Theory of the Firm

Market Structures

Classification Criteria

Market structures are classified along several dimensions:

• Number of firms: from many (perfect competition) to one (monopoly)
• Nature of the product: homogeneous (identical) or differentiated
• Barriers to entry: low to high
• Degree of market power: the ability of firms to influence price
• Information availability: perfect or imperfect

Perfect Competition

Assumptions:

1. Many buyers and sellers, none of whom can influence the market price (price takers)
2. Homogeneous (identical) products
3. Perfect information
4. Free entry and exit (no barriers)
5. Perfect factor mobility

Short-run equilibrium:

• The firm faces a perfectly elastic (horizontal) demand curve at the market price $P^*$
• Average Revenue (AR) $=$ Marginal Revenue (MR) $= P^*$
• The firm maximises profit where $\mathrm{MR} = \mathrm{MC}$
• In the short run, the firm may earn supernormal profit (if $P > \text{ATC}$), normal profit (if $P = \text{ATC}$), or make a loss (if $P < \text{ATC}$)
• The firm continues to produce in the short run as long as $P \geq \text{AVC}$ (the shutdown point)

Long-run equilibrium:

• Free entry and exit drive economic profit to zero ($P = \text{ATC} = \mathrm{MC}$)
• The firm produces at the minimum point of the ATC curve (productive efficiency)
• $P = \mathrm{MC}$ (allocative efficiency)
• Zero economic profit, but normal profit is earned

$\text{Short-run: } P \geq \text{AVC}, \text{ produce where MR} = \text{MC}$ $\text{Long-run: } P = \text{ATC}_{\min} = \text{MC}$

Monopoly

Assumptions:

1. Single seller (or one dominant firm)
2. No close substitutes
3. High barriers to entry (legal barriers such as patents, natural monopoly due to economies of scale, ownership of essential resources, predatory pricing)
4. Price maker

Revenue curves:

• The monopoly faces the market demand curve (downward-sloping)
• $\mathrm{AR} = P$ (the demand curve)
• MR lies below AR because to sell an additional unit, the monopolist must lower the price on all units sold
• For a linear demand curve $P = a - bQ$: $\mathrm{MR} = a - 2bQ$

Profit maximisation:

The monopolist produces where $\mathrm{MR} = \mathrm{MC}$ and charges the price found on the demand Curve at that quantity.

$\text{Profit} = (P - \text{ATC}) \times Q$

In the long run, the monopolist can earn supernormal profit because barriers to entry prevent new Firms from entering the market.

Inefficiencies of monopoly:

• Allocative inefficiency: $P > \mathrm{MC}$Meaning the value consumers place on the last unit exceeds the cost of producing it. Too little is produced relative to the social optimum
• Productive inefficiency: the monopolist does not produce at the minimum of ATC
• Deadweight loss: the loss of consumer and producer surplus due to reduced output and higher prices compared to perfect competition
• X-inefficiency: lack of competitive pressure may allow the monopolist to operate with higher costs than necessary

Arguments in favour of monopoly:

• Economies of scale: a single large firm may produce at lower average cost than multiple small firms (natural monopoly, e.g., water supply, electricity distribution)
• Research and development: supernormal profits can fund R&D, leading to innovation and dynamic efficiency
• International competitiveness: large firms may be better able to compete in global markets

Price discrimination occurs when a monopolist charges different prices to different consumers for The same good or service, not justified by differences in cost. Conditions for price discrimination:

1. Market power (price maker)
2. Ability to separate markets (prevent resale)
3. Different price elasticities of demand in different markets

Degrees of price discrimination:

• First-degree (perfect): charge each consumer their maximum willingness to pay. Captures all consumer surplus
• Second-degree: charge different prices based on the quantity purchased (bulk discounts)
• Third-degree: charge different prices to different consumer groups (e.g., student discounts, senior citizen discounts, peak/off-peak pricing)

Monopolistic Competition

Assumptions:

1. Many firms
2. Differentiated products (branding, quality, location, service)
3. Low barriers to entry and exit
4. Some degree of market power (firms are price makers to a limited extent)

Short-run equilibrium:

• Each firm faces a downward-sloping demand curve (due to product differentiation)
• Profit maximisation at $\mathrm{MR} = \mathrm{MC}$
• Firms can earn supernormal profit, normal profit, or losses in the short run

Long-run equilibrium:

• Free entry and exit drives economic profit to zero ($P = \text{ATC}$)
• Unlike perfect competition, the demand curve is downward-sloping, so the tangency with ATC occurs to the left of the minimum ATC
• Excess capacity: the firm produces at a lower output than the output that minimises ATC
• Allocative inefficiency: $P > \mathrm{MC}$

$\text{Long-run: } P > \mathrm{MC} \text{ and } P = \text{ATC} > \text{ATC}_{\min}$

Non-price competition: firms compete through advertising, branding, product differentiation, and Customer service rather than solely through price.

Oligopoly

Assumptions:

1. A few large firms dominate the market
2. Interdependence: each firm”s actions affect, and are affected by, the actions of rivals
3. High barriers to entry (economies of scale, brand loyalty, patents, strategic barriers)
4. Products may be homogeneous (e.g., oil) or differentiated (e.g., cars, smartphones)

Key features:

• Kinked demand curve model: if a firm raises its price, rivals do not follow (demand is elastic above the kink); if a firm lowers its price, rivals match the cut (demand is inelastic below the kink). This creates price rigidity and explains why prices in oligopolistic markets tend to be stable
• Collusion: firms may coordinate to act as a monopoly, setting prices and output to maximise joint profit. Collusion may be explicit (cartel, e.g., OPEC) or tacit (price leadership, conscious parallelism)
• Game theory: oligopoly is the market structure most analysed using game theory (see the Game Theory and Behavioural Economics chapter)
• Non-price competition: advertising, branding, product development, and loyalty programmes are more common than price competition
• Contestable market theory: even if an industry has few firms, the threat of potential entry may discipline incumbents to keep prices close to competitive levels

Cartels:

A cartel is a formal agreement among competing firms to coordinate prices, output, or market shares. Cartels are inherently unstable because each member has an incentive to cheat by secretly lowering Prices or exceeding its quota (prisoner’s dilemma). Cartels are illegal in most countries under Anti-trust/competition law.

Theory of the Firm

Costs of Production

Total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC):

$\mathrm{TC} = \mathrm{TFC} + \mathrm{TVC}$

• Fixed costs: costs that do not vary with output in the short run (rent, salaries of permanent staff, insurance)
• Variable costs: costs that vary directly with output (raw materials, hourly wages, energy)

Average costs:

$\mathrm{AFC} = \frac{\mathrm{TFC}}{Q} \qquad \mathrm{AVC} = \frac{\mathrm{TVC}}{Q} \qquad \mathrm{ATC} = \frac{\mathrm{TC}}{Q} = \mathrm{AFC} + \mathrm{AVC}$

Marginal cost (MC): the additional cost of producing one more unit:

$\mathrm{MC} = \frac{\Delta \mathrm{TC}}{\Delta Q}$

Short-Run Cost Curves

• MC initially falls (due to increasing marginal returns from better utilisation of fixed factors) then rises (due to diminishing marginal returns as the fixed factor becomes a constraint)
• AVC follows MC: when MC $<$ AVC, AVC is falling; when MC $>$ AVC, AVC is rising. MC intersects AVC at its minimum point
• ATC follows MC similarly: MC intersects ATC at its minimum point
• AFC declines continuously as output increases (spreading fixed costs over more units)
• The gap between ATC and AVC equals AFC at every level of output

The Law of Diminishing Marginal Returns

In the short run, as more of a variable factor (e.g., labour) is added to a fixed factor (e.g., Capital), the marginal product of the variable factor eventually declines. This is not caused by Reduced quality of the variable factor but by the increasing ratio of variable to fixed factors.

$\mathrm{MP}_L = \frac{\Delta Q}{\Delta L} \qquad \text{Initially rises, then falls}$

The relationship between production and cost:

$\mathrm{MC} = \frac{w}{\mathrm{MP}_L}$

Where $w$ is the wage rate. When MP is rising, MC is falling; when MP is falling, MC is rising.

Long-Run Costs

In the long run, all factors of production are variable. The firm can choose its optimal scale of Production.

• Long-run average cost (LRAC) curve: the envelope of all short-run ATC curves. It shows the lowest average cost at each output level when the firm can adjust all inputs
• Economies of scale: LRAC falls as output increases. Sources include:
• Technical economies: specialisation, indivisibility of capital, the “container principle”
• Purchasing economies: bulk buying discounts on raw materials
• Managerial economies: specialisation of management functions
• Financial economies: lower borrowing costs for larger firms
• Risk-bearing economies: diversification of products and markets
• Constant returns to scale: LRAC is flat; doubling all inputs exactly doubles output
• Diseconomies of scale: LRAC rises as output increases. Causes include:
• Communication and coordination problems in large organisations
• Alienation and reduced motivation of workers
• Bureaucratic inefficiency and red tape

The minimum efficient scale (MES) is the lowest output at which LRAC is minimised. Firms that do Not reach MES may be unable to compete with larger rivals.

Revenue

• Total Revenue (TR) $= P \times Q$
• Average Revenue (AR) $= \frac{\mathrm{TR}}{Q} = P$ (the demand curve)
• Marginal Revenue (MR) $= \frac{\Delta \mathrm{TR}}{\Delta Q}$

Relationship between AR and MR:

• Under perfect competition: AR $=$ MR $= P$ (horizontal demand curve)
• Under monopoly and monopolistic competition: MR $<$ AR because the firm must lower price on all units to sell additional units

Profit Maximisation

A firm maximises profit by producing the quantity where:

$\mathrm{MR} = \mathrm{MC}$

Derivation: profit $\pi = \mathrm{TR} - \mathrm{TC}$. Profit is maximised where the first Derivative equals zero:

$\frac{d\pi}{dQ} = \frac{d\mathrm{TR}}{dQ} - \frac{d\mathrm{TC}}{dQ} = \mathrm{MR} - \mathrm{MC} = 0$

Second-order condition: $\frac{d^2\pi}{dQ^2} < 0$Meaning MC must be rising at the point where MR $=$ MC (MC cuts MR from below).

• If $\mathrm{MR} > \mathrm{MC}$: producing an additional unit adds more to revenue than to cost, so the firm should expand output
• If $\mathrm{MR} < \mathrm{MC}$: producing an additional unit adds more to cost than to revenue, so the firm should reduce output

Shutdown condition: in the short run, a firm should continue to produce as long as $P \geq$ AVC. If $P <$ AVC, the firm cannot cover its variable costs and should shut down immediately, losing Only its fixed costs. If AVC $\leq P <$ ATC, the firm makes a loss but continues to produce because It covers its variable costs and contributes partially to fixed costs.

Normal profit: the minimum profit necessary to keep a firm in the industry (the opportunity cost Of the entrepreneur’s time and capital). Normal profit is included in ATC as a cost. When Economists say “zero economic profit,” they mean normal profit is being earned.

Production Theory (HL Extension)

Isoquants and Isocost Lines

An isoquant shows all combinations of two inputs ( capital $K$ and labour $L$) that Produce the same level of output. Isoquants are analogous to indifference curves in consumer theory.

Properties of isoquants:

1. Downward-sloping: to maintain the same output, using more of one input requires using less of the other
2. Convex to the origin: due to the diminishing marginal rate of technical substitution (MRTS)
3. Higher isoquants represent higher output levels

The marginal rate of technical substitution (MRTS) measures the rate at which one input can be Substituted for another while maintaining output:

$\mathrm{MRTS}_{LK} = -\frac{\Delta K}{\Delta L} = \frac{MP_L}{MP_K}$

An isocost line shows all combinations of inputs that cost the same total amount. If the wage Rate is $w$ and the rental rate of capital is $r$:

$wL + rK = C$

The slope of the isocost line is $-w/r$.

Cost Minimisation

A firm minimises the cost of producing a given level of output where the isoquant is tangent to the Isocost line:

$\mathrm{MRTS}_{LK} = \frac{w}{r}$

Or equivalently:

$\frac{MP_L}{w} = \frac{MP_K}{r}$

This condition states that the marginal product per dollar spent must be equal across all inputs.

Returns to Scale

Returns to scale describe how output changes when all inputs are increased proportionally:

• Constant returns to scale: doubling all inputs exactly doubles output. $f(tK, tL) = t \cdot f(K, L)$
• Increasing returns to scale: doubling all inputs more than doubles output. $f(tK, tL) > t \cdot f(K, L)$
• Decreasing returns to scale: doubling all inputs less than doubles output. $f(tK, tL) < t \cdot f(K, L)$

Returns to scale determine the shape of the long-run average cost (LRAC) curve: increasing returns Produce a downward-sloping LRAC, constant returns produce a flat LRAC, and decreasing returns Produce an upward-sloping LRAC.

Cobb-Douglas Production Function

The Cobb-Douglas production function is widely used in economics:

$Q = A \cdot K^\alpha \cdot L^\beta$

Where $A$ is total factor productivity, $\alpha$ is the output elasticity of capital, and $\beta$ is The output elasticity of labour.

Returns to scale with Cobb-Douglas:

• If $\alpha + \beta = 1$: constant returns to scale
• If $\alpha + \beta > 1$: increasing returns to scale
• If $\alpha + \beta < 1$: decreasing returns to scale

Marginal products:

$MP_K = \frac{\partial Q}{\partial K} = \alpha \cdot A \cdot K^{\alpha - 1} \cdot L^\beta = \alpha \cdot \frac{Q}{K}$

$MP_L = \frac{\partial Q}{\partial L} = \beta \cdot A \cdot K^\alpha \cdot L^{\beta - 1} = \beta \cdot \frac{Q}{L}$

Worked example: A firm has the production function Q = 10K^{0.4}L^{0.6}$$w = 20$$r = 40.

Cost minimisation: $\frac{MP_L}{w} = \frac{MP_K}{r}$

$\frac{0.6 \cdot 10K^{0.4}L^{-0.4}}{20} = \frac{0.4 \cdot 10K^{-0.6}L^{0.6}}{40}$

$\frac{0.6L^{-0.4}K^{0.4}}{20} = \frac{0.4K^{-0.6}L^{0.6}}{40}$

$\frac{0.6}{20} \cdot \frac{K^{0.4}}{L^{0.4}} = \frac{0.4}{40} \cdot \frac{L^{0.6}}{K^{0.6}}$

$0.03 \cdot \left(\frac{K}{L}\right)^{0.4} = 0.01 \cdot \left(\frac{L}{K}\right)^{0.6}$

$3 \cdot \left(\frac{K}{L}\right)^{0.4} = \left(\frac{L}{K}\right)^{0.6}$

$3 = \left(\frac{L}{K}\right)^{0.6} \cdot \left(\frac{L}{K}\right)^{0.4} = \frac{L}{K}$

$L = 3K$

The optimal capital-labour ratio is $K/L = 1/3$. For every unit of capital, the firm should employ 3 units of labour.

Oligopoly Models in Depth (HL Extension)

Cournot Duopoly

In the Cournot model (1838), each firm independently chooses its output quantity, taking the rival’s Output as given. Firms choose quantities simultaneously.

Setup: Two firms (1 and 2) produce a homogeneous good with market demand $P = a - bQ$Where $Q = q_1 + q_2$. Each firm has constant marginal cost $c$.

Firm 1’s profit:

$\pi_1 = P \cdot q_1 - c \cdot q_1 = (a - bq_1 - bq_2 - c) \cdot q_1$

Best response function: maximising $\pi_1$ with respect to $q_1$:

$\frac{\partial \pi_1}{\partial q_1} = a - 2bq_1 - bq_2 - c = 0$

$q_1 = \frac{a - c}{2b} - \frac{q_2}{2}$

By symmetry, Firm 2’s best response is:

$q_2 = \frac{a - c}{2b} - \frac{q_1}{2}$

Nash equilibrium (Cournot equilibrium): substituting one best response into the other:

$q_1^* = q_2^* = \frac{a - c}{3b}$

$Q^* = \frac{2(a - c)}{3b}, \quad P^* = \frac{a + 2c}{3}$

Comparison with monopoly and perfect competition:

Cournot output is between monopoly and perfect competition. As the number of firms increases, Cournot output approaches the competitive level.

Bertrand Duopoly

In the Bertrand model (1883), each firm independently chooses its price, taking the rival’s price As given. Firms set prices simultaneously.

Result with homogeneous goods: the Nash equilibrium is both firms setting $P = MC = c$.

If $P_1 > P_2 = c$Firm 1 sells nothing. If $P_1 < P_2$Firm 1 captures the entire market. Each firm has an incentive to undercut the other until price equals marginal cost. This is known as The Bertrand paradox: just two firms are sufficient to achieve the perfectly competitive outcome When products are homogeneous and firms compete on price.

With differentiated products: the demand for each firm depends on both prices. If demand is:

$q_1 = a - bP_1 + dP_2$ $q_2 = a - bP_2 + dP_1$

Where $d$ measures the degree of substitutability ($0 < d < b$). In this case, prices exceed Marginal cost, and the equilibrium depends on the degree of differentiation.

Stackelberg Duopoly

In the Stackelberg model, one firm (the leader) moves first by choosing its quantity, and the Other firm (the follower) observes this and then chooses its quantity.

Solution:

1. The follower solves its Cournot best response given the leader’s output $q_1$: $q_2 = \frac{a - c}{2b} - \frac{q_1}{2}$

2. The leader anticipates this response and maximises its profit: $\pi_1 = (a - bq_1 - bq_2(q_1) - c) \cdot q_1$ $\pi_1 = \left(a - bq_1 - b\left(\frac{a-c}{2b} - \frac{q_1}{2}\right) - c\right) q_1$ $\pi_1 = \left(\frac{a - c}{2} - \frac{bq_1}{2}\right) q_1$

Maximising: $\frac{\partial \pi_1}{\partial q_1} = \frac{a - c}{2} - bq_1 = 0$

$q_1^* = \frac{a - c}{2b}, \quad q_2^* = \frac{a - c}{4b}$

First-mover advantage: the Stackelberg leader produces twice as much as the follower and earns Higher profit. Total output is $Q^* = \frac{3(a-c)}{4b}$Which exceeds Cournot output but is Still less than competitive output. This demonstrates the value of commitment and strategic Leadership.

Kinked Demand Curve: Formal Analysis

The kinked demand curve model (Sweezy, 1939) explains price rigidity in oligopoly. The model Assumes:

• If a firm raises its price, rivals do not follow (demand is elastic above the kink)
• If a firm lowers its price, rivals match the cut (demand is inelastic below the kink)

This creates a discontinuity in the MR curve at the current price and quantity. The result is that Small changes in marginal cost within the gap in the MR curve do not change the profit-maximising Price, explaining price rigidity.

Limitations of the kinked demand curve model:

• It does not explain how the initial price is determined
• It assumes asymmetric behaviour by rivals (matching price cuts but not price increases)
• Empirical evidence for the model is mixed; price rigidity may be better explained by menu costs or implicit collusion

Game Theory and Oligopoly

Game theory provides a rigorous framework for analysing strategic interaction in oligopoly.

Payoff matrix example — pricing game:

Two firms, A and B, can each set a High price or a Low price. Payoffs (profit in millions):

Analysis:

• If B chooses High: A earns 10 (High) vs. 12 (Low). A chooses Low.
• If B chooses Low: A earns 2 (High) vs. 5 (Low). A chooses Low.
• Low is A’s dominant strategy. By symmetry, Low is B’s dominant strategy.
• Nash equilibrium: (Low, Low) with payoffs (5, 5).
• Both would be better off at (High, High) with (10, 10) — a prisoner’s dilemma.

Collusion and cartels as a prisoner’s dilemma:

If firms successfully collude (agree to restrict output and raise prices), joint profits are Maximised. However, each firm has an incentive to cheat by secretly lowering price or exceeding its Quota. The payoff structure mirrors the prisoner’s dilemma:

The Nash equilibrium is (Cheat, Cheat), which is Pareto inferior to (Comply, Comply). This is why Cartels are inherently unstable and require enforcement mechanisms (monitoring, penalties, or Repeated interaction with the threat of punishment).

Sequential games in oligopoly:

In a sequential (Stackelberg) game, the first mover gains an advantage. The leader commits to a High output, and the follower responds with a lower output. This can be analysed using backward Induction.

Common Pitfalls in Oligopoly

• Confusing Cournot and Bertrand models. Cournot assumes firms choose quantities; Bertrand assumes firms choose prices. The outcomes differ significantly.
• Stating that the kinked demand curve explains why prices change. It actually explains why prices are stable (rigid).
• Assuming that oligopoly always leads to higher prices than monopoly. In Bertrand competition with homogeneous goods, price equals marginal cost.
• Forgetting that game theory predictions depend on the payoff structure. Different assumptions about demand, costs, and firm behaviour lead to different equilibria.

Price Discrimination in Depth (HL Extension)

First-Degree (Perfect) Price Discrimination

The monopolist charges each consumer their exact maximum willingness to pay. The monopolist captures The entire consumer surplus.

Welfare effects:

• Consumer surplus falls to zero
• Producer surplus increases by the full amount of the former consumer surplus
• Deadweight loss is eliminated — the monopolist produces the competitive quantity
• Total output equals the perfectly competitive output (where $P = MC$)
• Allocative efficiency is achieved, but all surplus goes to the producer

$\text{Profit} = \text{Total consumer surplus (under single price)} + \text{Producer surplus (under single price)}$

Requirements for first-degree price discrimination:

1. Perfect knowledge of every consumer’s willingness to pay
2. Ability to prevent resale
3. Market power

In practice, perfect price discrimination is rare because firms cannot perfectly observe each Consumer’s willingness to pay. Approximations include personalised pricing (online, based on Browsing history), negotiation (car dealerships, real estate), and auctions.

Second-Degree Price Discrimination

The monopolist offers different pricing options (quantity-based blocks, versioning, self-selection), And consumers self-select into the option that maximises their utility.

Block pricing: the price per unit varies with the quantity purchased:

$\text{Total revenue} = P_1 Q_1 + P_2 (Q_2 - Q_1) + P_3 (Q_3 - Q_2) + \cdots$

Where $P_1 > P_2 > P_3$ (declining block pricing). This captures some consumer surplus from Consumers who buy in larger quantities.

Numerical example: A cinema charges USD 8 for the first ticket, USD 6 for the second, and USD 4 for Each additional ticket (up to 5). A consumer who buys 4 tickets pays:

$\text{Total} = 8 + 6 + 4 + 4 = \text{USD 22}$

Average price per ticket = 22/4 = \text{USD 5.50Which is less than the single-ticket price of USD 8.}$

Third-Degree Price Discrimination

The monopolist separates consumers into groups with different price elasticities of demand and charges Each group a different price.

Rule: charge the higher price to the group with the less elastic demand.

Mathematical derivation:

For each market segment $i$The monopolist maximises:

$\pi_i = P_i(Q_i) \cdot Q_i - C(Q_1 + Q_2 + \cdots + Q_n)$

The first-order condition is:

$\mathrm{MR}_i = MC \quad \forall \; i$

Since $\mathrm{MR}_i = P_i(1 + 1/\mathrm{PED}_i)$And $\mathrm{MR}_i = MC$ for all segments:

$P_i(1 + 1/\mathrm{PED}_i) = P_j(1 + 1/\mathrm{PED}_j) = MC$

Rearranging:

$\frac{P_i}{P_j} = \frac{1 + 1/\mathrm{PED}_j}{1 + 1/\mathrm{PED}_i}$

If $|\mathrm{PED}_i| < |\mathrm{PED}_j|$ (market $i$ has less elastic demand), then $P_i > P_j$.

Worked example: A monopolist serves two markets with demand curves:

Market 1 (adults): $P_1 = 40 - Q_1$, $\mathrm{PED}_1 = -2$ at equilibrium Market 2 (students): $P_2 = 25 - Q_2$, $\mathrm{PED}_2 = -3$ at equilibrium Total cost: $\mathrm{TC} = 50 + 5(Q_1 + Q_2)$So $MC = 5$.

For each market: $MR = MC = 5$.

Market 1: $\mathrm{MR}_1 = 40 - 2Q_1 = 5 \implies Q_1 = 17.5$, $P_1 = 40 - 17.5 = 22.5$

Market 2: $\mathrm{MR}_2 = 25 - 2Q_2 = 5 \implies Q_2 = 10$, $P_2 = 25 - 10 = 15$

Total profit $= P_1 Q_1 + P_2 Q_2 - \mathrm{TC} = 22.5(17.5) + 15(10) - 50 - 5(27.5)$ $= 393.75 + 150 - 50 - 137.5 = 356.25$

Verification: $\frac{P_1}{P_2} = \frac{22.5}{15} = 1.5$

$\frac{1 + 1/\mathrm{PED}_2}{1 + 1/\mathrm{PED}_1} = \frac{1 + 1/(-3)}{1 + 1/(-2)} = \frac{1 - 1/3}{1 - 1/2} = \frac{2/3}{1/2} = \frac{4}{3} \approx 1.33$

The slight discrepancy arises because PED values vary along the demand curve; the condition holds Exactly only at the equilibrium quantities.

Conditions for price discrimination:

1. Market power (price maker)
2. Ability to segment the market (prevent arbitrage/resale between segments)
3. Different price elasticities of demand in different segments

Welfare effects of third-degree price discrimination:

• Consumer surplus decreases in the less elastic market (higher price) and may increase in the more elastic market (lower price)
• Total output may increase or decrease relative to single-price monopoly
• If total output increases, welfare may increase (the DWL reduction from higher output may offset the DWL from misallocation between markets)
• If total output decreases, welfare unambiguously decreases

Common Pitfalls in Price Discrimination

• Assuming that price discrimination always reduces consumer surplus. Consumers in the more elastic market may face lower prices than under uniform pricing.
• Confusing price discrimination with price differentiation due to cost differences. Price discrimination requires the same product to be sold at different prices not justified by cost differences.
• Stating that a monopolist charges “whatever they want” under price discrimination. Even with price discrimination, the monopolist must optimise within the constraints of each market’s demand curve.

Factor Markets (HL Extension)

Factor Demand

A firm demands factors of production (labour, capital, land) to produce output. The demand for a Factor is a derived demand — on the demand for the product that the factor produces.

Marginal Revenue Product (MRP)

The marginal revenue product of labour is the additional revenue generated by employing one more Unit of labour:

$\mathrm{MRP}_L = \mathrm{MR} \times \mathrm{MP}_L$

Where $\mathrm{MP}_L$ is the marginal product of labour and $\mathrm{MR}$ is marginal revenue.

Under perfect competition in the product market ($\mathrm{MR} = P$):

$\mathrm{MRP}_L = P \times \mathrm{MP}_L = \mathrm{VMP}_L$

Where $\mathrm{VMP}_L$ is the value of the marginal product.

Under monopoly ($\mathrm{MR} < P$):

$\mathrm{MRP}_L < \mathrm{VMP}_L$

A profit-maximising firm hires labour up to the point where:

$\mathrm{MRP}_L = \mathrm{MRC}_L$

Where $\mathrm{MRC}_L$ (marginal resource cost) is the additional cost of hiring one more unit of Labour.

Marginal Resource Cost (MRC)

In a perfectly competitive labour market, the firm is a wage taker and $\mathrm{MRC}_L = w$ (the Wage rate). The firm faces a horizontal supply curve for labour.

$\text{Labour demand rule (perfect competition): } \mathrm{MRP}_L = w$

Monopsony

A monopsony is a market with a single buyer of a factor of production ( labour). The Monopsonist faces an upward-sloping supply curve for labour and must pay a higher wage to attract Additional workers.

If the labour supply curve is $w = a + bL$The total cost of labour is:

$\mathrm{TC}_L = w \cdot L = (a + bL) \cdot L = aL + bL^2$

$\mathrm{MRC}_L = \frac{d\mathrm{TC}_L}{dL} = a + 2bL$

The MRC curve lies above the supply (average cost of labour) curve. The monopsonist hires where $\mathrm{MRP}_L = \mathrm{MRC}_L$But pays the wage indicated by the supply curve at that Quantity.

Comparison with competitive labour market:

• A monopsony hires fewer workers than a competitive market
• A monopsony pays a lower wage than a competitive market
• There is a deadweight loss from the underemployment of labour

Worked example: A monopsonist faces labour supply $w = 20 + 2L$ and $\mathrm{MRP}_L = 100 - 2L$.

$\mathrm{MRC}_L = 20 + 4L$

Setting $\mathrm{MRP}_L = \mathrm{MRC}_L$:

$100 - 2L = 20 + 4L \implies 80 = 6L \implies L^* = 13.33$

Wage paid $= 20 + 2(13.33) = 46.67$

Under competitive conditions: $\mathrm{MRP}_L = w$So $100 - 2L = 20 + 2L \implies 80 = 4L \implies L_c = 20$ $w_c = 20 + 2(20) = 60$.

The monopsony hires 13.33 workers at a wage of 46.67, compared to 20 workers at a wage of 60 under Competition. The deadweight loss arises from the 6.67 workers who would be employed competitively (between $L^* = 13.33$ and $L_c = 20$) but are not hired by the monopsonist.

Transfer Earnings and Economic Rent

Transfer earnings are the minimum payment required to keep a factor of production in its current Use. If a factor earns less than its transfer earnings, it will move to its next best alternative.

Economic rent is any payment above transfer earnings:

$\text{Economic rent} = \text{Total factor income} - \text{Transfer earnings}$

The proportion of economic rent to total income depends on the elasticity of the factor supply:

• Perfectly inelastic supply (vertical): all income is economic rent (e.g., land in the short run)
• Perfectly elastic supply (horizontal): all income is transfer earnings (e.g., unskilled labour in a competitive market)
• Upward-sloping supply: income is a mix of transfer earnings and economic rent

Factor mobility:

• Occupationally mobile: workers can move between different types of jobs (requires training, education)
• Geographically mobile: workers can move between different locations
• High factor mobility increases the elasticity of factor supply, reducing economic rent
• Low factor mobility decreases the elasticity of factor supply, increasing economic rent

Common Pitfalls in Factor Markets

• Confusing MRP with VMP. MRP $= MR \times MP_L$; VMP $= P \times MP_L$. They are equal only under perfect competition in the product market.
• Confusing monopsony with monopoly. Monopoly is a single seller; monopsony is a single buyer.
• Stating that a minimum wage always reduces employment. In a monopsony, a minimum wage set at or below the competitive wage can increase both employment and wages.
• Confusing transfer earnings with economic profit. Transfer earnings are a cost to the firm; they are part of the normal return to the factor.

Additional Practice Problems

Contestable Markets (HL Extension)

Theory of Contestable Markets

A contestable market is one with no barriers to entry or exit, even if there is only one Firm (a natural monopoly). The threat of potential entry constrains the behaviour of the incumbent.

Key conditions:

1. No sunk costs: firms can enter and exit without irrecoverable costs
2. No barriers to entry: no legal, technological, or strategic barriers
3. Perfect information: potential entrants know the incumbent’s costs and demand
4. Hit-and-run entry: firms can enter, capture profits, and exit before the incumbent can respond

The Contestable Market Outcome

Even a monopoly in a perfectly contestable market will set $P = \text{AC}$ (average cost pricing) And produce at the efficient scale. If $P > \text{AC}$Potential entrants can profitably enter, Drive the price down to AC, and earn zero economic profit.

$\text{Sustainable monopoly: } P = \text{AC}, \pi = 0$

This is in contrast to an unregulated monopoly, which sets $P > \text{AC}$ and earns positive Economic profit.

Comparison: Contestable vs. Monopolistic Market

Limitations of Contestable Market Theory

1. Sunk costs are pervasive: most industries have significant sunk costs (brand development, specialised equipment, regulatory compliance)
2. Strategic barriers: incumbents can engage in limit pricing, predatory pricing, or excess capacity to deter entry
3. Information asymmetry: potential entrants rarely have perfect information about the incumbent’s costs
4. Speed of response: in many industries, incumbents can respond quickly enough to prevent profitable hit-and-run entry

Worked Examples: Microeconomics (HL Extension)

Common Pitfalls: Microeconomics (Comprehensive)

• Confusing the Gini coefficient with the Palma ratio. The Gini captures overall inequality; the Palma focuses on the tails and may give a different picture
• Assuming that contestable markets achieve allocative efficiency. Contestable markets achieve $P = \text{AC}$ (productive efficiency) but not $P = \text{MC}$ (allocative efficiency) unless MC is constant
• Assuming that loss aversion is the same as risk aversion. Loss aversion is a separate bias from diminishing marginal utility; it applies even for small stakes where risk aversion should be negligible
• Assuming that government intervention always improves outcomes. Government failure can make outcomes worse than the market failure it aims to correct
• Confusing absolute and relative poverty measures. A country can have zero absolute poverty but high relative poverty
• Ignoring the behavioural responses to redistribution. High marginal tax rates may reduce labour supply and investment, partially offsetting the redistribution
• Assuming that nudges are always benign. Choice architecture can be manipulative and may not reflect genuine informed consent
• Applying prospect theory’s value function parameters universally. The loss aversion parameter $\lambda$ varies across individuals, cultures, and contexts

Price Discrimination: Advanced Analysis (HL Extension)

Conditions for Price Discrimination

1. Market power: the firm must face a downward-sloping demand curve
2. Market segmentation: the firm must be able to identify and separate consumer groups with different price elasticities of demand
3. No arbitrage: consumers must be unable to resell the good between market segments

Three Degrees of Price Discrimination

First degree (perfect) price discrimination: the firm charges each consumer their maximum Willingness to pay. The firm captures the entire consumer surplus.

$\text{Profit} = \int_0^Q P(Q) dQ - \text{TC}(Q)$

Output is at the socially efficient level ($P = \text{MC}$) because the firm captures the Marginal benefit of each unit. There is no deadweight loss, but all surplus goes to the producer.

Second degree (self-selection): the firm offers different quantity or quality options, and Consumers self-select into the option designed for them. Examples: quantity discounts, versioning (software, airline tickets), two-part tariffs.

Third degree (market segmentation): the firm charges different prices to different Identifiable groups (e.g., student discounts, senior citizen discounts, geographic pricing).

Third-Degree Price Discrimination: Formal Treatment

A monopolist serves two markets with demand functions:

Market 1: $P_1 = a_1 - b_1 Q_1$ Market 2: $P_2 = a_2 - b_2 Q_2$

Total cost: $\text{TC} = c(Q_1 + Q_2) + F$

The firm maximises: $\pi = P_1 Q_1 + P_2 Q_2 - c(Q_1 + Q_2) - F$

FOC for each market:

$\text{MR}_1 = \text{MC}: \quad a_1 - 2b_1 Q_1 = c \implies Q_1 = \frac{a_1 - c}{2b_1}$

$\text{MR}_2 = \text{MC}: \quad a_2 - 2b_2 Q_2 = c \implies Q_2 = \frac{a_2 - c}{2b_2}$

The price in each market:

$P_1 = \frac{a_1 + c}{2}, \quad P_2 = \frac{a_2 + c}{2}$

The higher-price market has the less elastic demand (more inelastic).

Inverse elasticity rule:

$\frac{P_1 - \text{MC}}{P_1} = \frac{1}{|\epsilon_1|}, \quad \frac{P_2 - \text{MC}}{P_2} = \frac{1}{|\epsilon_2|}$

The Lerner index (mark-up over MC as a proportion of price) equals the inverse of the price Elasticity of demand. The market with the less elastic demand has the higher mark-up.

Numerical Example

A monopolist serves two markets:

Market 1 (business travellers): $P_1 = 200 - Q_1$ Market 2 (leisure travellers): $P_2 = 120 - Q_2$ $\text{MC} = 20$, $F = 500$

Without price discrimination (uniform price):

Total demand: $Q = Q_1 + Q_2 = (200 - P) + (120 - P) = 320 - 2P$

Inverse demand: $P = 160 - Q/2$

$\text{MR} = 160 - Q$

$\text{MR} = \text{MC}: 160 - Q = 20 \implies Q = 140$