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Market Failure

Market Failure

Market failure occurs when the free market fails to allocate resources efficiently, resulting in a Loss of social welfare. The condition for allocative efficiency is:

MSB=MSC\mathrm{MSB} = \mathrm{MSC}

When MSB differs from MSC, the market produces either too much or too little of the good relative to The socially optimal quantity.

Externalities

An externality is a spill-over effect of production or consumption on third parties who are not Involved in the transaction.

Negative production externalities (e.g., factory pollution):

  • Marginal Social Cost (MSC) >> Marginal Private Cost (MPC)
  • MSC == MPC ++ Marginal External Cost (MEC)
  • Overproduction occurs relative to the socially optimal level
  • Deadweight loss arises from units produced where MSC >> Marginal Social Benefit (MSB)

The welfare analysis:

DWL=12×MEC×(QprivateQsocial)\text{DWL} = \frac{1}{2} \times \text{MEC} \times (Q_{\text{private}} - Q_{\text{social}})

Positive production externalities (e.g., research and development):

  • Marginal Social Benefit (MSB) >> Marginal Private Benefit (MPB)
  • MSB == MPB ++ Marginal External Benefit (MEB)
  • Underproduction occurs relative to the socially optimal level

Negative consumption externalities (e.g., smoking in public, driving a car that emits pollution):

  • MSC >> MSB at the private equilibrium (or equivalently, MPB >> MSB)
  • Overconsumption relative to the social optimum

Positive consumption externalities (e.g., vaccination, education):

  • MSB >> MPB at the private equilibrium
  • Underconsumption relative to the social optimum

Diagrammatic Analysis of Externalities

For a negative production externality, the MSC curve lies above the MPC curve. The free market Equilibrium is at the intersection of MPC and MPB (demand). The socially optimal equilibrium is at The intersection of MSC and MSB. The difference in quantity between the two represents the Overproduction, and the triangle between MSC, MSB, and the two quantities is the deadweight loss.

For a positive consumption externality, the MSB curve lies above the MPB (demand) curve. The free Market underproduces relative to the social optimum. The deadweight loss is the triangle between MPB, MSB, and the two quantities.

Public Goods

Public goods are non-excludable and non-rivalrous. Because of these properties, they suffer from the free-rider problem: individuals have no incentive to pay for the good since they cannot be Excluded from consumption. This leads to market under-provision or zero provision.

Characteristics:

  • Non-excludable: it is not possible (or prohibitively costly) to prevent someone from consuming the good
  • Non-rivalrous: one person”s consumption does not reduce the amount available to others

Classification of goods:

ExcludableNon-excludable
RivalrousPrivate goodsCommon resources
Non-rivalrousClub goodsPublic goods

Pure public goods (e.g., national defence, street lighting, lighthouses) contrast with private Goods (excludable and rivalrous), quasi-public goods (partially excludable or congestible, Such as toll roads), and common resources (non-excludable but rivalrous, such as fish stocks, Leading to the tragedy of the commons).

Tragedy of the Commons

Common resources are non-excludable but rivalrous. Since no individual has property rights, each user Has an incentive to consume the resource before others do, leading to overexploitation and Depletion. Examples include overfishing, deforestation of unowned land, and groundwater depletion.

Solutions include:

  • Privatization (establishing property rights)
  • Government regulation (quotas, licences, seasonal bans)
  • Community management with social norms and local enforcement

Merit and Demerit Goods

Merit goods are under-consumed in the free market because individuals underestimate their Private benefits (information failure). Examples include education and healthcare. They generate Positive externalities.

Demerit goods are over-consumed because individuals underestimate their private costs. Examples Include tobacco, alcohol, and illicit drugs. They generate negative externalities.

Information Failure

Information failure occurs when consumers or producers lack accurate or complete information, Leading to inefficient market outcomes.

Types of information failure:

  • Asymmetric information: one party to a transaction has more information than the other. In the market for used cars, the seller knows the vehicle’s condition better than the buyer (adverse selection). In insurance markets, individuals who purchase insurance may take greater risks (moral hazard)
  • Imperfect information: consumers lack full knowledge of product quality, long-term health effects, or environmental impacts
  • Information overload: when the volume of information available is so large that consumers cannot process it effectively

Factor Immobility

Occupational immobility: workers lack the skills to move between industries (e.g., a coal miner Cannot become a software engineer). This contributes to structural unemployment.

Geographical immobility: workers cannot or will not relocate to areas with job vacancies due to Housing costs, family ties, language barriers, or lack of information about opportunities.

Government Intervention

Price Controls

Price ceilings (maximum prices) are set below the equilibrium price, to make essential Goods more affordable (e.g., rent controls). Consequences include:

  • Shortages (excess demand): at the ceiling price, quantity demanded exceeds quantity supplied
  • Black markets where goods are sold illegally above the ceiling
  • Reduced quality as producers cut costs to maintain profitability
  • Misallocation of resources: goods may not reach those who value them most (rationing mechanisms such as queues or favouritism replace the price mechanism)
  • Reduced producer surplus and potential long-run supply reductions

Price floors (minimum prices) are set above the equilibrium price, to protect Producers’ incomes (e.g., minimum wages, agricultural price supports). Consequences include:

  • Surpluses (excess supply): at the floor price, quantity supplied exceeds quantity demanded
  • Government purchases or destruction of surplus (in agriculture)
  • Inefficient overproduction
  • Higher costs passed to consumers
  • Potential for government budget burdens

Indirect Taxes

An indirect tax is levied on goods and services. A specific tax is a fixed amount per unit sold; An ad valorem tax is a percentage of the price.

Taxes shift the supply curve upward (or leftward) by the amount of the tax. The tax incidence (burden distribution between consumers and producers) depends on PED and PES:

Consumer burdenProducer burden=PESPED\frac{\text{Consumer burden}}{\text{Producer burden}} = \frac{\text{PES}}{|\text{PED}|}

  • The more inelastic side of the market bears a larger share of the tax burden
  • If demand is perfectly inelastic, consumers bear the entire burden
  • If supply is perfectly elastic, consumers bear the entire burden

A tax creates a deadweight loss because some mutually beneficial transactions no longer occur:

DWL=12×t×(Q0Qt)\mathrm{DWL} = \frac{1}{2} \times t \times (Q_0 - Q_t)

Where tt is the tax per unit, Q0Q_0 is the pre-tax quantity, and QtQ_t is the post-tax quantity.

Tax revenue is:

Taxrevenue=t×Qt\mathrm{Tax revenue} = t \times Q_t

Subsidies

A subsidy is a payment by the government to producers (or consumers) per unit of output. It shifts The supply curve downward (or rightward), lowering the market price and increasing quantity.

Effects of subsidies include:

  • Lower prices for consumers
  • Higher producer revenues
  • Correction of positive externalities (if set at the socially optimal level)
  • Government expenditure (opportunity cost)
  • Potential overproduction and inefficiency
  • Deadweight loss if the subsidy causes production beyond the socially optimal quantity

The total cost to the government is:

Subsidy cost=subsidy per unit×Qnew\text{Subsidy cost} = \text{subsidy per unit} \times Q_{\text{new}}

Regulation

Governments can directly regulate markets by setting standards, banning certain activities, or Requiring permits. Examples include:

  • Pollution emission limits (command-and-control regulation)
  • Minimum quality standards (food safety, building codes)
  • Bans on harmful substances (CFCs, certain pesticides)
  • Mandatory labelling requirements

Regulation has the advantage of certainty (firms know exactly what is required) but may be Inflexible and costly to enforce.

Tradable Pollution Permits

A market-based approach to correcting negative externalities. The government sets a total cap on Emissions and issues permits that firms can trade among themselves. Firms with low abatement costs Reduce emissions and sell their surplus permits; firms with high abatement costs buy permits instead Of reducing emissions.

Advantages:

  • Ensures the environmental target is met (total emissions are capped)
  • Allocates emission reductions efficiently (firms with the lowest abatement costs reduce first)
  • Provides incentives for innovation in pollution-reduction technology

Disadvantages:

  • Initial allocation of permits (windfall profits if permits are given away rather than auctioned)
  • Price volatility of permits
  • Difficulty in setting the correct cap
  • Monitoring and enforcement costs

Government Failure

Government failure occurs when government intervention worsens the allocation of resources rather Than improving it. Causes include:

  • Regulatory capture: regulators serve the interests of the industry they regulate rather than the public interest
  • Information problems: governments lacking sufficient information to set optimal policies
  • Unintended consequences: price ceilings causing shortages, subsidies causing overproduction
  • Administrative costs: the cost of implementing and enforcing policies may exceed the benefits
  • Political pressures leading to short-term thinking and populist measures
  • Principal-agent problems: government officials (agents) may not act in the interests of citizens (principals)

Government Intervention: Welfare Analysis (HL Extension)

Deadweight Loss Calculations

The deadweight loss (DWL) from any government intervention that creates a wedge between the Marginal benefit and marginal cost of a good can be calculated using the formula:

DWL=12×(Pdistortion)×(Qloss)\mathrm{DWL} = \frac{1}{2} \times (P_{\text{distortion}}) \times (Q_{\text{loss}})

Where PdistortionP_{\text{distortion}} is the difference between the marginal benefit and marginal cost at the Distorted quantity, and QlossQ_{\text{loss}} is the reduction in quantity from the efficient level.

Comprehensive Welfare Analysis of a Tax

For a specific tax tt on a good with linear demand P=abQP = a - bQ and supply P=c+dQP = c + dQ:

Pre-tax equilibrium:

abQ=c+dQ    Q0=acb+d,P0=ad+bcb+da - bQ = c + dQ \implies Q_0 = \frac{a - c}{b + d}, \quad P_0 = \frac{ad + bc}{b + d}

Post-tax equilibrium: supply shifts to P=c+dQ+tP = c + dQ + t:

abQt=c+dQt+t    Qt=actb+da - bQ_t = c + dQ_t + t \implies Q_t = \frac{a - c - t}{b + d}

Pd=abQt=ab(act)b+d=a(b+d)b(act)b+d=ad+bc+btb+dP_d = a - bQ_t = a - \frac{b(a - c - t)}{b + d} = \frac{a(b + d) - b(a - c - t)}{b + d} = \frac{ad + bc + bt}{b + d}

Ps=Pdt=ad+bcdtb+dP_s = P_d - t = \frac{ad + bc - dt}{b + d}

Welfare changes:

ΔCS=12(PdP0)(Q0+Qt)\Delta\mathrm{CS} = -\frac{1}{2}(P_d - P_0)(Q_0 + Q_t)

ΔPS=12(P0Ps)(Q0+Qt)\Delta\mathrm{PS} = -\frac{1}{2}(P_0 - P_s)(Q_0 + Q_t)

Tax revenue=t×Qt\text{Tax revenue} = t \times Q_t

DWL=12×t×(Q0Qt)=t22(b+d)\mathrm{DWL} = \frac{1}{2} \times t \times (Q_0 - Q_t) = \frac{t^2}{2(b + d)}

Welfare Analysis of a Subsidy

For a per-unit subsidy ssThe supply curve shifts downward to P=c+dQsP = c + dQ - s:

abQ=c+dQs    Qs=ac+sb+da - bQ = c + dQ - s \implies Q_s = \frac{a - c + s}{b + d}

Pd=abQs=ad+bcbsb+dP_d = a - bQ_s = \frac{ad + bc - bs}{b + d}

Ps=Pd+s=ad+bc+dsb+dP_s = P_d + s = \frac{ad + bc + ds}{b + d}

The subsidy cost is s×Qss \times Q_s. The DWL of the subsidy is:

DWL=12×s×(QsQ0)=s22(b+d)\mathrm{DWL} = \frac{1}{2} \times s \times (Q_s - Q_0) = \frac{s^2}{2(b + d)}

Welfare Analysis of a Price Ceiling

A binding price ceiling Pceil<P0P_{\text{ceil}} < P_0 creates:

  • Quantity demanded: Qd=(aPceil)/bQ_d = (a - P_{\text{ceil}}) / b
  • Quantity supplied: Qs=(Pceilc)/dQ_s = (P_{\text{ceil}} - c) / d
  • Shortage: QdQsQ_d - Q_s

ΔCS=(P0Pceil)Qs12(P0Pceil)(Q0Qs)12(P0Pceil)(QdQ0)\Delta\mathrm{CS} = (P_0 - P_{\text{ceil}})Q_s - \frac{1}{2}(P_0 - P_{\text{ceil}})(Q_0 - Q_s) - \frac{1}{2}(P_0 - P_{\text{ceil}})(Q_d - Q_0)

The first term is the gain to consumers who still buy the good. The second and third terms are losses From reduced consumption. The net effect is ambiguous and depends on the parameters.

DWL=12(Pceilc)(Q0Qs)+12(aPceil)(QdQ0)\mathrm{DWL} = \frac{1}{2}(P_{\text{ceil}} - c)(Q_0 - Q_s) + \frac{1}{2}(a - P_{\text{ceil}})(Q_d - Q_0)

The first triangle is the loss from inefficiently low production. The second is the loss from Foregone mutually beneficial transactions.

Welfare Analysis of a Price Floor

A binding price floor Pfloor>P0P_{\text{floor}} > P_0 creates:

  • Quantity demanded: Qd=(aPfloor)/bQ_d = (a - P_{\text{floor}}) / b
  • Quantity supplied: Qs=(Pfloorc)/dQ_s = (P_{\text{floor}} - c) / d
  • Surplus: QsQdQ_s - Q_d

DWL=12(Pfloorc)(QsQ0)+12(aPfloor)(Q0Qd)\mathrm{DWL} = \frac{1}{2}(P_{\text{floor}} - c)(Q_s - Q_0) + \frac{1}{2}(a - P_{\text{floor}})(Q_0 - Q_d)

If the government purchases the surplus at the floor price, the total cost is Pfloor×(QsQd)P_{\text{floor}} \times (Q_s - Q_d)Adding to the welfare loss.

Common Pitfalls in Welfare Analysis

  • Confusing the change in consumer surplus with the change in total welfare. A tax reduces both CS and PS, and the net welfare loss is the DWL.
  • Forgetting that the DWL triangle depends on the change in quantity, not the change in price.
  • Calculating government revenue from a quota as positive. Unless licences are auctioned, the quota revenue may accrue to foreign producers or importers, not the government.
  • Drawing the DWL on the wrong side of the supply and demand curves. Always identify the pre- and post-intervention quantities and the area between the supply and demand curves.

Prospect Theory and Behavioural Biases (HL Extension)

Kahneman and Tversky’s Prospect Theory

Prospect theory (1979) challenges the standard expected utility model by demonstrating that Individuals evaluate outcomes relative to a reference point, overweight small probabilities, and Are loss-averse.

Key departures from expected utility theory:

  1. Reference dependence: utility is measured from gains and losses relative to a reference point, not from absolute wealth levels
  2. Loss aversion: losses loom larger than equivalent gains. The pain of losing USD 100 is approximately twice the pleasure of gaining USD 100
  3. Diminishing sensitivity: the marginal impact of gains or losses decreases with distance from the reference point
  4. Probability weighting: individuals overweight small probabilities and underweight large probabilities

The value function:

v(x)={xαif x0 (gains)λ(x)βif x<0 (losses)v(x) = \begin{cases} x^\alpha & \text{if } x \geq 0 \text{ (gains)} \\ -\lambda(-x)^\beta & \text{if } x < 0 \text{ (losses)} \end{cases}

Where α,β<1\alpha, \beta < 1 (diminishing sensitivity), λ>1\lambda > 1 (loss aversion; λ2.25\lambda \approx 2.25).

The probability weighting function:

π(p)=pγ(pγ+(1p)γ)1/γ\pi(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}

Where γ<1\gamma < 1 for most individuals, causing the inverse-S-shaped weighting function.

Implications for Economic Behaviour

  1. Endowment effect: people value goods they own more than identical goods they do not own. This is explained by loss aversion: giving up a good is perceived as a loss, which is weighted more heavily than the equivalent gain from acquiring it
  2. Status quo bias: the tendency to prefer the current state of affairs. Changing the status quo involves potential losses (what might go wrong) that are overweighted
  3. Framing effects: the same outcome presented differently (as a gain or a loss) leads to different choices. A surgery with a “90% survival rate” is preferred to one with a “10% mortality rate” despite being identical
  4. Mental accounting: individuals categorise money into different “accounts” (rent, food, entertainment) and treat money differently depending on the account, violating fungibility

Numerical Example: Loss Aversion

An individual with loss aversion parameter λ=2\lambda = 2 is offered a gamble:

  • 50% chance of winning USD 200
  • 50% chance of losing USD 100

Expected value =0.5×200+0.5×(100)=+50= 0.5 \times 200 + 0.5 \times (-100) = +50

Under expected utility theory, a risk-neutral individual would accept (positive expected value).

Under prospect theory (assuming linear value function for simplicity):

V(gamble)=0.5×v(200)+0.5×v(100)=0.5×200+0.5×(2×100)V(\text{gamble}) = 0.5 \times v(200) + 0.5 \times v(-100) = 0.5 \times 200 + 0.5 \times (-2 \times 100) =100100=0= 100 - 100 = 0

The individual is indifferent between the gamble and the status quo, despite the positive expected Value. With λ=2.5\lambda = 2.5:

V=0.5×200+0.5×(2.5×100)=100125=25V = 0.5 \times 200 + 0.5 \times (-2.5 \times 100) = 100 - 125 = -25

The individual rejects the gamble, illustrating loss aversion.

Nudge Theory (Thaler and Sunstein)

A nudge is any aspect of the choice architecture that alters people’s behaviour in a Predictable way without forbidding any options or significantly changing their economic incentives.

Examples of nudges in policy:

  1. Default options: organ donation (opt-out systems have 90%+ participation vs. 15% in opt-in systems), pension plan enrolment
  2. Social norms: displaying energy consumption relative to neighbours reduces energy use by 2—6%
  3. Simplified information: clearer nutrition labels, plain-language financial disclosures
  4. Commitment devices: pre-commitment to savings goals, with penalties for withdrawal
  5. Framing: presenting tax as a contribution to public goods rather than a burden

Evaluation of nudge theory:

  • Advantages: low cost, preserves freedom of choice, empirically effective in many contexts
  • Disadvantages: may be manipulative, effects may be small and temporary, raises ethical questions about who decides what behaviour is “correct,” may distract from structural reforms

Anchoring and Adjustment Heuristic (HL Extension)

Definition and Mechanism

Anchoring is a cognitive bias whereby individuals rely too heavily on an initial piece of Information (the “anchor”) when making decisions, even when the anchor is irrelevant.

Mechanism: individuals start from the anchor and adjust insufficiently to reach their final Estimate. The adjustment process is cognitively effortful, so people tend to “stick” close to the Anchor.

Experimental Evidence

Kahneman and Tversky (1974): participants were asked to estimate the percentage of African Countries in the UN. Those who first saw the number 65 guessed 45% on average; those who saw 10 Guessed 25%. A completely irrelevant number significantly influenced estimates.

Ariely, Loewenstein, and Prelec (2003): students wrote down the last two digits of their Social security number and then bid on items (wine, chocolate, books). Students with higher SSN digits bid 60—120% more than those with lower digits.

Economic Applications

  1. Wage negotiations: the first number mentioned in a salary negotiation serves as an anchor, significantly influencing the final outcome
  2. Pricing strategies: “was USD 200, now USD 100” uses the original price as an anchor to make the discount appear larger
  3. Real estate: listing prices anchor buyer expectations. Properties listed 10% above market value still sell close to that price
  4. Courtroom damages: plaintiffs who request higher initial awards tend to receive higher settlements, even when judges and jurors are instructed to ignore the request

Efficiency vs. Equity: Detailed Analysis (HL Extension)

The Fundamental Trade-off

Efficiency refers to maximising total surplus (the sum of consumer and producer surplus). Equity refers to the fairness of the distribution of surplus among members of society.

The trade-off arises because policies that improve equity (e.g., redistribution through taxation) reduce efficiency (e.g., by creating deadweight loss from taxation).

Types of Efficiency

  1. Allocative efficiency: P=MCP = \text{MC} (the value consumers place on the last unit equals the cost of producing it)
  2. Productive efficiency: production at minimum average cost
  3. Dynamic efficiency: the rate of innovation and technological progress over time
  4. Pareto efficiency: no reallocation can make anyone better off without making someone worse off

Types of Equity

  1. Horizontal equity: equals should be treated equally (people in similar circumstances should pay similar taxes)
  2. Vertical equity: unequals should be treated unequally (those with greater ability to pay should pay more)
  3. Intergenerational equity: fairness between current and future generations
  4. Procedural equity: fairness of the process by which outcomes are determined

The Equity-Efficiency Trade-off in Practice

Progressive taxation:

A progressive income tax with a top marginal rate of 50% reduces inequality but creates a Deadweight loss. The DWL depends on the elasticity of labour supply:

DWL12×ϵL×t2×w×L\text{DWL} \approx \frac{1}{2} \times \epsilon_L \times t^2 \times w \times L

Where ϵL\epsilon_L is the labour supply elasticity, tt is the tax rate, ww is the wage rate, And LL is labour supply.

If ϵL=0.5\epsilon_L = 0.5 and t=0.5t = 0.5:

DWL12×0.5×0.25×w×L=0.0625×w×L\text{DWL} \approx \frac{1}{2} \times 0.5 \times 0.25 \times w \times L = 0.0625 \times w \times L

The DWL is 6.25% of total labour income. Whether this trade-off is worthwhile depends on the Social value placed on equality.

Rawlsian vs. Utilitarian perspectives:

  • Rawls (maximin): policy should maximise the welfare of the worst-off member of society. Redistribution is justified even at significant efficiency cost
  • Utilitarian: policy should maximise total welfare. Redistribution is justified only if the marginal utility of income for the poor exceeds the marginal efficiency loss from taxation
  • Nozick (entitlement): any redistribution beyond voluntary exchange is unjust. The distribution resulting from free exchange is inherently fair

Government Failure (HL Extension)

Definition

Government failure occurs when government intervention in the market leads to a net Reduction in economic welfare, i.e., the costs of intervention exceed the benefits.

Types of Government Failure

  1. Information failure: governments may lack the information needed to design effective policies. Central planners cannot aggregate dispersed knowledge as effectively as price signals (Hayek’s knowledge problem)
  2. Regulatory capture: regulated industries influence the regulators to act in the industry’s interest rather than the public interest. Agencies may become “captured” by the firms they regulate
  3. Principal-agent problems: elected officials (principals) may not be able to control bureaucrats (agents) who pursue their own objectives (budget maximisation, empire building)
  4. Short-termism: democratic political cycles incentivise policies with immediate, visible benefits and deferred costs (e.g., debt accumulation, underinvestment in infrastructure)
  5. Rent-seeking: resources are wasted on lobbying for government favours rather than productive activity. The total cost of rent-seeking can exceed the deadweight loss of the market failure it aims to correct
  6. Government bureaucracy and inflexibility: government agencies may be slower to adapt than private firms, leading to inefficiency
  7. Unintended consequences: policies may have secondary effects that offset or exceed the intended benefits

Rent-Seeking: Detailed Analysis

Definition: rent-seeking is the expenditure of resources to obtain a transfer of wealth Without creating any new wealth.

Example: Suppose the government introduces a tariff that transfers USD 100 million from Consumers to producers. The DWL of the tariff is USD 20 million. Producers may spend up to USD 100 million on lobbying to secure the tariff. The total social cost is:

Total cost=DWL+Rent-seeking expenditure=20+100=120\text{Total cost} = \text{DWL} + \text{Rent-seeking expenditure} = 20 + 100 = 120

The total social cost of the tariff exceeds the DWL by six times, because the rent-seeking Expenditure is a pure waste of resources.

Tullock’s paradox: why is rent-seeking expenditure much smaller than the potential Transfer? Possible explanations include: free-rider problems among beneficiaries, uncertainty About policy outcomes, and ethical constraints on bribery.

Poverty and Inequality Measurement (HL Extension)

Measuring Inequality

Lorenz curve: plots the cumulative share of income (or wealth) received by the cumulative Share of the population, ordered from poorest to richest.

Gini coefficient:

G=AA+BG = \frac{A}{A + B}

Where AA is the area between the line of perfect equality and the Lorenz curve, and BB is The area under the Lorenz curve. G[0,1]G \in [0, 1]Where 0 is perfect equality and 1 is perfect Inequality.

Interpretation of Gini coefficients:

  • G<0.25G < 0.25: low inequality (e.g., Denmark 0.28, Norway 0.27)
  • 0.25G<0.350.25 \leq G < 0.35: moderate inequality (e.g., UK 0.35, France 0.32)
  • 0.35G<0.500.35 \leq G < 0.50: high inequality (e.g., USA 0.41, China 0.47)
  • G0.50G \geq 0.50: very high inequality (e.g., South Africa 0.63, Brazil 0.53)

The Palma Ratio

The Palma ratio is the ratio of the income share of the top 10% to the income share of the Bottom 40%:

Palma=Stop 10%Sbottom 40%\text{Palma} = \frac{S_{\text{top 10\%}}}{S_{\text{bottom 40\%}}}

The Palma ratio focuses on the “tails” of the distribution because the middle 50% of the Population captures approximately 50% of income in most countries, so inequality is driven Primarily by differences at the extremes.

Advantages over the Gini coefficient:

  • More intuitive and easier to interpret
  • More sensitive to changes at the top and bottom of the distribution
  • Less sensitive to middle-income changes that are less policy-relevant

Measuring Poverty

  1. Absolute poverty: income below a fixed threshold (World Bank: USD 2.15/day at 2017 PPP)
  2. Relative poverty: income below a percentage of median income (OECD: below 60% of median equivalised disposable income)
  3. Multidimensional Poverty Index (MPI): measures poverty across health, education, and living standards (10 indicators including nutrition, school attendance, electricity, sanitation)
  4. Human Development Index (HDI): composite of life expectancy, education (mean and expected years of schooling), and GNI per capita

Numerical example: A country has the following income distribution (quintiles):

QuintileShare of income
Bottom 20%5%
Second 20%10%
Middle 20%15%
Fourth 20%20%
Top 20%50%

Gini coefficient approximation:

G=1i=15(XiXi1)(Yi+Yi1)G = 1 - \sum_{i=1}^{5} (X_i - X_{i-1})(Y_i + Y_{i-1})

Where XiX_i is the cumulative population share and YiY_i is the cumulative income share.

iiXiX_iYiY_iXiXi1X_i - X_{i-1}Yi+Yi1Y_i + Y_{i-1}Product
000
10.20.050.20.050.010
20.40.150.20.200.040
30.60.300.20.450.090
40.80.500.20.800.160
51.01.000.21.500.300

G=1(0.010+0.040+0.090+0.160+0.300)=10.600=0.400G = 1 - (0.010 + 0.040 + 0.090 + 0.160 + 0.300) = 1 - 0.600 = 0.400

This indicates high inequality (comparable to the USA).

Palma ratio =50%/15%=3.33= 50\% / 15\% = 3.33.

Worked Examples

Example 1: Negative Externality of Production

A steel factory produces steel with marginal private cost (MPC) of QQ and marginal social cost (MSC) of Q+20Q + 20 (due to pollution). Demand (marginal private benefit) is P=100QP = 100 - Q.

Market equilibrium (MPB = MPC): 100Q=Q    Q=50,P=50100 - Q = Q \implies Q = 50, P = 50

Social optimum (MSB = MSC): 100Q=Q+20    2Q=80    Q=40,P=60100 - Q = Q + 20 \implies 2Q = 80 \implies Q = 40, P = 60

The externality causes overproduction of 10 units. A Pigouvian tax of $20 per unit would internalise the externality.

Example 2: Public Good Provision

A lighthouse costs 1,000,0001,000,000 to build and provides 5050 of benefit to each of 30,00030,000 ships per year (1,500,0001,500,000 total benefit). No private firm will build it because ships cannot be excluded from using the light (non-excludable). Government provision is necessary because total benefit (1,500,0001,500,000) exceeds cost (1,000,0001,000,000).

Summary

  • Market failure occurs when the free market fails to allocate resources efficiently (MSB ≠ MSC)
  • Externalities (positive and negative, production and consumption) cause divergence between private and social costs/benefits
  • Public goods (non-excludable, non-rivalrous) are underprovided by the market due to the free-rider problem
  • Information asymmetry leads to adverse selection and moral hazard
  • Government intervention (taxes, subsidies, regulation, provision) can correct market failure but may cause government failure
  • Government failure includes regulatory capture, excessive bureaucracy, and unintended consequences
  • Key diagrams: negative externality (MSC > MPC), positive externality (MSB > MPB), tax/subsidy welfare analysis

Common Pitfalls

  • Confusing terminology or concepts that appear similar but have distinct meanings.
  • Overlooking key assumptions or boundary conditions that limit applicability.