable at higher rates
• Housing: mortgage interest is a significant component of housing costs. Higher rates reduce housing demand, construction activity, and house prices
• Consumer durables: purchases of cars, appliances, and furniture are often financed, so they are sensitive to interest rate changes
• Consumption generally: the substitution effect of higher rates encourages saving over spending; the income effect (higher interest income for savers) partially offsets this

Exchange Rate Channel

1. Central bank raises domestic interest rates
2. Higher returns attract foreign capital inflows (hot money)
3. Increased demand for the domestic currency causes appreciation
4. Appreciation makes exports more expensive and imports cheaper
5. Net exports ($X - M$) fall, reducing AD

$r \uparrow \implies \text{Capital inflows} \uparrow \implies \text{Exchange rate} \uparrow \implies (X - M) \downarrow \implies \text{AD} \downarrow$

Asset Price Channel

1. Central bank lowers interest rates
2. Lower rates make bonds less attractive relative to equities and property
3. Increased demand for equities and property raises their prices
4. Higher asset prices increase household wealth (wealth effect), boosting consumption
5. Higher share prices lower the cost of equity financing for firms, encouraging investment
6. Higher property values increase collateral for borrowing, relaxing credit constraints

$r \downarrow \implies \text{Asset prices} \uparrow \implies \text{Wealth} \uparrow \implies C \uparrow \implies \text{AD} \uparrow$

Expectations Channel (Forward Guidance)

Central bank communication about the expected future path of policy rates shapes expectations:

• If the central bank signals that rates will remain low for an extended period, households and firms may bring forward spending and investment decisions
• If the central bank credibly commits to an inflation target, inflation expectations remain anchored, reducing the sacrifice ratio
• Forward guidance can be effective even when policy rates are at the zero lower bound

Credit Channel

1. Central bank raises reserve requirements or conducts open market sales
2. Bank reserves decrease, reducing banks' capacity to lend
3. Banks tighten lending standards (higher collateral requirements, stricter credit assessments)
4. Credit-constrained households and firms reduce spending and investment
5. AD falls

The credit channel amplifies the interest rate channel and is particularly important during financial crises when banks are reluctant to lend.

Limitations of Monetary Policy

• Zero lower bound (ZLB): nominal interest rates cannot fall significantly below zero (otherwise cash would be preferable to bank deposits). At the ZLB, conventional monetary policy is exhausted, requiring unconventional measures (quantitative easing, negative interest rates, forward guidance)
• Lags: monetary policy works with long and variable lags (typically 12--18 months for the full effect on inflation)
• Velocity of circulation: if $V$ falls (as during a liquidity trap), increasing $M$ may not increase $P \times Y$
• Banking sector health: if banks are undercapitalised, they may not transmit lower policy rates to lending rates
• Global factors: in small open economies, domestic interest rates are constrained by international capital flows (the trilemma: cannot simultaneously have fixed exchange rate, free capital movement, and independent monetary policy)

Fiscal Policy in Depth (HL Extension)

Automatic Stabilisers

Automatic stabilisers are features of the tax and transfer system that automatically dampen economic fluctuations without any deliberate policy action:

• Progressive income taxes: as incomes rise during booms, taxpayers move into higher brackets, paying a larger fraction of income in tax. During recessions, falling incomes reduce tax liabilities, leaving more disposable income
• Unemployment benefits: when unemployment rises during recessions, transfer payments automatically increase, supporting household incomes and cushioning the fall in consumption
• Welfare benefits: means-tested benefits automatically increase when incomes fall
• Corporate taxes: profits fall during recessions, reducing corporate tax liabilities

Effect on the multiplier: automatic stabilisers reduce the effective multiplier by increasing the cyclically-adjusted budget deficit during recessions (providing stimulus) and reducing it during booms (restraining demand).

Discretionary vs. Automatic Fiscal Policy

Feature	Automatic	Discretionary
Timing	Immediate (built into the system)	Subject to recognition, decision, and implementation lags
Political process	No legislation required	Requires legislative approval
Cyclical sensitivity	Automatically counter-cyclical	May be pro-cyclical if poorly timed
Predictability	Highly predictable	Uncertain (depends on political negotiations)

Crowding Out

Full crowding out: in a classical (full-employment) economy, increased government spending raises demand for loanable funds, increasing the interest rate and reducing private investment by exactly the amount of the fiscal expansion. $\Delta G$ is fully offset by $\Delta I$.

$\Delta Y = 0 \text{ (in the classical case)}$

Partial crowding out: in a Keynesian framework with idle resources, the interest rate rise reduces some investment but not all. The net increase in output is positive but smaller than the simple multiplier predicts.

$0 < \Delta Y < k \cdot \Delta G$

No crowding out: at the zero lower bound or in a deep recession (liquidity trap), increased government spending does not raise interest rates because the central bank accommodates the fiscal expansion. The full multiplier operates:

$\Delta Y = k \cdot \Delta G$

Factors determining the degree of crowding out:

• State of the economy: more crowding out at full employment, less during recessions
• Elasticity of investment demand for interest rates: more elastic investment $\implies$ more crowding out
• Central bank response: if the central bank accommodates (maintains interest rates), crowding out is minimised
• Openness of the economy: higher interest rates attract capital inflows, appreciating the exchange rate and reducing net exports (further crowding out)

Ricardian Equivalence

Proposed by Robert Barro (1974), Ricardian equivalence states that households are forward-looking and understand that current deficit spending must be financed by future taxes. Therefore:

$\text{Tax cut today} = \text{Tax increase tomorrow (with interest)}$

Households save the entire tax cut to pay future taxes, leaving consumption unchanged:

$\Delta C = 0, \quad \Delta S = \Delta T_{\text{cut}}$

Conditions for Ricardian equivalence to hold:

1. Perfect capital markets (households can borrow and save freely)
2. Infinite horizons (households care about their descendants' welfare through bequests)
3. Lump-sum taxes (not distortionary)
4. Full information about future government obligations

Why Ricardian equivalence typically fails in practice:

• Borrowing constraints: liquidity-constrained households cannot save a tax cut for future taxes
• Myopia: many households do not plan beyond the short term
• Finite lives: people do not fully internalise the tax burden on future generations
• Distortionary taxes: future taxes are not lump-sum but affect incentives
• Uncertainty: households may not know the timing or magnitude of future tax increases

Empirical evidence overwhelmingly rejects Ricardian equivalence. Tax cuts do stimulate consumption, particularly for liquidity-constrained households, but the multiplier is smaller than predicted by simple Keynesian models.

Common Pitfalls in Fiscal Policy

• Confusing the cyclical deficit with the structural deficit. The cyclical deficit reflects the state of the economy; only the structural deficit reflects the government's discretionary fiscal stance.
• Assuming crowding out is always significant. In a recession with idle resources and low interest rates, crowding out may be negligible.
• Stating that government debt is always harmful. If debt is used to finance productive investment (infrastructure, education), it can enhance growth and be self-financing.

Supply-Side Policies: Laffer Curve (HL Extension)

The Laffer Curve

The Laffer curve illustrates the theoretical relationship between the tax rate and tax revenue:

$\text{Tax revenue} = t \times Y(t)$

Where $Y(t)$ is the tax base (income, output), which depends on the tax rate. At $t = 0$, revenue is zero. At $t = 100\%$, revenue is also zero (no one works or invests if all income is taxed). Between these extremes, there is a revenue-maximising tax rate $t^*$.

Implications:

• For tax rates above $t^*$, reducing the tax rate can increase revenue by stimulating economic activity
• For tax rates below $t^*$, reducing the tax rate decreases revenue
• The position of $t^*$ is empirically uncertain and debated. Most estimates for income tax place it between 50% and 70%
• The Laffer curve does not imply that all tax cuts pay for themselves. Empirical evidence suggests that tax cuts typically reduce revenue, though they may partly pay for themselves through growth effects

Market-Based vs. Interventionist Supply-Side Policies: Evaluation

Criterion	Market-Based	Interventionist
Speed of impact	Faster (tax cuts work quickly)	Slower (education, infrastructure take years)
Fiscal cost	Revenue loss (tax cuts)	Direct spending required
Equity impact	May increase inequality	Can reduce inequality
Risk of government failure	Lower (less direct intervention)	Higher (inefficient allocation, corruption)
Risk of market failure	Higher (deregulation may cause externalities)	Lower (government can correct failures)
Political feasibility	Varies (tax cuts popular, deregulation controversial)	Varies (spending popular, taxes unpopular)

Economic Growth Models (HL Extension)

Solow Growth Model: Comprehensive Analysis

The Solow model (1956) explains long-run economic growth through capital accumulation, labour growth, and technological progress.

Production function:

$Y = F(K, L)$

In per-worker terms ($y = Y/L$, $k = K/L$):

$y = f(k)$

Capital accumulation:

$\dot{k} = s \cdot f(k) - (n + \delta)k$

Where $s$ is the savings rate, $n$ is the population growth rate, and $\delta$ is the depreciation rate.

• $s \cdot f(k)$: investment per worker (a fraction $s$ of output per worker)
• $(n + \delta)k$: break-even investment (the investment needed to maintain the existing capital-labour ratio as the labour force grows and capital depreciates)

Steady state: where $\dot{k} = 0$, so $s \cdot f(k^*) = (n + \delta)k^*$.

At the steady state, capital per worker and output per worker are constant.

Convergence:

Starting from any $k_0$, the economy converges to $k^*$ because:

• If $k < k^*$: $s \cdot f(k) > (n + \delta)k$, so $k$ rises
• If $k > k^*$: $s \cdot f(k) < (n + \delta)k$, so $k$ falls

Effect of parameter changes:

• Higher savings rate $s$: shifts the investment curve upward; $k^*$ increases; higher output per worker in the long run, but NOT higher long-run growth (output per worker is constant at the steady state)
• Higher population growth $n$: shifts the break-even investment line upward; $k^*$ decreases; lower output per worker (more workers sharing the same capital stock)
• Higher depreciation $\delta$: same effect as higher $n$
• Technological progress: shifts the production function upward; increases $k^*$ and $y^*$; is the only source of sustained growth in output per worker

Golden Rule of capital accumulation: the savings rate that maximises steady-state consumption per worker:

$c^* = f(k^*) - (n + \delta)k^*$

Consumption is maximised where the slope of the production function equals $(n + \delta)$:

$f'(k^{**}) = n + \delta$

$\text{MPK} = n + \delta$

If the actual savings rate is higher than the golden rule rate, the economy is dynamically inefficient: reducing saving would increase both current and future consumption.

Human Capital in the Solow Model

An augmented Solow model (Mankiw, Romer, Weil, 1992) includes human capital $H$:

$Y = K^\alpha H^\beta (AL)^{1-\alpha-\beta}$

Where $H$ represents the stock of human capital. This model explains more of the cross-country variation in income per capita than the basic Solow model, but still predicts convergence (albeit conditional on human capital).

Productivity and Total Factor Productivity (TFP)

Total factor productivity (TFP, or the Solow residual) measures the portion of output growth not explained by growth in inputs (capital and labour):

$\frac{\Delta A}{A} = \frac{\Delta Y}{Y} - \alpha \frac{\Delta K}{K} - (1 - \alpha) \frac{\Delta L}{L}$

Where $A$ is TFP and $\alpha$ is capital's share of income (approximately $1/3$ in most economies).

TFP captures:

• Technological progress
• Institutional quality
• Resource allocation efficiency
• Management practices
• Knowledge spillovers

In most advanced economies, TFP accounts for the majority of long-run growth. In developing countries, capital accumulation typically accounts for a larger share.

Additional Practice Problems

Problem 8: Comprehensive Multiplier Analysis

An economy has the following characteristics:

• Autonomous consumption: USD 100 billion
• MPC: 0.75
• Proportional tax rate: 20%
• MPM: 0.15
• Investment: USD 250 billion
• Government spending: USD 300 billion
• Exports: USD 120 billion
• Autonomous imports: USD 40 billion

(a) Calculate the equilibrium level of output.

(b) Calculate the spending multiplier, tax multiplier, and balanced budget multiplier.

(c) If the government wants to close a recessionary gap of USD 80 billion, by how much should it increase government spending? By how much should it cut taxes to achieve the same result?

(a) $k = \frac{1}{\mathrm{MPS} + t \cdot \mathrm{MPC} + \mathrm{MPM}} = \frac{1}{0.25 + 0.2 \times 0.75 + 0.15} = \frac{1}{0.25 + 0.15 + 0.15} = \frac{1}{0.55} = 1.818$

Autonomous expenditure $= C_{\text{aut}} + I + G + X - M_{\text{aut}} = 100 + 250 + 300 + 120 - 40 = 730$

$Y^* = k \times \text{Autonomous expenditure} = 1.818 \times 730 = 1327.3$ billion USD

(b) Spending multiplier: $k_G = 1.818$

Tax multiplier: $k_T = \frac{-\mathrm{MPC}}{1 - \mathrm{MPC}(1-t) + \mathrm{MPM}} = \frac{-0.75}{0.55} = -1.364$

Balanced budget multiplier: $k_B = k_G + k_T = 1.818 + (-1.364) = 0.454$

(With proportional taxes, the balanced budget multiplier is not exactly 1; it depends on the tax rate. For lump-sum taxes, $k_B = 1$.)

(c) Using government spending: $\Delta Y = k_G \cdot \Delta G \implies 80 = 1.818 \cdot \Delta G \implies \Delta G = 44.0$ billion

Using tax cuts: $\Delta Y = k_T \cdot \Delta T \implies 80 = -1.364 \cdot \Delta T \implies \Delta T = -58.6$ billion (a tax cut of 58.6 billion)

Government spending is more effective than tax cuts (a smaller change is needed) because the full spending injection goes directly into aggregate expenditure, whereas a tax cut is partly saved.

Problem 9: AD-AS with Simultaneous Shocks

An economy is in long-run equilibrium. Simultaneously, consumer confidence falls and the government implements a major infrastructure programme.

(a) Analyse the short-run effects on output, employment, and the price level.

(b) Explain the long-run adjustment process.

(c) Under what conditions would the price level remain unchanged in the short run?

(a) Two simultaneous shifts:

1. Consumer confidence falls $\implies$ AD shifts leftward (reducing output, employment, and the price level)
2. Infrastructure programme $\implies$ both AD shifts rightward (increasing $G$) and LRAS shifts rightward (increasing productive capacity)

The net short-run effect depends on the relative magnitudes:

• If the AD shift from infrastructure exceeds the AD shift from lost confidence, AD shifts net-rightward: output, employment, and price level rise
• If the AD shifts offset each other, but LRAS shifts right: output rises, price level may fall
• If the confidence effect dominates, AD shifts net-leftward: output, employment, and price level fall

(b) In the long run, the economy self-corrects to potential output. If short-run output is above potential, wages and prices rise, shifting SRAS leftward. If below potential, wages and prices fall, shifting SRAS rightward. The LRAS shift from infrastructure is permanent, so long-run potential output is higher than originally.

(c) The price level remains unchanged if the leftward AD shift from falling confidence exactly offsets the rightward AD shift from government spending. In this case, AD does not shift net, but LRAS shifts rightward. Output increases while the price level stays the same. This is the ideal supply-side outcome: growth without inflation.

Problem 10: Expectations-Augmented Phillips Curve

An economy has a natural rate of unemployment of $5\%$ and a Phillips curve parameter $\alpha = 0.5$. Initially, inflation is $2\%$ and unemployment is $5\%$. In period 1, the government stimulates the economy, reducing unemployment to $3\%$. Assume adaptive expectations.

(a) Calculate inflation in periods 1 through 5.

(b) What happens to the short-run Phillips curve over time?

(c) How much output is gained permanently from this policy?

(a) Period 0: $u = 5\%$, $\pi = 2\%$, $\pi^e = 2\%$

Period 1: $u = 3\%$. $\pi_1 = \pi_0 - 0.5(3 - 5) = 2 - 0.5(-2) = 2 + 1 = 3\%$

Period 2: $\pi_2^e = \pi_1 = 3\%$. If $u = 3\%$ still: $\pi_2 = 3 - 0.5(-2) = 4\%$

Period 3: $\pi_3^e = 4\%$. $\pi_3 = 4 - 0.5(-2) = 5\%$

Period 4: $\pi_4^e = 5\%$. $\pi_4 = 5 - 0.5(-2) = 6\%$

Period 5: $\pi_5^e = 6\%$. $\pi_5 = 6 - 0.5(-2) = 7\%$

Inflation accelerates by 1 percentage point per period: 2%, 3%, 4%, 5%, 6%, 7%.

(b) The SRPC shifts upward by 1 percentage point each period as expectations adjust. Each SRPC is parallel to the previous one but shifted upward by the change in expected inflation.

(c) Zero. The permanent output gain is zero because in the long run, unemployment returns to the natural rate ($5\%$) and output returns to potential. The only permanent effect is higher inflation. The government cannot permanently reduce unemployment below the NAIRU through demand-side policies alone.

Problem 11: Solow Model Comparative Statics

An economy has a Cobb-Douglas production function $y = k^{0.3}$ (per-worker terms). The savings rate is $s = 0.2$, the population growth rate is $n = 0.02$, and the depreciation rate is $\delta = 0.05$.

(a) Find the steady-state capital per worker and output per worker.

(b) What happens to steady-state output per worker if the savings rate increases to $s = 0.3$?

(c) What happens if population growth increases to $n = 0.04$?

(a) Steady state: $s \cdot k^{0.3} = (n + \delta)k$

$0.2 \cdot k^{0.3} = 0.07 \cdot k$

$0.2 = 0.07 \cdot k^{0.7}$

$k^{0.7} = 0.2 / 0.07 = 2.857$

$k^* = 2.857^{1/0.7} = 2.857^{1.429}$

$\ln k^* = 1.429 \times \ln 2.857 = 1.429 \times 1.050 = 1.500$

$k^* = e^{1.500} = 4.482$

$y^* = k^{*0.3} = 4.482^{0.3}$

$\ln y^* = 0.3 \times \ln 4.482 = 0.3 \times 1.500 = 0.450$

$y^* = e^{0.450} = 1.568$

(b) With $s = 0.3$: $0.3 \cdot k^{0.3} = 0.07 \cdot k$

$k^{0.7} = 0.3/0.07 = 4.286$

$k^* = 4.286^{1.429}$

$\ln k^* = 1.429 \times 1.455 = 2.079$

$k^* = e^{2.079} = 7.997$

$y^* = 7.997^{0.3}$

$\ln y^* = 0.3 \times 2.079 = 0.624$

$y^* = e^{0.624} = 1.866$

Steady-state output per worker rises from 1.568 to 1.866 (a 19% increase). However, the growth rate of output per worker in the steady state remains zero -- the higher savings rate produces a one-time level effect, not a permanent growth effect.

(c) With $n = 0.04$, $s = 0.2$: $0.2 \cdot k^{0.3} = 0.09 \cdot k$

$k^{0.7} = 0.2/0.09 = 2.222$

$k^* = 2.222^{1.429}$

$\ln k^* = 1.429 \times 0.799 = 1.142$

$k^* = e^{1.142} = 3.133$

$y^* = 3.133^{0.3}$

$\ln y^* = 0.3 \times 1.142 = 0.343$

$y^* = e^{0.343} = 1.409$

Higher population growth reduces steady-state output per worker from 1.568 to 1.409 (a 10% decline). More workers share the same capital stock, reducing capital per worker. This explains why rapidly growing populations may experience lower growth in output per capita.

Problem 12: Monetary and Fiscal Policy Coordination

An economy is in a deep recession with output 15% below potential. The central bank has already cut interest rates to near zero (the zero lower bound). Evaluate the effectiveness of monetary and fiscal policy in this situation, using IS-LM analysis.

Monetary policy at the ZLB:

With interest rates at or near zero, conventional monetary policy is exhausted. The LM curve is horizontal at the ZLB (liquidity trap). Further increases in the money supply do not lower interest rates because the opportunity cost of holding money is already negligible. Monetary policy is ineffective in stimulating output.

Options:

• Quantitative easing (QE): central bank purchases long-term bonds and other assets to reduce long-term interest rates and increase the money supply. May have limited effectiveness if banks hold the excess reserves rather than lending them out.
• Forward guidance: committing to keep rates low for an extended period to shape expectations. Can reduce long-term rates and boost confidence.
• Negative interest rates: technically possible but may cause cash hoarding and distort bank profitability.

Fiscal policy at the ZLB:

Fiscal policy is highly effective at the ZLB because there is no crowding out. The IS curve shifts rightward, but since the LM curve is horizontal, the interest rate does not rise. The full multiplier operates:

$\Delta Y = k \cdot \Delta G$

There is no offsetting increase in interest rates to crowd out private investment.

Policy coordination:

• Expansionary fiscal policy shifts IS rightward, increasing output
• If the central bank accommodates by keeping rates low (LM does not shift), there is no crowding out and the full multiplier operates
• If fiscal expansion raises inflation expectations, real interest rates fall further (the Fisher effect), providing additional stimulus
• Coordination between fiscal and monetary authorities is essential: the central bank must commit to maintaining low rates despite potential inflationary pressure from fiscal expansion

This analysis supports the use of aggressive fiscal stimulus during deep recessions at the ZLB, as demonstrated by fiscal responses to the 2008 financial crisis and the COVID-19 pandemic.

Exchange Rate Systems and the Trilemma (HL Extension)

The Impossible Trinity (Trilemma)

A country cannot simultaneously maintain all three of:

1. Fixed exchange rate
2. Free capital movement
3. Independent monetary policy

It must choose two of the three.

Choice	Examples	Implications
Fixed rate + Free capital	Hong Kong (USD peg), Eurozone	No independent monetary policy
Fixed rate + Independent monetary policy	China (pre-2005, capital controls)	Must restrict capital flows
Free capital + Independent monetary policy	US, UK, Australia, Canada	Floating exchange rate

Floating Exchange Rate: Advantages and Disadvantages

Advantages:

• Automatic stabiliser: the exchange rate adjusts to correct current account imbalances
• Independent monetary policy: the central bank can set interest rates for domestic objectives
• No need for large foreign exchange reserves (the market determines the rate)
• Absorbs external shocks: a commodity exporter facing a terms-of-trade shock sees its currency depreciate, cushioning the impact on the domestic economy

Disadvantages:

• Volatility: exchange rate fluctuations create uncertainty for trade and investment
• Speculation: speculative capital flows can cause excessive volatility (as in the 1997 Asian financial crisis)
• Imported inflation: depreciation raises the cost of imports
• Lack of discipline: governments may pursue irresponsible fiscal or monetary policies, knowing the exchange rate will adjust

Fixed Exchange Rate: Advantages and Disadvantages

Advantages:

• Certainty for traders and investors (reduces transaction costs and exchange rate risk)
• Disciplines monetary and fiscal policy (the government must maintain the peg)
• Anchors inflation expectations (particularly when pegged to a low-inflation currency)
• Facilitates trade and investment with the anchor currency country

Disadvantages:

• Loss of independent monetary policy (the central bank must set rates to maintain the peg)
• Need for large foreign exchange reserves (to defend against speculative attacks)
• Vulnerability to speculative attacks (if markets believe the peg is unsustainable)
• Misalignment: the fixed rate may diverge from the equilibrium rate, causing trade imbalances
• "Imported" monetary policy: the country effectively adopts the anchor country's monetary policy, which may not be appropriate for its economic conditions

The Mundell-Fleming Model

The Mundell-Fleming model extends the IS-LM framework to an open economy with international capital mobility.

Key result with floating exchange rates and perfect capital mobility:

• Fiscal policy is ineffective: an increase in government spending raises interest rates, attracting capital inflows that appreciate the exchange rate, reducing net exports and offsetting the fiscal expansion. Output is unchanged
• Monetary policy is highly effective: an increase in the money supply lowers interest rates, causing capital outflows that depreciate the exchange rate, increasing net exports. Output increases by the full multiplier

$\Delta G > 0 \implies \Delta Y = 0 \quad \text{(fiscal policy is fully crowded out)}$ $\Delta M^s > 0 \implies \Delta Y > 0 \quad \text{(monetary policy is fully effective)}$

Key result with fixed exchange rates and perfect capital mobility:

• Fiscal policy is highly effective: an increase in government spending raises interest rates, attracting capital inflows. The central bank must intervene (buy foreign currency, sell domestic currency) to prevent appreciation. This increases the money supply, amplifying the fiscal expansion
• Monetary policy is ineffective: the central bank cannot independently change the money supply. Any attempt to increase the money supply lowers interest rates, causing capital outflows and downward pressure on the exchange rate. The central bank must sell reserves to defend the peg, reversing the money supply increase

$\Delta G > 0 \implies \Delta Y > 0 \quad \text{(fiscal policy is amplified)}$ $\Delta M^s > 0 \implies \Delta Y = 0 \quad \text{(monetary policy is fully offset)}$

Currency Crises: First-Generation and Second-Generation Models

First-generation models (Krugman, 1979): currency crises are caused by fundamental inconsistencies between domestic macroeconomic policies and the fixed exchange rate. If a government runs persistent fiscal deficits financed by central bank credit creation, foreign exchange reserves are depleted and the peg becomes unsustainable. The crisis occurs when reserves reach a critical threshold.

Second-generation models (Obstfeld, 1994): currency crises can be self-fulfilling. Even if the government's policies are consistent with maintaining the peg, a speculative attack may raise the cost of defending the peg (through higher interest rates that cause a recession). The government may rationally choose to abandon the peg if the economic costs of defense exceed the costs of devaluation. If speculators anticipate this, they attack, and the crisis becomes a self-fulfilling prophecy.

Policy implications:

• Maintaining a fixed exchange rate requires fiscal and monetary discipline
• Large reserves and strong institutional credibility reduce vulnerability to speculative attacks
• Flexible exchange rates provide an automatic adjustment mechanism but create uncertainty
• Capital controls can provide a buffer but come at the cost of reduced access to international capital markets

Common Pitfalls in Exchange Rate Analysis

• Confusing nominal and real exchange rates. A nominal depreciation does not always improve competitiveness if it is offset by higher domestic inflation
• Assuming that a current account deficit is always caused by an overvalued exchange rate. It may reflect excess domestic demand or structural factors
• Stating that a fixed exchange rate eliminates exchange rate risk. It eliminates nominal risk but not real risk (if the peg is abandoned, the adjustment can be sudden and large)
• Confusing the trilemma options. Many countries operate managed floats that are neither fully fixed nor fully floating, occupying an intermediate position

Additional Practice Problems

Problem 13: Trilemma and Policy Analysis

Country Z has a fixed exchange rate pegged to the US dollar. Capital flows are freely mobile.

(a) If the US Federal Reserve raises interest rates, what must Country Z's central bank do?

(b) If Country Z wants to reduce unemployment through monetary stimulus, what trade-off does it face?

(c) Evaluate the options available to Country Z.

(a) If the Fed raises US interest rates, the interest rate differential (US rate minus Country Z rate) increases. Capital flows from Z to the US, putting downward pressure on Z's currency.

To maintain the peg, Country Z's central bank must:

1. Raise its own interest rates to match or exceed the Fed's increase (losing monetary policy independence)
2. Sell foreign exchange reserves to buy its own currency (depleting reserves)

Option 1 is the sustainable approach; option 2 is temporary.

(b) To reduce unemployment, Country Z would need to lower interest rates (expansionary monetary policy). But this would:

• Increase the interest rate differential against the US, causing capital outflows
• Put downward pressure on the exchange rate
• Require the central bank to sell reserves

If the central bank persists, reserves will be depleted and the peg will collapse. This is the fundamental trade-off: Country Z cannot have an independent monetary policy while maintaining a fixed peg with free capital mobility.

(c) Options for Country Z:

1. Maintain the peg and accept US monetary policy: sacrifice domestic objectives (unemployment remains high) for exchange rate stability. This is the current position

2. Abandon the peg (float): regain monetary policy independence. The currency will depreciate, boosting exports but causing imported inflation and higher foreign debt costs. This solves the policy trade-off but creates exchange rate uncertainty

3. Impose capital controls: restrict capital outflows, allowing some monetary independence while maintaining the peg. Effective in the short run but distorts capital allocation, reduces investor confidence, and is difficult to enforce

4. Establish a currency board: a stronger form of fixed exchange rate where the domestic currency is fully backed by foreign reserves. Provides maximum credibility but eliminates all monetary flexibility

5. Join a monetary union: adopt the US dollar (dollarisation) or join a regional monetary union. Eliminates exchange rate risk entirely but permanently sacrifices monetary sovereignty

The optimal choice depends on Country Z's specific circumstances: the importance of trade with the US, the credibility of its institutions, the depth of its financial markets, and the nature of the shocks it faces.

Problem 14: Mundell-Fleming Comparative Analysis

An open economy with perfect capital mobility and a floating exchange rate. The IS curve is $Y = 800 - 40r$ and the LM curve is $Y = 400 + 20r$. The net export function is $NX = 100 - 5e$ where $e$ is the exchange rate (higher $e$ means depreciation).

(a) Find the initial equilibrium.

(b) The government increases spending by 50. Analyse the impact on output, interest rates, and the exchange rate.

(c) The central bank increases the money supply, shifting LM to $Y = 500 + 20r$. Analyse the impact.

(a) $800 - 40r = 400 + 20r \implies 400 = 60r \implies r = 6.67\%$

$Y = 800 - 40(6.67) = 800 - 266.7 = 533.3$

(b) New IS: $Y = 850 - 40r$

$850 - 40r = 400 + 20r \implies 450 = 60r \implies r = 7.5\%$

But with perfect capital mobility and floating rates, the interest rate is pinned to the world rate. The IS shift raises the interest rate, attracting capital inflows. The exchange rate appreciates ($e$ falls), reducing net exports. The IS curve shifts back to its original position.

$\Delta Y = 0$: fiscal policy is completely ineffective under floating rates with perfect capital mobility.

(c) New LM: $Y = 500 + 20r$

$800 - 40r = 500 + 20r \implies 300 = 60r \implies r = 5.0\%$

$Y = 800 - 40(5.0) = 800 - 200 = 600$

The interest rate falls from 6.67% to 5.0%, causing capital outflows and exchange rate depreciation. The depreciation increases net exports, shifting IS rightward and amplifying the monetary stimulus.

$\Delta Y = 600 - 533.3 = 66.7$: monetary policy is highly effective under floating rates.

Deflation Spiral (HL Extension)

Mechanism of Deflation

A deflationary spiral is a self-reinforcing cycle of falling prices, rising real debt burdens, reduced spending, falling output, and further price declines:

$\text{Prices fall} \implies \text{Real interest rates rise} \implies \text{Borrowing costs increase}$ $\implies \text{Investment falls} \implies \text{Aggregate demand falls}$ $\implies \text{Output falls} \implies \text{Unemployment rises}$ $\implies \text{Demand falls further} \implies \text{Prices fall more}$

This vicious cycle is difficult to escape because:

• Rising real debt burdens lead to defaults, bank failures, and credit contraction
• Falling demand discourages investment (the investment paradox: if prices are falling, firms delay investment because goods will be cheaper in the future)
• Consumers defer purchases, reducing aggregate demand further
• Central banks may be constrained by the zero lower bound on nominal interest rates

Fisher Debt Deflation

Irving Fisher (1933) argued that deflation increases the real burden of debt:

$r_{\text{real}} = i - \pi$

When $\pi < 0$ (deflation), the real interest rate exceeds the nominal rate. If firms and households borrowed expecting inflation, deflation increases the real value of their debts, potentially triggering defaults.

Numerical example: A firm borrows USD 100 million at a nominal rate of 5%, expecting 2% inflation.

Expected real rate $= 5\% - 2\% = 3\%$.

If deflation of 3% occurs instead:

Actual real rate $= 5\% - (-3\%) = 8\%$.

The real debt burden is nearly triple the expected level, potentially pushing the firm into bankruptcy.

Historical Examples

Japan's Lost Decades: Since the 1990s, Japan has experienced persistent mild deflation (approximately 0.5% per year). Despite near-zero nominal interest rates, the economy has struggled to achieve sustained growth. The nominal interest rate was cut to zero in 1999 and negative in 2016, but deflationary expectations persisted. This is consistent with the liquidity trap: monetary policy lost traction because the nominal interest rate could not fall far enough to achieve a negative real rate sufficient to stimulate borrowing.

The Great Depression (1929--1933): US prices fell by approximately 25% between 1929 and 1933. The deflation spiral was amplified by bank failures (over 9,000 US banks failed between 1930 and 1933), which destroyed the money supply and further deepened the crisis.

Policy Responses to Deflation

1. Quantitative easing (QE): large-scale asset purchases by the central bank to lower long-term interest rates and increase the money supply, even when short-term rates are at the ZLB
2. Inflation targeting with overshoot: committing to achieve an inflation target above zero (e.g., 2%) to manage expectations and prevent deflationary psychology
3. Fiscal expansion: government spending increases aggregate demand directly, bypassing the monetary transmission mechanism
4. Negative interest rates: charging banks for holding excess reserves, encouraging lending (adopted by the ECB, Bank of Japan, and others since 2014)

Quantitative Easing: Mechanics (HL Extension)

How QE Works

When the policy rate is at or near zero, the central bank cannot stimulate further through conventional interest rate cuts. QE involves the central bank purchasing financial assets (typically government bonds and, in some cases, corporate bonds and mortgage-backed securities) from the private sector.

Mechanism:

1. Central bank creates bank reserves to purchase assets
2. Asset prices rise (increased demand for bonds pushes up prices, lowering yields)
3. Lower long-term yields reduce borrowing costs for firms and households
4. Portfolio rebalancing: investors sell bonds to the central bank and purchase other assets (equities, corporate bonds, real estate), raising their prices
5. The wealth effect (higher asset prices) increases consumption
6. Lower borrowing costs stimulate investment

Balance sheet effects:

$\text{CB purchases bonds} \implies \text{Bank reserves increase} \implies \text{Lending capacity rises}$

$\text{Bond prices rise} \implies \text{Long-term yields fall} \implies \text{Investment increases}$

QE in Practice

Federal Reserve (2008--2014): three rounds of QE purchased approximately USD 3.5 trillion in assets, expanding the Fed's balance sheet from USD 900 billion to USD 4.5 trillion.

ECB (2015--2018): the Asset Purchase Programme (APP) purchased EUR 1.7 trillion in government bonds and EUR 132 billion in corporate bonds. The Pandemic Emergency Purchase Programme (PEPP, 2020) added EUR 1.85 trillion.

Bank of Japan (2001--): QQE (Quantitative and Qualitative Easing) has expanded the BoJ balance sheet to over JPY 700 trillion (approximately 130% of GDP), making it the most aggressive QE programme among major central banks.

Limitations of QE

1. Uncertain transmission: the link between QE and real economic activity is less direct than conventional monetary policy
2. Asset price inflation: QE may inflate asset prices (stocks, bonds, real estate) without corresponding increases in real output, exacerbating wealth inequality
3. Exit strategy risk: unwinding a large balance sheet without destabilising markets
4. Distributional effects: QE benefits asset holders disproportionately, while the benefits to non-asset holders are indirect
5. Diminishing returns: the marginal impact of additional QE declines as the balance sheet grows

Fiscal Rules (HL Extension)

Types of Fiscal Rules

Fiscal rules constrain government discretion over spending and taxation:

1. Budget balance rule: the budget must be balanced (or the deficit must not exceed X% of GDP)
2. Debt-to-GDP rule: public debt must not exceed a ceiling (e.g., the Maastricht Treaty's 60% ceiling)
3. Expenditure growth rule: government spending growth must not exceed a specified rate (e.g., the EU's expenditure benchmark)
4. Cyclical adjustment rule: the structural (cyclically-adjusted) balance must meet a target, allowing the actual balance to fluctuate with the cycle
5. Revenue rule: government revenue must not fall below a specified share of GDP

The EU's Fiscal Rules

The Stability and Growth Pact (SGP) has evolved through several iterations:

1. Original SGP (1997): deficit $< 3\%$ of GDP; debt $< 60\%$ of GDP
2. Reformed SGP (2005): introduced cyclical adjustment, allowing temporary deviations
3. Fiscal Compact (2012): introduced structural balance requirements
4. New SGP (2024): introduced an expenditure benchmark alongside the structural balance requirement

Evaluation of Fiscal Rules

Advantages:

• Credibility: fiscal rules signal commitment to sustainable public finances
• Counter-cyclical design (with cyclical adjustment) allows automatic stabilisers to operate during recessions
• Discipline: constrains the political incentive for deficit spending
• Transparency: requires governments to publish medium-term fiscal plans

Disadvantages:

• Pro-cyclical bias: many fiscal rules have been pro-cyclical, requiring austerity during recessions (as during the Eurozone crisis)
• Inflexibility: rigid rules may prevent necessary stimulus during crises
• Gaming: governments may manipulate forecasts to meet the rule (e.g., overly optimistic growth projections)
• One-size-fits-all: the same rule may not be appropriate for all countries
• Complexity: cyclical adjustment requires estimating potential output, which is imprecise

Structural Unemployment and Hysteresis (HL Extension)

Hysteresis in Labour Markets

Hysteresis refers to the persistence of unemployment even after the economy recovers from recession. Long-term unemployment erodes skills, reduces employability, and can permanently raise the natural rate of unemployment.

Mechanism:

1. Skills atrophy: unemployed workers lose job-specific and general skills over time
2. Discouragement: long-term unemployed exit the labour force, reducing the measured participation rate and the effective labour supply
3. Insider-outsider dynamics: employed workers ("insiders") negotiate wages that do not fall enough to employ the long-term unemployed ("outsiders")
4. Capital decumulation: during prolonged recessions, capital stock depreciates, reducing the economy's productive capacity
5. Scarring effects: workers who experience unemployment may become less employable due to psychological and health effects

Empirical evidence:

After the 2008 financial crisis:

• The average duration of unemployment in the EU rose from 6 to 18 months
• In Greece, youth unemployment exceeded 50% for a decade
• Many advanced economies saw their labour force participation rate decline permanently

Mathematical representation:

If the natural rate depends on the actual unemployment rate:

$u_{n,t} = u_{n,0} + \alpha(u_{t-1} - u_{n,t-1})$

Where $\alpha > 0$ is the hysteresis parameter. If unemployment was high last period ($u_{t-1} > u_{n,t-1}$), the natural rate adjusts upward.

Policy implications:

1. Active labour market policies (ALMPs): job search assistance, retraining programmes, wage subsidies
2. Early intervention: the longer unemployment persists, the harder it is to reverse
3. Demand-side support: maintaining aggregate demand during recessions prevents the rise in unemployment that causes hysteresis
4. Job guarantees: government employment programmes prevent skills atrophy and discouragement

Productivity Paradox (HL Extension)

The Solow Paradox

Robert Solow (1987) observed that "you can see the computer age everywhere but in the productivity statistics." Despite massive investment in ICT, measured productivity growth in advanced economies slowed in the 1970s and 1980s.

$\text{Massive ICT investment} + \text{Slow productivity growth} = \text{The Solow Paradox}$

Possible Explanations

1. Measurement error: GDP statistics may not fully capture the quality improvements from ICT. Free digital services (search engines, social media, mapping) are not included in GDP
2. Adjustment costs: firms need time to reorganise production around new technologies, and the transition period involves disruption
3. Skill-biased technical change: ICT requires complementary human capital (digital literacy, problem-solving, creativity) that takes time to develop
4. General-purpose technology (GPT) diffusion: GPTs (like the steam engine or electricity) require complementary innovations across the economy. The full productivity impact may take decades to materialise
5. Redistributive effects: ICT may displace low-skilled workers while benefiting high-skilled workers, contributing to inequality
6. Misallocation: resources may flow to unproductive uses (entertainment, social media) rather than productive investments

The "AI Productivity Question"

The current debate parallels the Solow Paradox: will artificial intelligence drive productivity growth, or will it follow the pattern of earlier ICT waves? Early evidence suggests AI could be more transformative than previous technologies due to its ability to automate cognitive tasks across all sectors, but measurement challenges persist.

Crowding Out: Detailed Analysis (HL Extension)

Full Theoretical Framework

Crowding out occurs when increased government borrowing raises interest rates, reducing private investment. The extent of crowding out depends on the source of financing and the state of the economy.

In the loanable funds market:

$S_{\text{private}} + S_{\text{government}} = I_{\text{private}} + I_{\text{government}}$

When government saving falls (deficit increases), the supply of loanable funds shifts leftward, raising the real interest rate and reducing private investment.

The degree of crowding out:

1. Complete crowding out: in the classical model (vertical AS), an increase in $G$ exactly offsets $\Delta I$, so $\Delta Y = 0$. This occurs when the economy is at full employment
2. Partial crowding out: in the Keynesian model (upward-sloping AS), some investment is displaced but output still increases
3. No crowding out: at the zero lower bound (horizontal LM curve), government borrowing does not raise interest rates because the central bank accommodates the fiscal expansion

Open-Economy Crowding Out

In an open economy, higher interest rates attract foreign capital inflows, appreciating the exchange rate:

$G \uparrow \implies r \uparrow \implies \text{Capital inflows} \uparrow \implies \text{Exchange rate} \uparrow$ $\implies (X - M) \downarrow \implies \text{Further reduction in AD}$

This creates double crowding out: higher interest rates reduce both domestic investment and net exports. Small open economies with mobile capital are particularly vulnerable.

Numerical example:

An economy has MPC $= 0.75$, MPM $= 0.2$, and a 1 percentage point increase in $r$ reduces investment by USD 2 billion. The government increases spending by USD 10 billion.

Closed-economy multiplier: $\frac{1}{1 - \text{MPC}} = \frac{1}{0.25} = 4$.

Open-economy multiplier: $\frac{1}{\text{MPM} + \text{MPS}} = \frac{1}{0.2 + 0.25} = \frac{1}{0.45} = 2.22$.

Simple increase: $\Delta Y = 2.22 \times 10 = 22.2$ billion.

With crowding out: if government borrowing raises $r$ by 2 percentage points, investment falls by $2 \times 2 = 4$ billion, and the exchange rate appreciation reduces net exports by USD 1 billion.

Total offset $= 4 + 1 = 5$ billion.

$\Delta Y = 22.2 - 5 = 17.2$ billion. Crowding out reduces the stimulus effect by approximately 23%.

Worked Examples: Macroeconomics (HL Extension)

Problem 15: Deflation Spiral

An economy has nominal GDP of USD 500 billion and total outstanding debt (public + private) of USD 600 billion. The economy enters a deflation of 2% per year for 5 years. Nominal GDP grows at only 1% per year (because real GDP falls while prices fall by 2%).

(a) Calculate the debt-to-GDP ratio at the start and after 5 years.

(b) Calculate the real interest rate if the nominal rate is 2%.

(c) Explain why deflation makes debt reduction harder.

(a) Initial debt-to-GDP ratio $= 600/500 = 120\%$

After 5 years:

• GDP grows at 1% per year: $Y_5 = 500 \times 1.01^5 = 500 \times 1.0510 = 525.5$ billion
• Debt grows (assuming primary deficit) at 3% per year: $D_5 = 600 \times 1.03^5 = 600 \times 1.1593 = 695.6$ billion

Debt-to-GDP ratio after 5 years $= 695.6 / 525.5 = 132.4\%$

The debt-to-GDP ratio rises despite nominal GDP growth because debt grows faster than GDP (3% vs. 1%).

(b) Real interest rate $= i - \pi = 2\% - (-2\%) = 4\%$

The real interest rate is double the nominal rate due to deflation.

(c) Deflation makes debt reduction harder because:

1. Real debt burden increases: with 4% real interest rates, servicing debt consumes a larger share of GDP
2. Nominal GDP growth is lower: deflation reduces prices and nominal wages, leading to lower tax revenues
3. Debt-deflation spiral: as the debt burden rises, the government may cut spending, further reducing aggregate demand, causing more deflation and more revenue decline
4. Private sector: deflation increases real debt burdens for households and firms, leading to defaults, bank failures, and credit contraction

Problem 16: QE and Balance Sheet Effects

A central bank purchases USD 500 billion of government bonds. The reserve requirement is 10%. The banking system has USD 2 trillion in deposits and USD 1.5 trillion in loans.

(a) Calculate the change in the monetary base (high-powered money).

(b) If banks lend out all excess reserves, what is the theoretical maximum expansion of broad money from the additional reserves?

(c) Evaluate the effectiveness of QE in stimulating the real economy.

(a) The central bank creates USD 500 billion in bank reserves to purchase bonds. The monetary base (high-powered money $=$ currency + bank reserves) increases by USD 500 billion.

(b) Assuming initial reserves of USD 200 billion ($10\% \times 2\,000$), new reserves $= 700$ billion.

The simple deposit multiplier $= 1/0.10 = 10$. Maximum expansion from additional reserves $= 500 / 0.10 = 5\,000$ billion.

Note: this is a theoretical maximum. In practice, banks may not lend out all excess reserves because of weak demand for loans, risk aversion, or regulatory constraints.

(c) Effectiveness evaluation:

1. Interest rate channel: QE lowered long-term yields, reducing borrowing costs. US 10-year Treasury yields fell from 3.8% (2007) to 1.4% (2012)
2. Portfolio rebalancing: investors shifted from bonds to equities, contributing to the post-2009 stock market recovery
3. Limited bank lending: banks held excess reserves rather than lending them out, so the credit channel was weak
4. Wealth effects: rising asset prices increased household net worth, but primarily for asset holders
5. Distributional effects: the top 10% of US households own approximately 80% of equities, so QE gains were concentrated
6. Inflation: despite massive monetary expansion, inflation remained below the 2% target throughout most of the QE period

Overall, QE was partially effective at preventing a deeper recession but failed to generate strong, inclusive growth.

Problem 17: Fiscal Rules and Cyclical Adjustment

The government of Country Z is subject to a fiscal rule requiring the structural budget deficit not to exceed 0.5% of GDP. Currently:

• Potential GDP = USD 1000 billion
• Actual GDP = USD 950 billion
• Nominal GDP = USD 990 billion
• Government spending = USD 280 billion
• Tax revenue = USD 255 billion
• Tax elasticity with respect to output $= 1.0$

(a) Calculate the actual and structural budget balances.

(b) Is the government complying with the fiscal rule?

(c) The government plans to increase spending by USD 20 billion. Assuming the spending multiplier is 2 and potential GDP remains unchanged, what is the new structural deficit?

(a) Actual balance $= T - G = 255 - 280 = -25$ billion (deficit of USD 25 billion)

Actual deficit as % of GDP $= 25/990 = 2.53\%$

Output gap $= (950 - 1000)/1000 = -5\%$ (recessionary gap)

Cyclical component of tax revenue: with tax elasticity of 1.0, the cyclical shortfall in tax revenue $= 5\% \times 255 = 12.75$ billion.

Structural deficit $= 25 - 12.75 = 12.25$ billion

Structural deficit as % of potential GDP $= 12.25 / 1000 = 1.23\%$

(b) The structural deficit is 1.23% of GDP, which exceeds the 0.5% ceiling. The government is NOT complying with the fiscal rule.

(c) New government spending $= 300$ billion. Spending multiplier $= 2$, so $\Delta Y = 40$ billion.

New actual GDP $= 950 + 40 = 990$. New output gap $= (990 - 1000)/1000 = -1\%$.

New tax revenue (assuming tax elasticity 1.0, proportional tax): tax revenue rises by 1% proportionally. Approximate new tax revenue $= 255 \times (990/950) = 255 \times 1.0421 = 265.7$ billion.

New actual deficit $= 265.7 - 300 = -34.3$ billion.

Cyclical component $= 1\% \times 265.7 = 2.66$ billion.

Structural deficit $= 34.3 - 2.66 = 31.64$ billion $= 3.16\%$ of potential GDP.

The spending increase worsens the structural deficit from 1.23% to 3.16%, further violating the fiscal rule.

Problem 18: Hysteresis in the Labour Market

An economy has a natural rate of unemployment of 5%. A financial crisis causes a recession, and the actual unemployment rate rises to 10% for 3 years. The hysteresis parameter $\alpha = 0.15$.

(a) Calculate the natural rate of unemployment after 1, 2, and 3 years of high unemployment.

(b) If the economy recovers to potential output after year 3, what is the equilibrium unemployment rate?

(c) Calculate the GDP loss from hysteresis using Okun's law: $\Delta Y/Y = -2(u - u_n)$.

(a) Using $u_{n,t} = u_{n,0} + \alpha(u_{t-1} - u_{n,t-1})$:

Year 1: $u_{n,1} = 5\% + 0.15(10\% - 5\%) = 5\% + 0.75\% = 5.75\%$

Year 2: $u_{n,2} = 5.75\% + 0.15(10\% - 5.75\%) = 5.75\% + 0.6375\% = 6.39\%$

Year 3: $u_{n,3} = 6.39\% + 0.15(10\% - 6.39\%) = 6.39\% + 0.541\% = 6.93\%$

After 3 years, the natural rate has risen from 5% to 6.93%.

(b) The equilibrium unemployment rate is now 6.93%, not 5%. The economy has a permanently higher natural rate due to hysteresis. Even after recovery, approximately 1.93% more of the labour force remains unemployed compared to the pre-crisis natural rate.

(c) Using Okun's law with $u = 6.93\%$ and original $u_n = 5\%$:

$\Delta Y/Y = -2(6.93\% - 5\%) = -2(1.93\%) = -3.86\%$

The economy loses approximately 3.86% of potential GDP permanently due to hysteresis. If potential GDP was USD 1 trillion, the permanent loss is USD 38.6 billion per year.

Common Pitfalls: Macroeconomics (Comprehensive)

• Assuming that deflation is always harmful. Mild deflation due to productivity growth can benefit consumers, but demand-driven deflation triggers the spiral
• Confusing QE with money printing. QE expands bank reserves, not currency in circulation; the link between reserves and broad money depends on bank lending behaviour
• Assuming that fiscal multipliers are constant. Multipliers are larger during recessions (when there is slack) and smaller during booms
• Assuming the natural rate of unemployment is fixed. Hysteresis means the natural rate can shift upward after prolonged recessions
• Confusing the zero lower bound with an absolute lower bound. Nominal rates can go slightly negative, but deeply negative rates have adverse effects on bank profitability
• Overstating the crowding-out effect during recessions. When resources are idle and the ZLB binds, government borrowing may not raise interest rates significantly
• Ignoring the distributional consequences of QE. Asset price inflation benefits asset holders disproportionately
• Applying fiscal rules mechanically without cyclical adjustment. Pro-cyclical austerity during recessions deepens downturns
• Confusing real and nominal interest rates during deflation. When $\pi < 0$, $r_{\text{real}} > i$, making debt servicing more expensive in real terms

The Phillips Curve: Advanced Analysis (HL Extension)

The Expectations-Augmented Phillips Curve

Milton Friedman (1968) and Edmund Phelps (1967) argued that the traditional Phillips curve trade-off between inflation and unemployment is only temporary. In the long run, unemployment returns to the natural rate regardless of inflation:

$\pi = \pi^e - \beta(u - u_n) + \epsilon$

Where:

• $\pi$ = actual inflation
• $\pi^e$ = expected inflation
• $u$ = actual unemployment rate
• $u_n$ = natural rate of unemployment (NAIRU)
• $\beta$ = slope of the Phillips curve
• $\epsilon$ = supply shock

Short-run Phillips curve: for a given $\pi^e$, there is a trade-off between $\pi$ and $u$. The central bank can reduce $u$ below $u_n$ by creating unexpected inflation ($\pi > \pi^e$).

Long-run Phillips curve: when $\pi = \pi^e$, $u = u_n$. The long-run Phillips curve is vertical at the natural rate.

The Sacrifice Ratio

The sacrifice ratio measures the cumulative loss in output required to reduce inflation by 1 percentage point:

$\text{Sacrifice ratio} = \frac{\sum \Delta Y}{\Delta \pi}$

Historical estimates:

• US Volcker disinflation (1980--85): inflation fell from 13.5% to 3.2% (10.3 percentage points). Cumulative output loss: approximately 21% of one year's GDP. Sacrifice ratio $= 21/10.3 \approx 2.0$

• UK (1979--82): sacrifice ratio $\approx 2.5$

• New Zealand (1990--92): sacrifice ratio $\approx 1.0$

The sacrifice ratio depends on the credibility of the disinflation policy. If the central bank credibly commits to low inflation, expectations adjust quickly and the output loss is smaller.

Numerical Example: Disinflation

The economy has:

• Natural rate of unemployment $u_n = 5\%$
• Current unemployment $u = 5\%$
• Current inflation $\pi = 8\%$
• Phillips curve: $\pi = \pi^e - 2(u - 5)$

The central bank wants to reduce inflation to 2%.

Scenario 1: Cold turkey (immediate, credible announcement)

If the announcement is fully credible, $\pi^e$ falls immediately to 2%. With $\pi = \pi^e = 2\%$:

$2 = 2 - 2(u - 5) \implies u = 5\%$.

No increase in unemployment. Sacrifice ratio $= 0$. (Ideal but unrealistic.)

Scenario 2: Adaptive expectations ($\pi^e_t = \pi_{t-1}$)

Year 1: $\pi^e = 8\%$. Central bank tightens policy. $\pi = 8 - 2(u_1 - 5)$.

If the central bank sets $u_1 = 7\%$: $\pi_1 = 8 - 2(2) = 4\%$.

Year 2: $\pi^e = 4\%$. $\pi_2 = 4 - 2(u_2 - 5)$.

If $u_2 = 5.5\%$: $\pi_2 = 4 - 2(0.5) = 3\%$.

Year 3: $\pi^e = 3\%$. $\pi_3 = 3 - 2(u_3 - 5)$.

If $u_3 = 5.25\%$: $\pi_3 = 3 - 2(0.25) = 2.5\%$.

Year 4: $\pi^e = 2.5\%$. $\pi_4 = 2.5 - 2(5 - 5) = 2.5\%$.

Using Okun's law ($\Delta Y/Y = -2 \Delta u$):

Year 1: output gap $= -2(7-5) = -4\%$ Year 2: output gap $= -2(5.5-5) = -1\%$ Year 3: output gap $= -2(5.25-5) = -0.5\%$

Total output loss $= 4 + 1 + 0.5 = 5.5\%$ of GDP. Inflation reduction $= 8 - 2.5 = 5.5$ percentage points. Sacrifice ratio $= 5.5/5.5 = 1.0$.

Rational Expectations and Policy Ineffectiveness

If agents have rational expectations, they anticipate the central bank's actions and adjust $\pi^e$ accordingly. In this case:

1. Anticipated monetary policy is neutral: if the central bank announces a disinflation and agents believe it, $\pi^e$ adjusts immediately and there is no output loss
2. Only unanticipated policy has real effects: only surprise changes in the money supply affect output
3. Time inconsistency: the central bank has an incentive to create surprise inflation (to boost output), but rational agents anticipate this, so $\pi^e$ rises and the result is higher inflation without any output gain (Kydland and Prescott, 1977)

The Barro-Gordon model (1983):

The central bank minimises a loss function:

$L = (u - u_n)^2 + \alpha(\pi - \pi^*)^2$

Where $\pi^*$ is the optimal inflation rate and $\alpha$ measures the weight on inflation stability.

Under rational expectations, the equilibrium inflation rate is:

$\pi = \pi^* + \frac{\beta^2}{\alpha} > \pi^*$

The economy experiences an inflation bias: even though the central bank targets $\pi^*$, equilibrium inflation is higher because of the time inconsistency problem.

Solution: independent central bank with a conservative governor. If the central bank governor places a higher weight on inflation stability ($\alpha$ is larger), the inflation bias is smaller. This is the rationale for central bank independence.

The IS-LM-BP Model: Complete Treatment (HL Extension)

The BP Curve

The BP (balance of payments) curve shows combinations of $Y$ and $r$ that maintain balance of payments equilibrium:

$\text{Current account} + \text{Capital account} = 0$

$\text{NX}(Y, e) + \text{CF}(r) = 0$

The slope of the BP curve depends on capital mobility:

• Perfect capital mobility: BP is horizontal at $r = r^*$ (the world interest rate)
• Imperfect capital mobility: BP is upward-sloping (higher $r$ attracts capital inflows, which finance a larger current account deficit, which requires higher $Y$ and more imports)
• No capital mobility: BP is vertical at the level of $Y$ where the current account is balanced

Policy Effectiveness under Different Exchange Rate Regimes

Policy	Fixed rates	Floating rates
Fiscal expansion	Effective (no crowding out from capital flows)	Ineffective (appreciation crowds out NX)
Monetary expansion	Ineffective (capital outflows force reversal)	Effective (depreciation stimulates NX)

Numerical Example: IS-LM-BP

An economy has:

• IS: $Y = 1000 - 50r + 2G$
• LM: $Y = 200 + 100r + 5M/P$
• BP: $Y = 400 + 50r$ (imperfect capital mobility, upward-sloping)
• World interest rate: $r^* = 4\%$
• $G = 200$, $M/P = 100$

(a) Find the initial equilibrium.

(b) The government increases $G$ by 100. Analyse under fixed and floating exchange rates.

(a) IS: $Y = 1000 - 50r + 400 = 1400 - 50r$ LM: $Y = 200 + 100r + 500 = 700 + 100r$

IS = LM: $1400 - 50r = 700 + 100r \implies 700 = 150r \implies r = 4.67\%$

$Y = 700 + 100(4.67) = 1167$

BP at $r = 4.67$: $Y_{BP} = 400 + 50(4.67) = 633$.

At $Y = 1167$, the economy is above the BP curve ($Y > Y_{BP}$), indicating a balance of payments surplus (capital inflows exceed the current account deficit).

(b) Fixed exchange rates: The BoP surplus causes the central bank to buy foreign currency and sell domestic currency, increasing the money supply. The LM shifts right until the three curves intersect.

New IS: $Y = 1500 - 50r$.

IS = LM: $1500 - 50r = 700 + 100r + 5\Delta M/P$

At the BP intersection: $r = 4$, $Y = 600$. But IS at $r=4$: $Y = 1300$. This does not intersect BP at $r=4$.

Let me solve properly. Under fixed rates, the final equilibrium is where IS and BP intersect (the money supply adjusts to make LM pass through this point):

IS: $Y = 1500 - 50r$. BP: $Y = 400 + 50r$.

$1500 - 50r = 400 + 50r \implies 1100 = 100r \implies r = 11$.

$Y = 400 + 50(11) = 950$.

The equilibrium moves to $r = 11\%$, $Y = 950$.

Fiscal expansion is effective under fixed rates: output increases from 1167 to... wait, this seems wrong. Let me re-examine.

Actually, at the initial equilibrium $Y = 1167 > Y_{BP} = 633$, so the economy has a BoP surplus. Under fixed rates, the money supply increases, shifting LM right, which lowers $r$ and raises $Y$ further. The process continues until IS = LM = BP.

At the intersection of IS and BP: $r = 11$, $Y = 950$. But this gives lower $Y$ than the initial 1167, which cannot be right for a fiscal expansion.

The issue is that the BP curve's position relative to the initial equilibrium matters. Let me recalculate more carefully.

Initial: $r = 4.67$, $Y = 1167$. BP at $r = 4.67$: $Y_{BP} = 400 + 50(4.67) = 633$.

$Y > Y_{BP}$ means the current account deficit is smaller than the capital account surplus (BoP surplus). The central bank buys USD, sells domestic currency, expanding M.

LM shifts right $\implies r$ falls, $Y$ rises. As $Y$ rises, the current account worsens (more imports). As $r$ falls, capital inflows decrease. The BoP surplus shrinks.

New IS after $G$ increase: $Y = 1500 - 50r$.

The process continues until $Y_{IS} = Y_{BP}$:

$1500 - 50r = 400 + 50r \implies r = 11$, $Y = 950$.

Hmm, $Y$ fell from 1167 to 950 despite fiscal expansion. This seems contradictory. The problem is that the BP curve is very low relative to the initial equilibrium, suggesting the capital account response is weak. This leads to a large interest rate increase that crowds out investment significantly.

Let me use more realistic parameters. Suppose instead:

• BP: $Y = 800 + 80r$ (steeper BP, implying stronger capital mobility)

Initial IS = LM: $r = 4.67$, $Y = 1167$. BP at $r = 4.67$: $Y_{BP} = 800 + 373 = 1173$.

Now $Y \approx Y_{BP}$ (the economy is near BP equilibrium). This is more realistic.

After $G$ increase: IS = BP: $1500 - 50r = 800 + 80r \implies 700 = 130r \implies r = 5.38$.

$Y = 800 + 80(5.38) = 1231$.

Under fixed rates: output rises from 1167 to 1231, an increase of 64. Fiscal policy is effective.

Under floating rates: the BoP surplus (initially) causes appreciation, reducing NX and shifting IS left until IS = LM = BP at the original $Y$ (approximately). Monetary policy effectiveness depends on the exchange rate regime.

Exam-Style Questions: Macroeconomics (Additional)

Problem 19: Phillips Curve and Disinflation

An economy has a Phillips curve: $\pi = \pi^e - 1.5(u - 5)$. The natural rate is 5%. Current inflation is 10% and expected inflation equals last period's actual inflation.

(a) The central bank wants to reduce inflation to 3%. Under adaptive expectations, calculate the unemployment rate and inflation rate for each of the first 4 years, assuming the central bank holds $u$ constant at 7%. [6 marks]

(b) Calculate the sacrifice ratio. [2 marks]

(c) How would the results differ under rational expectations? [2 marks]

(a) Year 1: $\pi^e = 10\%$. $u = 7\%$.

$\pi_1 = 10 - 1.5(7-5) = 10 - 3 = 7\%$

Year 2: $\pi^e = 7\%$. $u = 7\%$.

$\pi_2 = 7 - 1.5(2) = 4\%$

Year 3: $\pi^e = 4\%$. $u = 7\%$.

$\pi_3 = 4 - 1.5(2) = 1\%$

Year 4: $\pi^e = 1\%$. $u = 7\%$.

$\pi_4 = 1 - 1.5(2) = -2\%$

The economy overshoots the target, producing deflation by year 4. The central bank should gradually relax the policy as inflation approaches the target.

Better approach: adjust $u$ each year:

Year 1: target $\pi = 7\%$, set $u$ to achieve this: $7 = 10 - 1.5(u-5) \implies u = 7$ Year 2: target $\pi = 4.5\%$: $4.5 = 7 - 1.5(u-5) \implies u = 6.67$ Year 3: target $\pi = 3.5\%$: $3.5 = 4.5 - 1.5(u-5) \implies u = 5.67$

(b) Output loss using Okun's law ($\Delta Y/Y = -2\Delta u$):

Year 1: gap $= -2(7-5) = -4\%$ Year 2: gap $= -2(7-5) = -4\%$ Year 3: gap $= -4\%$

Total output loss $= 12\%$ of GDP. Inflation reduction $= 10 - 1 = 9$ percentage points. Sacrifice ratio $= 12/9 = 1.33$.

(c) Under rational expectations with a credible disinflation programme, $\pi^e$ adjusts immediately to the central bank's target. If agents believe the central bank will achieve $\pi = 3\%$:

$\pi = 3 - 1.5(u-5) = 3 \implies u = 5\%$.

No output loss. Sacrifice ratio $= 0$. The central bank achieves disinflation without recession if its commitment is credible.

Problem 20: IS-LM-BP with Capital Mobility

A small open economy with perfect capital mobility ($r = r^* = 5\%$). Floating exchange rate.

IS: $Y = 800 - 40r + 4e$ (where $e$ is the exchange rate, higher = depreciation) LM: $Y = 500 + 20r$ BP: $r = 5\%$ (horizontal)

(a) Find the initial equilibrium (assume $e = 10$). [2 marks]

(b) The government increases spending by 50. Analyse the impact. [4 marks]

(c) The central bank increases the money supply, shifting LM to $Y = 600 + 20r$. Analyse the impact. [4 marks]

(a) IS: $Y = 800 - 40(5) + 4(10) = 800 - 200 + 40 = 640$.

LM: $Y = 500 + 20(5) = 600$.

IS $\neq$ LM, so $e$ must adjust. At $r = 5\%$:

IS: $Y = 600 + 4e$. LM: $Y = 600$.

For equilibrium: $600 + 4e = 600 \implies e = 0$. This is unrealistic. Let me adjust the parameters.

Let IS: $Y = 600 - 40r + 4e$, LM: $Y = 400 + 20r$, $r^* = 5$.

IS at $r=5$: $Y = 600 - 200 + 4e = 400 + 4e$. LM at $r=5$: $Y = 500$.

$400 + 4e = 500 \implies e = 25$. $Y = 500$.

(b) New IS: $Y = 650 - 40r + 4e$ (G increases by 50, so intercept increases by 50).

At $r = 5$: $Y = 650 - 200 + 4e = 450 + 4e$.

IS = LM: $450 + 4e = 500 \implies 4e = 50 \implies e = 12.5$.

$Y = 500$. The exchange rate appreciates from 25 to 12.5 (a 50% appreciation).

$\Delta Y = 0$: fiscal policy is completely ineffective under floating rates with perfect capital mobility. The appreciation reduces net exports by exactly the amount of the fiscal expansion.

(c) New LM: $Y = 600 + 20r$. At $r = 5$: $Y = 700$.

IS at $r=5$: $Y = 400 + 4e$. $400 + 4e = 700 \implies 4e = 300 \implies e = 75$.

The exchange rate depreciates from 25 to 75 (a 200% depreciation).

$\Delta Y = 700 - 500 = 200$: monetary policy is highly effective. The depreciation amplifies the monetary stimulus through net exports.

The fiscal multiplier is 0; the monetary multiplier is $200/(\Delta M/P)$. If the money supply increase was $\Delta M/P = 10$ (shifting LM intercept from 400 to 600, i.e., $\Delta = 200$ at $r=0$, which corresponds to $\Delta M/P = 10$ given the LM slope of 20), the monetary multiplier is $200/10 = 20$.

Okun's Law: Advanced Treatment (HL Extension)

The Okun Relationship

Okun's law describes the empirical relationship between changes in unemployment and changes in output:

$\Delta u = -\beta \left( \frac{\Delta Y}{Y} - g^* \right)$

Where:

• $\Delta u$ = change in the unemployment rate
• $\Delta Y/Y$ = GDP growth rate
• $g^*$ = the growth rate of potential output (trend growth)
• $\beta$ = Okun's coefficient (typically 0.4--0.5 in the US)

Alternative form:

$\frac{Y - Y^*}{Y^*} = -\gamma (u - u^*)$

Where $\gamma = 1/\beta \approx 2$ in the US. A 1 percentage point increase in the unemployment rate is associated with a 2% decline in output relative to potential.

Why Okun's Coefficient Exceeds 1

The output loss from unemployment exceeds the proportional increase in unemployment because:

1. Labour hoarding: during recessions, firms retain workers but reduce hours (part-time work, reduced overtime) rather than laying off workers. Output falls more than employment
2. Discouraged workers: unemployed workers exit the labour force, reducing the measured unemployment rate even as output falls
3. Productivity procyclicality: labour productivity rises during booms (high-capacity utilisation, capital deepening) and falls during recessions
4. ** labour force growth:** the labour force continues to grow during recessions, increasing the gap between actual and potential output

Numerical Example: Output Gap Estimation

An economy has:

• Potential GDP growth rate: $g^* = 2.5\%$
• Actual GDP growth: 1.0%
• Initial unemployment rate: 6.0%
• Okun's coefficient: $\beta = 0.5$

$\Delta u = -0.5(1.0\% - 2.5\%) = -0.5(-1.5\%) = +0.75$ percentage points.

New unemployment rate $= 6.0 + 0.75 = 6.75\%$.

Output gap $= -(u - u^*) \times \gamma$. If $u^* = 5\%$:

Output gap $= -(6.75 - 5) \times 2 = -3.5\%$.

The economy is operating 3.5% below potential output.

GDP loss from the recession:

If potential GDP is USD 1 trillion, the output gap is USD 35 billion.

The "sacrifice" of the recession: $35 billion in lost output and 0.75 percentage points of additional unemployment.

The Taylor Rule (HL Extension)

The Rule

John Taylor (1993) proposed a rule for setting the central bank policy rate:

$i = r^* + \pi + 0.5(\pi - \pi^*) + 0.5(y - y^*)$

Where:

• $i$ = nominal policy rate
• $r^*$ = equilibrium real interest rate (typically 2%)
• $\pi$ = current inflation rate
• $\pi^*$ = target inflation rate (typically 2%)
• $y - y^*$ = output gap (percentage deviation of output from potential)

The Taylor rule responds to two gaps:

1. Inflation gap ($\pi - \pi^*$): if inflation exceeds the target, raise the rate
2. Output gap ($y - y^*$): if output exceeds potential, raise the rate

Numerical Example

$\pi^* = 2\%$, $r^* = 2\%$.

Scenario 1: $\pi = 2\%$, $y = y^*$ (output at potential).

$i = 2 + 2 + 0.5(0) + 0.5(0) = 4\%$.

Scenario 2: $\pi = 5\%$, $y = y^*$.

$i = 2 + 5 + 0.5(3) + 0.5(0) = 8.5\%$.

The central bank raises the rate by 4.5 percentage points to combat inflation.

Scenario 3: $\pi = 2\%$, output gap $= -3\%$ (recession).

$i = 2 + 2 + 0.5(0) + 0.5(-3) = 2.5\%$.

The central bank cuts the rate by 1.5 percentage points to stimulate the economy.

Scenario 4 (stagflation): $\pi = 7\%$, output gap $= -2\%$.

$i = 2 + 7 + 0.5(5) + 0.5(-2) = 9 + 2.5 - 1 = 10.5\%$.

The central bank raises the rate (inflation gap dominates), even though the economy is in recession. This illustrates the policy dilemma of stagflation.

Taylor Rule and Central Bank Policy

Evaluation:

Advantages:

1. Provides a systematic, transparent framework for monetary policy
2. Anchors inflation expectations by providing a predictable policy response
3. Prevents discretionary policy errors (too loose for too long, or too tight)
4. Empirically: the Taylor rule fits the historical behaviour of the Fed reasonably well (pre-2000)

Limitations:

1. Measurement problems: the output gap and equilibrium real rate are unobservable and must be estimated, which introduces significant uncertainty
2. Financial stability: the Taylor rule does not account for financial stability risks (asset bubbles, credit growth). The Fed kept rates low during 2002--2004 following the Taylor rule, which may have contributed to the housing bubble
3. Zero lower bound: the rule may prescribe negative rates during deep recessions
4. Multiple equilibria: the rule may not be unique; different parameter values can justify different policy paths

Real-World Central Bank Rates vs. Taylor Rule

Federal Reserve (2000--2023):

• 2000--2004: the Fed's actual rate was below the Taylor rule prescription, contributing to the housing bubble
• 2008--2015: the ZLB prevented the Fed from following the Taylor rule (which prescribed negative rates). The Fed used QE instead
• 2021--2023: the Taylor rule prescribed rate hikes earlier and larger than the Fed actually implemented, contributing to the inflation surge

ECB:

The ECB's deposit facility rate has generally tracked a Taylor-type rule, but with greater emphasis on inflation (reflecting the ECB's single mandate) and less weight on the output gap.

Secular Stagnation (HL Extension)

The Hypothesis

Larry Summers (2013) revived Alvin Hansen's (1938) "secular stagnation" hypothesis: the economy may face a persistent shortfall of aggregate demand due to structural factors, leading to chronically low growth, low inflation, and low interest rates.

Key indicators of secular stagnation:

1. Declining neutral real interest rate ($r^*$): estimates suggest $r^*$ has fallen from approximately 3% (1990s) to approximately 0.5% (2020s) in advanced economies
2. Low inflation despite low rates: even with near-zero policy rates, inflation has remained below target in many advanced economies
3. Rising inequality: higher inequality increases the savings rate (the rich save a larger share of income), reducing aggregate demand
4. Declining productivity growth: slower productivity growth reduces investment demand

Causes of Declining $r^*$

1. Demographics: ageing populations increase the supply of savings (workers saving for retirement) and reduce investment demand (fewer workers, less capital needed)
2. Rising inequality: higher income shares for top earners increase the aggregate savings rate because the rich save more
3. Declining relative price of capital goods: the price of machinery and equipment has fallen, so less investment is needed to achieve a given capital stock
4. Increased demand for safe assets: regulatory changes (Basel III) and demographic shifts have increased demand for safe assets (government bonds), lowering the risk-free rate
5. Lower productivity growth: slower TFP growth reduces the marginal product of capital, lowering the equilibrium real rate

Policy Implications

1. Higher inflation target: a higher target (e.g., 4% instead of 2%) gives the central bank more room to cut rates before hitting the ZLB
2. Fiscal expansion: when monetary policy is constrained by the ZLB, fiscal policy must play a larger role in maintaining aggregate demand
3. Public investment: investment in infrastructure, education, and R&D raises both aggregate demand and potential output
4. Negative interest rates: central banks can push rates below zero, though with diminishing effectiveness
5. Structural reform: policies to boost productivity growth (competition, innovation, skills) can raise $r^*$ by increasing the marginal product of capital

Exam-Style Questions: Macroeconomics (Additional)

Problem 21: Taylor Rule Policy Analysis

The central bank follows the Taylor rule: $i = 2 + \pi + 0.5(\pi - 2) + 0.5(y - y^*)$.

The economy experiences the following shocks:

Shock A: inflation rises from 2% to 5% while output remains at potential. Shock B: a financial crisis causes output to fall 4% below potential while inflation remains at 2%. Shock C: a supply shock causes inflation to rise to 6% while output falls 2% below potential.

(a) Calculate the prescribed policy rate for each shock. [6 marks]

(b) Explain why the central bank faces a dilemma in Shock C. [2 marks]

(c) Evaluate the Taylor rule as a framework for monetary policy. [2 marks]

(a) Shock A: $\pi = 5$, $y - y^* = 0$.

$i = 2 + 5 + 0.5(5-2) + 0.5(0) = 7 + 1.5 = 8.5\%$

Shock B: $\pi = 2$, $y - y^* = -4$.

$i = 2 + 2 + 0.5(0) + 0.5(-4) = 4 + 0 - 2 = 2.0\%$

Shock C: $\pi = 6$, $y - y^* = -2$.

$i = 2 + 6 + 0.5(6-2) + 0.5(-2) = 8 + 2 - 1 = 9.0\%$

(b) In Shock C (stagflation), the Taylor rule prescribes $i = 9\%$, a large increase from the baseline 4%. The central bank must raise rates to fight inflation despite the economy being in recession. This is the fundamental policy dilemma of stagflation: the tools to fight inflation (higher rates) worsen the recession, and the tools to fight the recession (lower rates) worsen inflation.

(c) Evaluation:

Strengths: the Taylor rule provides a clear, systematic framework that enhances transparency and accountability. It prevents discretionary errors and anchors expectations.

Weaknesses: the rule does not account for financial stability risks, measurement uncertainty (output gap, $r^*$), or the zero lower bound. In Shock B, the rule prescribes 2%, leaving little room for further cuts if the recession deepens.

Problem 22: Okun's Law and Fiscal Policy (10 marks)

An economy has potential GDP of USD 2 trillion and potential growth of 3% per year. Okun's coefficient is $\gamma = 2$. The current unemployment rate is 7% and the natural rate is 5%.

(a) Calculate the output gap. [2 marks]

(b) The government increases spending by USD 30 billion with a multiplier of 1.8. Calculate the new output gap and the change in unemployment. [4 marks]

(c) Is the output gap fully closed? If not, what additional spending is needed? [4 marks]

(a) Output gap $= -\gamma(u - u^*) = -2(7\% - 5\%) = -4\%$.

Output gap in dollars $= -4\% \times 2000 = -80$ billion.

The economy is operating USD 80 billion below potential.

(b) Spending increase of USD 30 billion with multiplier 1.8:

$\Delta Y = 1.8 \times 30 = 54$ billion.

New output gap $= -80 + 54 = -26$ billion.

New output gap as % of potential $= -26/2000 = -1.3\%$.

Change in unemployment: $\Delta u = -\Delta Y/(Y^* \times \gamma) = -54/(2000 \times 2) = -1.35$ percentage points.

Wait: using $\Delta u = -(1/\gamma) \times (\Delta Y/Y^*) = -0.5 \times (54/2000) = -0.5 \times 0.027 = -0.0135 = -1.35$ percentage points.

New unemployment $= 7 - 1.35 = 5.65\%$.

(c) The output gap is not fully closed (still -26 billion, or -1.3% of potential).

To close the remaining gap:

Additional spending needed $= 26/1.8 = 14.4$ billion.

Total spending needed $= 30 + 14.4 = 44.4$ billion to fully close the output gap.

New unemployment $= 7 - 2(44.4 \times 1.8)/(2 \times 2000) = 7 - 2(80/2000) = 7 - 0.08 = 7 - 1.6 = 5.4\%$.

Wait, let me recalculate: $\Delta Y_{\text{total}} = 1.8 \times 44.4 = 79.9 \approx 80$ billion.

$\Delta u = -0.5 \times (80/2000) = -2.0$ percentage points.

New unemployment $= 7 - 2 = 5\%$ (the natural rate). The output gap is fully closed.