Difficulty: Intermediate to Advanced | Prerequisites: Consumer Theory and Demand Analysis study notes; Supply, Demand, and Elasticity study notes.
This is the supply side of the course, plus the strategic interactions that emerge when markets are not perfectly competitive. Production theory and cost analysis explain how firms decide what to produce and at what scale. Market structure determines pricing behaviour and welfare outcomes. Game theory provides the toolkit for understanding oligopoly, entry deterrence, and any setting where one agent's optimal choice depends on what others do. Together, these topics complete the intermediate micro framework: you now have both sides of the market, the welfare benchmarks to evaluate outcomes, and the strategic reasoning to handle imperfect competition.
Firms minimise costs by equating the marginal product per pound across inputs, then maximise profit by producing where marginal revenue equals marginal cost. In perfect competition this means P = MC and zero long-run profit; a monopolist restricts output, charges above MC, and creates deadweight loss. Price discrimination, bundling, and strategic interaction (game theory) extend the analysis to real-world markets with market power and interdependent decisions.
Production function
q = F(K, L). Maps inputs (capital, labour) to output.
Short run / long run
Short run: at least one input (usually capital) is fixed. Long run: all inputs are variable.
Marginal product (MP)
The additional output from one more unit of an input. MP_L = dq/dL.
Average product (AP)
Output per unit of input. AP_L = q/L.
Law of diminishing marginal returns
As more of a variable input is added to fixed inputs, MP eventually falls.
Isoquant
A curve showing all input combinations that produce the same output. The production-side analogue of an indifference curve.
Isocost line
All input combinations with the same total cost. Slope = -w/r (wage over rental rate of capital).
Marginal rate of technical substitution (MRTS)
The rate at which a firm can trade one input for another while holding output constant. MRTS = MP_L / MP_K.
Returns to scale
Constant: doubling inputs doubles output. Increasing: output more than doubles. Decreasing: output less than doubles.
Total cost (TC), average total cost (ATC), marginal cost (MC)
TC = fixed costs + variable costs. ATC = TC/q. MC = dTC/dq.
Long-run average total cost (LRATC)
The cost per unit when all inputs are variable. U-shaped due to economies then diseconomies of scale.
Perfect competition
Many firms, homogeneous goods, free entry/exit, price-taking.
Monopoly
Single seller with market power. Faces the entire market demand curve.
Marginal revenue (MR)
The additional revenue from selling one more unit. For a monopolist, MR < P.
Deadweight loss (DWL)
The reduction in total surplus from an inefficient allocation (e.g., monopoly restricting output).
Lerner Index
(P - MC) / P. Measures the degree of market power. Equals 1/|E_P| for a profit-maximising firm.
Price discrimination
Charging different prices to different consumers or for different units. Requires market power and prevention of resale.
Nash equilibrium
A set of strategies where no player can improve their payoff by unilaterally changing strategy.
Dominant strategy
A strategy that is best regardless of what others do.
Production function and inputs
q = F(K, L). In the short run, capital (K) is fixed; the firm chooses only how much labour to hire.
MP_L = dq/dL (marginal product of labour). AP_L = q/L (average product).
Law of diminishing marginal returns: holding K fixed, adding more L eventually lowers MP_L.
Cost minimisation
The firm chooses the input mix on the lowest isocost line tangent to the target isoquant.
At the optimum: MRTS = MP_L/MP_K = w/r (the ratio of input prices).
Equivalently: MP_L/w = MP_K/r (equal marginal product per pound across inputs).
Returns to scale
Constant: F(tK, tL) = tF(K, L). The LRATC curve is flat.
Increasing: F(tK, tL) > tF(K, L). Economies of scale; LRATC falls.
Decreasing: F(tK, tL) < tF(K, L). Diseconomies of scale; LRATC rises.
Technological change
Shifts the production function upward, increasing total factor productivity (A). More output from the same inputs, which reduces costs.
Cost curves
TC = FC + VC. In the short run, FC is fixed.
ATC = TC/q. MC = dTC/dq.
MC crosses ATC at ATC's minimum (if MC < ATC, ATC is falling; if MC > ATC, ATC is rising).
The LRATC curve is the envelope of short-run ATC curves and is typically U-shaped.
Perfect competition
Many firms, homogeneous goods, free entry/exit, perfect information.
Each firm faces a perfectly elastic (horizontal) demand curve at the market price.
Profit max: produce where P = MC.
Total profit: pi = (P - ATC) x Q. Positive profit if P > ATC; zero profit if P = ATC; loss if P < ATC.
Shutdown rule: if P < AVC in the short run, shut down (losses from operating exceed losses from just paying fixed costs).
Short-run supply curve = the MC curve above AVC.
Long run: free entry and exit drive economic profit to zero. Price settles at the minimum of LRATC.
Long-run industry supply
Constant-cost industry: horizontal long-run supply.
Increasing-cost industry: upward-sloping (input prices rise as the industry expands).
Decreasing-cost industry: downward-sloping (learning effects or economies of scale in input markets).
Monopoly
A single seller facing the market demand curve. Barriers to entry prevent competition.
MR < P because selling one more unit requires lowering the price on all units.
Profit max: MR = MC. Price is read off the demand curve above the MR = MC quantity.
Deadweight loss: the monopolist produces less than the competitive quantity, destroying surplus.
Lerner Index = (P - MC)/P = 1/|E_P|.
Government remedies for monopoly
Price regulation: set P = MC (first-best, but may require subsidies for natural monopolies) or P = ATC (second-best).
Antitrust: prevent collusion, mergers, predatory pricing.
Patents and licences: encourage innovation but create temporary monopolies.
Monopsony
A single buyer in an input market. Reduces input usage and pays below the competitive price, creating deadweight loss analogous to monopoly.
Price discrimination
First-degree (perfect): charge each buyer their willingness to pay. Captures all consumer surplus. No deadweight loss.
Second-degree: quantity discounts, bundling, coupons. Consumers self-select into pricing tiers.
Third-degree: segment the market by observable characteristics (age, location). Charge higher prices where demand is less elastic.
Requires market power and the ability to prevent resale.
Bundling and versioning
Bundling works best when consumers' valuations of the two goods are negatively correlated.
Versioning offers differentiated products (economy vs. premium) to extract surplus from different segments.
Incentive compatibility
Pricing schemes must ensure each consumer type selects the option designed for them, avoiding cannibalization and adverse selection.
Core framework
Players: the decision-makers (firms, consumers, governments).
Strategies: the complete plans of action each player can choose.
Payoffs: the outcomes each player receives, given everyone's strategies.
Normal-form (simultaneous) games
Represented as a payoff matrix.
Dominant strategy: best regardless of what the other player does.
Nash equilibrium: a pair of strategies where neither player can improve by unilaterally deviating.
A game can have zero, one, or multiple Nash equilibria.
Sequential (extensive-form) games
Represented as a decision tree (game tree).
Solved by backward induction: start at the final decision node and work backwards.
Can reveal first-mover advantages or credible threats.
Repeated games
When players interact repeatedly, cooperation can be sustained even when defection is the one-shot equilibrium.
Strategies like tit-for-tat and grim trigger punish defection in future rounds, making cooperation self-enforcing.
Cooperation is easier to sustain when the game is infinitely repeated (or the end date is uncertain) and the discount rate is low.
Applications
Oligopoly: firms set quantities (Cournot) or prices (Bertrand) strategically.
Prisoner's dilemma: mutual defection is the dominant-strategy equilibrium, even though mutual cooperation would make both players better off.
Entry deterrence: an incumbent may commit to aggressive pricing or capacity expansion to discourage entrants.
Bargaining and auctions: strategic offers and bidding behaviour.
Production
q = F(K, L). MP_L = dq/dL. AP_L = q/L.
Cost minimisation condition
MP_L / w = MP_K / r, equivalently MRTS = w/r
Cost curves
TC = FC + VC. ATC = TC/q. MC = dTC/dq.
Profit (perfect competition)
pi = (P - ATC) x Q. Produce where P = MC.
Profit (monopoly)
pi = (P - ATC) x Q. Produce where MR = MC. For linear demand P = a - bQ, MR = a - 2bQ.
Lerner Index
L = (P - MC) / P = 1 / |E_P|
Consumer surplus (linear demand)
CS = 0.5 x (choke price - market price) x Q
Producer surplus
PS = Revenue - Variable costs = area above MC curve, below price, up to Q.
Perfect competition is a reasonable model for commodity markets (wheat, crude oil) where products are near-identical and no single producer can influence the price. Monopoly analysis applies to utilities, patented pharmaceuticals, and tech platforms with strong network effects. Game theory explains phenomena like airline price wars, OPEC production decisions, and why competing mobile networks sometimes tacitly coordinate on pricing.
Students often confuse diminishing marginal returns (a short-run concept, one input fixed) with decreasing returns to scale (a long-run concept, all inputs changing). These are distinct ideas.
A widespread error is to think monopoly profit is guaranteed. A monopolist can still make losses if demand is low relative to costs.
Students sometimes assume that in a Nash equilibrium, both players are happy with the outcome. Nash equilibrium means neither can improve unilaterally; both may prefer a different outcome (as in the prisoner's dilemma).
A common mistake is to say first-degree price discrimination is inefficient. It is efficient (no deadweight loss) but inequitable (all surplus goes to the producer).
⚠️ Know the shutdown rule cold: in the short run, produce if P >= AVC; shut down if P < AVC. In the long run, exit if P < ATC.
⚠️ Be able to find the monopolist's profit-maximising output and price from MR = MC, and calculate the resulting deadweight loss.
⚠️ Lerner Index questions are common. Know that L = 1/|E_P| and be able to interpret the number.
⚠️ For game theory: be able to find Nash equilibria in a 2x2 payoff matrix, and solve a simple sequential game by backward induction.
⚠️ Price discrimination questions often ask you to explain the three types and say which produces no deadweight loss (first-degree).
True or false: In the long run under perfect competition, firms earn zero economic profit. (True.)
Fill in the blank: A monopolist maximises profit where _______ = MC. (MR / marginal revenue)
True or false: The short-run supply curve of a competitive firm is its MC curve above ATC. (False. It is the MC curve above AVC.)
Fill in the blank: In a Nash equilibrium, no player can improve their payoff by _______ changing their strategy. (unilaterally)
True or false: First-degree price discrimination eliminates deadweight loss. (True.)
Q: A competitive firm has TC = 100 + 2Q^2. The market price is 40. Find the profit-maximising output and the firm's profit.
A: MC = dTC/dQ = 4Q. Set P = MC: 40 = 4Q, so Q = 10. Profit = TR - TC = 40(10) - [100 + 2(100)] = 400 - 300 = 100.
Q: A monopolist faces demand P = 120 - 2Q and has MC = 20. Find the profit-maximising price and quantity, and the deadweight loss.
A: MR = 120 - 4Q. Set MR = MC: 120 - 4Q = 20, so Q_m = 25. P_m = 120 - 2(25) = 70. The competitive outcome would be P = MC = 20, Q_c = 50. DWL = 0.5 x (70 - 20) x (50 - 25) = 625.
Q: In the following payoff matrix, find the Nash equilibrium. Player 1 chooses rows, Player 2 columns. Payoffs are (P1, P2). Advertise/Don't: (10,10), (20,5) top row; (5,20), (15,15) bottom row.
A: If P2 advertises, P1 gets 10 (Advertise) vs. 5 (Don't): choose Advertise. If P2 doesn't, P1 gets 20 vs. 15: choose Advertise. Advertise is dominant for P1. By symmetry, Advertise is dominant for P2. Nash equilibrium: (Advertise, Advertise) with payoffs (10, 10). Both would prefer (Don't, Don't) = (15, 15), but neither can achieve it unilaterally.
Q: What type of price discrimination is a cinema offering student discounts?
A: Third-degree. The cinema segments the market by an observable characteristic (student status) and charges a lower price to the more elastic segment (students, who are more price-sensitive).
Production theory mirrors consumer theory: isoquants replace indifference curves, isocost lines replace budget lines, and MRTS = input price ratio replaces MRS = output price ratio. Perfect competition and monopoly are the polar cases; oligopoly (game theory) and monopolistic competition sit between them. The welfare analysis of deadweight loss ties directly back to consumer and producer surplus from the demand unit.
production function, marginal product, average product, diminishing returns, isoquant, isocost, MRTS, returns to scale, economies of scale, diseconomies of scale, total cost, average total cost, marginal cost, LRATC, perfect competition, price taker, profit maximisation, P = MC, MR = MC, shutdown rule, zero economic profit, long-run equilibrium, free entry, monopoly, market power, marginal revenue, deadweight loss, Lerner Index, natural monopoly, price regulation, antitrust, monopsony, price discrimination, first-degree, second-degree, third-degree, bundling, versioning, incentive compatibility, game theory, Nash equilibrium, dominant strategy, payoff matrix, backward induction, sequential game, repeated game, prisoner's dilemma, tit-for-tat, grim trigger, oligopoly, Cournot, Bertrand, entry deterrence