Theory of the Firm

We define the following cost concepts for a firm producing quantity $Q$:

• Total cost (TC): $TC(Q) = TFC + TVC(Q)$Where TFC = total fixed cost, TVC = total variable cost
• Average total cost (ATC): $ATC = \frac{TC}{Q} = AFC + AVC$
• Average fixed cost (AFC): $AFC = \frac{TFC}{Q}$
• Average variable cost (AVC): $AVC = \frac{TVC}{Q}$
• Marginal cost (MC): $MC = \frac{dTC}{dQ} = \frac{dTVC}{dQ}$

In the short run, at least one factor of production is fixed ( capital $K = \bar{K}$). The production function is $Q = f(L, \bar{K})$.

Law of diminishing marginal returns: as more of a variable factor (labour) is added to a fixed Factor (capital), the marginal product of labour eventually diminishes.

$MP_L = \frac{dQ}{dL}, \quad \frac{d^2 Q}{dL^2} < 0 \mathrm{ for } L > L^*$

Since $MC = \frac{dw}{dQ} = \frac{w}{MP_L}$ (where $w$ is the wage rate), diminishing marginal Returns ($MP_L$ falling) implies $MC$ is eventually rising.

In the long run, all factors are variable. The firm chooses the cost-minimising combination of Inputs:

$$\begin{aligned} \min_{L,K} \quad & wL + rK \\ \mathrm{s.t.} \quad & Q = f(L, K) \end{aligned}$$

The first-order condition gives the expansion path: $\frac{MP_L}{w} = \frac{MP_K}{r}$ (equating The marginal product per pound spent on each input).

We define economies of scale as the condition where long-run average cost (LRAC) falls as output Increases:

$\frac{d(LRAC)}{dQ} < 0$

Internal economies of scale:

Type	Mechanism
Technical	Indivisibilities, increased dimension, linking processes
Purchasing	Bulk-buying discounts
Financial	Lower interest rates for larger firms
Managerial	Specialisation of management functions
Risk-bearing	Diversification of product lines and markets

External economies of scale: cost advantages arising from the growth of the industry as a Whole (e.g., a skilled labour pool, specialised suppliers, knowledge spillovers in Silicon Valley).

Minimum efficient scale (MES): the lowest output at which LRAC is minimised. If MES is large Relative to market demand, the market can support only a few firms $\Rightarrow$ natural tendency Toward oligopoly or monopoly.

Diseconomies of scale: LRAC rises as output increases due to coordination difficulties, Communication problems, and alienation in very large organisations.

The long-run average cost curve is the envelope of all short-run average cost curves:

$LRAC(Q) = \min_{K} SRAC(Q; K)$

At each output level, the firm chooses the plant size (capital stock) that minimises average cost. The LRAC is U-shaped, reflecting economies of scale at low output and diseconomies at high Output.

• Total revenue: $TR = P \times Q$
• Average revenue: $AR = \frac{TR}{Q} = P$ (AR curve is the demand curve)
• Marginal revenue: $MR = \frac{dTR}{dQ}$

If demand is $P = a - bQ$Then:

$TR = P \times Q = aQ - bQ^2$

$MR = \frac{dTR}{dQ} = a - 2bQ$

Proposition: For a downward-sloping demand curve, $MR < AR$ (i.e., $MR < P$).

Proof. $MR = a - 2bQ < a - bQ = P$ for all $Q > 0$. The MR curve has the same intercept as the Demand curve but twice the slope. Intuition: to sell an additional unit, the firm must lower the Price on all units sold, not just the marginal unit. The revenue loss on inframarginal units means $MR < P$. $\blacksquare$

For a perfectly competitive firm (price taker), demand is perfectly elastic: $P$ is constant, so $MR = AR = P$.

The firm chooses output $Q$ to maximise economic profit:

$\pi(Q) = TR(Q) - TC(Q)$

First-order condition:

$\frac{d\pi}{dQ} = MR - MC = 0 \implies MR = MC$

Second-order condition (for maximum):

$\frac{d^2\pi}{dQ^2} = \frac{d(MR)}{dQ} - \frac{d(MC)}{dQ} < 0 \implies MC \mathrm{ cuts MR from below}$

Normal profit is the minimum profit necessary to keep a firm in the industry (included in total Cost as opportunity cost of capital). Economic profit (supernormal profit) is profit above Normal profit.

1. Many buyers and sellers (price takers)
2. Homogeneous (identical) product
3. Free entry and exit
4. Perfect information
5. Perfect factor mobility

The firm is a price taker: $P = MR = AR$. Profit maximisation: $MR = MC$.

$P = MC(Q_{SR})$

• If $P > ATC$: the firm earns supernormal profit ($\pi > 0$)
• If $P = ATC$: the firm earns normal profit ($\pi = 0$)
• If $AVC < P < ATC$: the firm makes a loss but continues producing (covers variable costs and contributes to fixed costs)
• If $P < AVC$: the firm shuts down in the short run ($\pi = -TFC$)

The firm”s short-run supply curve is the portion of the MC curve above AVC.

If firms earn supernormal profit, new firms enter. This shifts the market supply curve right, Reducing price until $P = ATC_{min}$. Conversely, if firms make losses, firms exit, supply shifts Left, price rises.

$P = MC = ATC_{min}$

Proposition: In long-run perfect competition, firms earn zero economic profit.

Proof. Free entry and exit drive price to the minimum of ATC. At $P = ATC_{min}$ $\pi = TR - TC = P \cdot Q - ATC \cdot Q = 0$. $\blacksquare$

• Allocative efficiency: $P = MC$ — the price consumers pay equals the marginal cost of production, so resources are allocated to produce the socially optimal quantity
• Productive efficiency: $P = ATC_{min}$ — production occurs at minimum cost per unit
• Dynamic efficiency: debatable — zero profit may reduce funds for R&D, but competitive pressure may spur innovation

1. Single seller (the firm is the industry)
2. No close substitutes
3. High barriers to entry
4. Price maker

• Natural monopoly: economies of scale make one large firm cheaper than many small ones
• Legal barriers: patents, licences, government-granted monopolies
• Strategic barriers: predatory pricing, limit pricing, excess capacity, brand loyalty
• Control of essential resources: e.g., De Beers’ control of diamond mines

The monopolist faces the market demand curve $P = a - bQ$.

$MR = a - 2bQ$

Profit maximisation: $MR = MC$.

$Q_m : a - 2bQ_m = MC(Q_m)$ $P_m = a - bQ_m$

Deadweight loss: The monopolist produces less and charges more than a competitive market.

$\mathrm{DWL} = \int_{Q_m}^{Q_c} [P(Q) - MC(Q)] \, dQ > 0$

Where $Q_c$ is the competitive output ($P = MC$).

Conditions for price discrimination:

1. The firm must have market power (downward-sloping demand)
2. The firm must be able to identify different consumer groups with different elasticities
3. The firm must be able to prevent arbitrage (resale between groups)

First-degree (perfect) price discrimination: the firm charges each consumer their maximum Willingness to pay. The firm captures all consumer surplus. Output increases to the competitive Level (MR = MC = P at each unit), so allocative efficiency is achieved, but all surplus goes to the Producer.

Second-degree price discrimination: the firm charges different prices for different quantities (e.g., bulk discounts, block pricing). Consumers self-select into different quantity brackets.

Third-degree price discrimination: the firm divides consumers into groups with different PEDs And charges a higher price to the less elastic group.

$\frac{P_1}{P_2} = \frac{1 - \frac{1}{|\mathrm{PED}_2|}}{1 - \frac{1}{|\mathrm{PED}_1|}}$

Group with lower $|\mathrm{PED}|$ pays higher price.

Example: Third-Degree Price Discrimination

A cinema charges £12 for adults and £6 for students. Adult demand: $P_A = 20 - Q_A$Student demand: $P_S = 14 - Q_S$, $MC = 2$.

Adult MR: $MR_A = 20 - 2Q_A$. Set $MR_A = MC$: $20 - 2Q_A = 2 \Rightarrow Q_A = 9$, $P_A = 11$. Student MR: $MR_S = 14 - 2Q_S$. Set $MR_S = MC$: $14 - 2Q_S = 2 \Rightarrow Q_S = 6$, $P_S = 8$.

Without discrimination (single price, aggregate demand): total demand $Q = Q_A + Q_S = (20 - P) + (14 - P) = 34 - 2P$So $P = 17 - Q/2$. $MR = 17 - Q$. Set $MR = 2 \Rightarrow Q = 15$, $P = 9.50$.

With discrimination: revenue = $11 \times 9 + 8 \times 6 = 99 + 48 = 147$. Without: $9.50 \times 15 = 142.50$. Discrimination increases profit.

Real-world examples of price discrimination:

• Airlines: Third-degree discrimination between business and leisure travellers. Business travellers have inelastic demand (flights are booked close to departure, often by employers). Leisure travellers book early and are price-sensitive. Airlines also use yield management (second-degree) — the same seat may sell for GBP 50 or GBP 500 depending on when it is booked, whether it is refundable, and whether baggage is included.
• Software and digital goods: Near-zero marginal cost makes price discrimination extremely profitable. Microsoft offers Windows in Home, Pro, and Enterprise editions at very different prices, despite the marginal cost of an additional download being negligible. Student discounts exploit differences in PED.
• Uber surge pricing: Second-degree discrimination based on real-time demand elasticity. When demand spikes (rain, events), the algorithm raises prices — consumers with inelastic demand still ride, while price-sensitive consumers wait or use alternatives.

Evaluation of price discrimination: The welfare effects depend on the type. First-degree Discrimination eliminates consumer surplus entirely but achieves allocative efficiency (output Equals the competitive level). Third-degree discrimination may increase total output compared to Single-price monopoly, but it also redistributes surplus from consumers with inelastic demand to the Firm. A strong evaluation point: price discrimination can be pro-competitive if it enables a Firm to enter a market that would otherwise be unprofitable (e.g., cross-subsidy between market Segments). However, it raises equity concerns — poorer consumers ( more price-elastic) may Benefit from lower prices, while less elastic groups face higher prices.

#### Natural Monopoly

A natural monopoly exists where LRAC falls continuously over the relevant output range (strong Economies of scale). One firm can supply the entire market at lower cost than two or more firms.

$LRAC(Q_{total}) < \sum_{i} LRAC(Q_i) \quad \mathrm{for any partition } Q_{total} = \sum Q_i$

Examples: water supply, electricity distribution, railway networks.

Problem: if a natural monopoly charges $P = MC$ (allocative efficiency), it makes a loss because $MC \lt AC$. Regulatory options: average cost pricing ($P = AC$), price cap regulation, public Ownership.

**Real-world example: UK water industry.** Thames Water and other regional water companies are Natural monopolies covering specific geographic areas — it would be deeply inefficient to run Multiple pipe networks through the same streets. Ofwat regulates prices using the RPI-X formula (prices can rise by RPI inflation minus an efficiency factor X). However, the 2023-2024 crisis at Thames Water (debt of GBP 14 billion, sewage discharge failures) illustrates the limits of Regulatory oversight when firms are privately owned but provide essential public services.

Real-world example: Tech monopolies. Google controls approximately 92% of the UK search engine Market, and Apple’s App Store charges a 30% commission on digital sales — both cases where network Effects create enormous barriers to entry. The European Commission’s Digital Markets Act (2024) Designates such firms as “gatekeepers” and mandates interoperability with third-party app stores. This raises the evaluation point: does regulation of tech monopolies promote competition, or does it Reduce the incentive to invest in platform quality?

Evaluation of monopoly: On balance, monopolies are most harmful when they arise from anti-competitive conduct rather than superior efficiency. A monopoly achieved through genuine Innovation (e.g., a pharmaceutical patent) may generate dynamic benefits that outweigh static Deadweight loss. The critical question for exam answers is always: does this monopoly exist because It is efficient, or because it has successfully blocked competition?

1. Many firms
2. Differentiated product (branding, quality, location)
3. Free entry and exit
4. Some market power (due to product differentiation)

Short run: like monopoly — the firm faces a downward-sloping demand curve, sets $MR = MC$And May earn supernormal profit.

Long run: free entry eliminates supernormal profit, but $P > MC$ and $P > AC_{min}$.

$\pi = 0 \implies P = AC$ $MR = MC \implies P > MC \mathrm{ (since } MR < P\mathrm{)}$

Excess capacity: the firm produces at an output below the output that minimises AC. The gap Between actual output and the minimum efficient scale output is excess capacity — a measure of Inefficiency.

$Q_{MC} < Q_{MES} \quad \mathrm{where } Q_{MES} \mathrm{ minimises AC}$

Evaluation of monopolistic competition: While the model predicts excess capacity and allocative Inefficiency ($P > MC$), it has important strengths that are often underemphasised in exam answers. Product differentiation generates consumer choice and variety — the value of having multiple Restaurants, coffee shops, or clothing brands may exceed the deadweight loss from pricing above Marginal cost. Additionally, the competitive pressure of free entry drives firms to innovate in Product quality and branding (dynamic efficiency). The advertising expenditure that characterises Monopolistic competition can be seen as wasteful (persuasive advertising shifts demand rather than Informs), but it can also be informative (reducing search costs for consumers). A balanced exam Answer should conclude that monopolistic competition is a realistic model that captures the Trade-off between efficiency and variety.

1. Few firms (interdependence is key)
2. High barriers to entry
3. Products may be homogeneous or differentiated
4. Firms are aware of their mutual dependence

Two firms (A and B) each choose whether to charge a high price or a low price.

	B: High Price	B: Low Price
A: High Price	A: £10m, B: £10m	A: £2m, B: £12m
A: Low Price	A: £12m, B: £2m	A: £5m, B: £5m

Nash equilibrium: each player’s strategy is optimal given the other player’s strategy. Firm A’s Dominant strategy: Low Price (regardless of B’s choice, A is better off). Same for B. Nash Equilibrium: (Low, Low) with payoffs (5, 5).

Pareto optimal outcome: (High, High) with payoffs (10, 10) — no other outcome makes both players Better off. But neither firm has an incentive to choose High Price unilaterally.

Proposition: The Nash equilibrium of the prisoner’s dilemma is not Pareto optimal.

Proof. At (Low, Low), if both firms switch to High Price, both are better off (£10m > £5m). But Each firm individually cannot improve by deviating from Low Price (given the other plays Low). Therefore (Low, Low) is Nash but not Pareto optimal. $\blacksquare$

Implications: individual rationality leads to collective suboptimality — explains why firms have Difficulty sustaining collusion without enforcement mechanisms.

The static prisoner’s dilemma predicts that collusion always fails. However, in the real world, Oligopolists interact repeatedly over many years. In an infinitely repeated game (or one with an Uncertain end date), the threat of future punishment can sustain cooperation.

Consider the discount factor $\delta \in (0, 1)$Which represents how much firms value future Profits relative to current profits. If both firms play tit-for-tat (cooperate in the first Round, then copy the opponent’s previous action), collusion is sustainable if:

$(\mathrm{Gain from cheating today}) \lt (\mathrm{Loss from future punishment})$

More : if firms are sufficiently patient ($\delta$ is close to 1), the long-run gains From cooperation outweigh the short-run temptation to cheat. This explains why OPEC has maintained Periods of effective output restriction despite the incentive to cheat.

Real-world application: supermarket pricing in the UK. Tesco, Sainsbury’s, Asda, and Morrisons Operate in a tight oligopoly with a combined market share of approximately 68%. The rise of Aldi and Lidl (which grew from approximately 5% to over 17% market share between 2010 and 2024) has Intensified competitive pressure. The incumbent supermarkets must balance cooperation (avoiding a Destructive price war that destroys margins for all) against competition (matching Aldi’s lower Prices to retain customers). This is a repeated game where the “punishment” for not matching prices Is loss of market share to discounters.

#### Kinked Demand Curve Model (Sweezy, 1939)

Assumptions:

• If a firm raises its price, competitors don’t follow $\Rightarrow$ demand is elastic above current price (the firm loses many customers)
• If a firm lowers its price, competitors do follow $\Rightarrow$ demand is inelastic below current price (the firm gains few customers)

This creates a kink in the demand curve at the current price, and a discontinuity in the MR curve. Result: prices tend to be rigid (sticky) even when costs change, as long as the MC curve passes Through the gap in the MR curve.

Limitation: the model explains price rigidity but not how the initial price is determined.

Evaluation of the kinked demand curve: While empirically relevant (prices in oligopolistic Markets do tend to be sticky — e.g., the price of a pint of milk changed very little between 2015 And 2022 despite cost fluctuations), the model has been largely superseded by game-theoretic Approaches. A strong evaluation point for exams: the kinked demand curve assumes asymmetric Reactions (competitors follow price cuts but not price rises), but in reality firms may also follow Price rises if costs have increased across the industry (e.g., energy cost increases post-2021). This makes the model overly rigid in its assumptions.

Cartel: a group of firms acting together as a monopoly to restrict output and raise prices.

Why cartels are unstable: each member has an incentive to secretly increase output above the Agreed quota (cheating), because the cartel price exceeds each firm’s marginal cost. The more Members cheat, the lower the price falls, and the cartel collapses.

OPEC is a well-known example: member countries frequently exceed production quotas, causing oil Prices to fluctuate.

Real-world example: the UK energy market. The “Big Six” energy suppliers (British Gas, EDF, E.ON, Npower, Scottish Power, SSE — now reduced through mergers to the “Big Five”) operated as an Effective oligopoly in UK residential energy supply for decades. Despite apparent competition, price Changes were highly correlated — when one firm raised prices, others followed within weeks (tacit Collusion rather than explicit agreement). The entry of smaller challenger suppliers (Octopus Energy, Bulb before its collapse) increased contestability. However, the 2021-2022 energy crisis Exposed the vulnerability of smaller firms — 29 UK energy suppliers collapsed between September 2021 And November 2022 because they could not hedge against the wholesale gas price spike. This Illustrates a critical evaluation point: barriers to entry in oligopoly are not always obvious — The need for working capital and hedging capacity acts as a significant barrier even where Regulation nominally encourages entry.

Evaluation of collusion: Tacit collusion is extremely difficult to prove legally because firms Independently arrive at similar pricing strategies without any formal agreement. The Competition and Markets Authority (CMA) can prosecute explicit cartel agreements under the Competition Act 1998 (fines of up to 10% of global turnover) and the Enterprise Act 2002 (criminal penalties including Imprisonment for individuals). However, the effectiveness of competition policy depends on the Regulator’s resources and information — asymmetric information between the CMA and firms is a Persistent problem.

A market is contestable if there are no barriers to entry or exit. Even with only one firm (monopoly), the threat of entry constrains the incumbent’s behaviour.

Hit-and-run entry: a new firm enters, captures profit, and exits if the incumbent responds by Lowering prices. For this to work, there must be no sunk costs.

Implication: in a perfectly contestable market, even a monopoly will charge $P = AC$ (zero Economic profit), because any supernormal profit would attract entry.

Conditions for contestability:

• No sunk costs (all costs are recoverable on exit)
• No legal barriers (licences, patents)
• Low consumer switching costs
• Access to the same technology as the incumbent

Evaluation of contestable market theory: The theory provides a powerful critique of the Traditional structure-conduct-performance paradigm — it suggests that market conduct (and threat Of entry) matters more than the number of firms. However, the assumption of zero sunk costs is Extremely restrictive. In practice, most industries involve significant sunk costs: a new airline Needs aircraft, airport slots, and brand recognition; a new energy supplier needs regulatory Approval and IT systems. The theory is therefore most applicable to markets with relatively low Capital requirements, such as taxi services (before Uber, local taxi licensing created barriers; Uber’s platform model dramatically increased contestability by reducing sunk costs for drivers) and online retail.

Example: The UK bus market after deregulation (1985 Transport Act) was intended to be highly Contestable — new operators could enter any route. In practice, the incumbent operator often had Advantages (depots, driver knowledge, existing contracts), and many routes remained de facto Monopolies. This illustrates the gap between theoretical contestability and real-world outcomes.

## 5. Comparative Table of Market Structures

Feature	Perfect Competition	Monopoly	Monopolistic Competition	Oligopoly
Number of firms	Very many	One	Many	Few
Product	Homogeneous	Unique	Differentiated	Homo./differentiated
Barriers to entry	None	Very high	Low	High
Price	Taker	Maker	Maker	Maker (interdependent)
Demand curve	Perfectly elastic ($P$)	Market demand	Downward-sloping	Downward-sloping (kinked?)
Equilibrium	$P = MC = AC_{min}$	MR = MC$$P > MC	P = AC$$P > MC	MR = MC$$P > MC
LR profit	Zero (normal)	Supernormal	Zero (normal)	Possibly supernormal
Allocative efficiency	Yes ($P = MC$)	No ($P > MC$)	No ($P > MC$)	No ($P > MC$)
Productive efficiency	Yes ($P = AC_{min}$)	No	No (excess capacity)	No
DWL	None	Yes	Yes	Yes
Examples	Agricultural commodities	National rail, water	Restaurants, hairdressers	Supermarkets, banking, oil

## 6. Critical Evaluation

• Provides a systematic way to analyse different market types
• Predicts efficiency outcomes based on market structure
• Useful for competition policy (identifying markets requiring regulation)

• Real-world markets rarely fit neatly into one category
• The theory focuses on static efficiency — dynamic efficiency (innovation, R&D) may be higher under monopoly (Schumpeterian hypothesis)
• Contestable market theory challenges the structural approach — behaviour matters more than structure
• Transaction cost economics (Coase, Williamson) suggests firm boundaries are determined by the relative costs of market transactions vs internal organisation

A critical evaluation theme across all exam boards is the trade-off between static efficiency (productive and allocative efficiency at a point in time) and dynamic efficiency (improvements In technology, products, and processes over time).

The Schumpeterian hypothesis argues that large firms with market power are better positioned to Innovate because:

• Supernormal profits fund R&D investment
• Large firms can spread the risk of innovation across a diversified product portfolio
• Patents (which create temporary monopoly power) are specifically designed to reward innovation

Counter-arguments:

• Competitive markets may innovate more because firms must innovate to survive (the “innovation stimulus” of competition)
• Monopolists may become complacent — X-inefficiency (Leibenstein, 1966) arises when firms lack competitive pressure to minimise costs
• Empirical evidence is mixed: small startups are responsible for many disruptive innovations (e.g., Dyson, Deliveroo), but large firms dominate R&D spending (Amazon invested USD 73 billion in R&D in 2023)

Exam technique: When evaluating market structures, always consider both static and dynamic Efficiency. A strong conclusion might be: “Perfect competition maximises static efficiency but may Underprovide dynamic efficiency; monopoly does the reverse. The optimal market structure depends on Whether the industry is characterised by rapid technological change (where dynamic efficiency is Paramount) or stable technology (where static efficiency dominates).”

Traditional theory of the firm assumes profit maximisation. Behavioural economics challenges this:

• Satisficing (Simon, 1955): managers may not maximise profit but instead aim for a “satisfactory” level of performance. This is particularly relevant in oligopoly where objectives may include market share, revenue growth, or managerial prestige.
• Principal-agent problem: in large corporations, shareholders (principals) cannot perfectly monitor managers (agents). Managers may pursue their own objectives (empire-building, higher salaries) rather than maximising shareholder profit. This is a form of market failure within the firm itself.
• Loss aversion: firms may react asymmetrically to price changes — cutting prices reluctantly but matching competitors’ cuts quickly (consistent with the kinked demand curve, but explained by psychology rather than game theory).

## 7. Problem Set

Problem 1. A firm has total cost $TC = 100 + 20Q - 5Q^2 + Q^3/3$. Find (a) the output at which Diminishing marginal returns set in, (b) the output at which average variable cost is minimised, (c) The output at which average total cost is minimised.

Hint

(a) $MC = 20 - 10Q + Q^2$. Diminishing returns: $MC$ starts rising, i.e., $MC' = -10 + 2Q = 0 \Rightarrow Q = 5$. (b) $AVC = 20 - 5Q + Q^2/3$. Minimise: $AVC' = -5 + 2Q/3 = 0 \Rightarrow Q = 7.5$. (c) $ATC = 100/Q + 20 - 5Q + Q^2/3$. $ATC' = -100/Q^2 - 5 + 2Q/3 = 0$. Solve numerically: $Q \approx 9.25$.

Problem 2. A perfectly competitive industry has market demand $Q_D = 500 - 10P$ and each firm Has cost function $TC = 50 + 2Q + Q^2$. In the long run, how many firms will there be? What is the Market price?

Hint

LR equilibrium: $P = MC = AC_{min}$. $MC = 2 + 2Q$$AC = 50/Q + 2 + Q$. Set $MC = AC$: $2 + 2Q = 50/Q + 2 + Q \Rightarrow Q = 50/Q \Rightarrow Q = \sqrt{50} \approx 7.07$. $AC_{min} = 50/7.07 + 2 + 7.07 \approx 16.14$. $P^* = 16.14$. Market demand: $Q_D = 500 - 161.4 = 338.6$. Number of firms: $338.6 / 7.07 \approx 47.9 \approx 48$ firms.

Problem 3. A monopolist faces demand $P = 100 - 2Q$ and has total cost $TC = 50 + 10Q + Q^2$. Find the profit-maximising price and quantity. Calculate the deadweight loss compared with the Competitive outcome.

Hint

$MR = 100 - 4Q$. $MC = 10 + 2Q$. Set $MR = MC$: $100 - 4Q = 10 + 2Q \Rightarrow Q_m = 15$$P_m = 70$. Profit $= 70 \times 15 - (50 + 150 + 225) = 1050 - 425 = 625$. Competitive: $P = MC \Rightarrow 100 - 2Q = 10 + 2Q \Rightarrow Q_c = 22.5$$P_c = 55$. DWL $= \frac{1}{2}(70 - 55)(22.5 - 15) = \frac{1}{2}(15)(7.5) = 56.25$.

Problem 4. A monopolist can identify two groups of consumers. Group 1 has demand $P_1 = 24 - Q_1$ and Group 2 has demand $P_2 = 16 - Q_2$. Total cost is $TC = 40 + 2(Q_1 + Q_2)$. Find the profit-maximising price and quantity for each group under third-degree price Discrimination. Compare total profit with the single-price monopoly outcome.

Hint

$MR_1 = 24 - 2Q_1 = 2 \Rightarrow Q_1 = 11$$P_1 = 13$. $MR_2 = 16 - 2Q_2 = 2 \Rightarrow Q_2 = 7$$P_2 = 9$. Profit $= 13(11) + 9(7) - 40 - 2(18) = 143 + 63 - 40 - 36 = 130$. Without discrimination: aggregate $P = 24 - Q_1 = 16 - Q_2$ for $P \leq 16$So $Q = Q_1 + Q_2 = (24 - P) + (16 - P) = 40 - 2P$$P = 20 - Q/2$. $MR = 20 - Q = 2 \Rightarrow Q = 18$$P = 11$. Profit $= 11(18) - 40 - 36 = 198 - 76 = 122$. Discrimination yields higher profit (£130 vs £122).

Problem 5. In a monopolistically competitive market, each firm has demand $P = 40 - Q$ and cost $TC = 100 + 10Q + Q^2$. Find the long-run equilibrium price, quantity, and the excess capacity.

Hint

SR: $MR = 40 - 2Q = MC = 10 + 2Q \Rightarrow 3Q = 30 \Rightarrow Q = 10$$P = 30$. Profit $= 300 - (100 + 100 + 100) = 0$ (already in LR equilibrium). $AC_{min}$: $AC = 100/Q + 10 + Q$. $AC' = -100/Q^2 + 1 = 0 \Rightarrow Q_{MES} = 10$. Since $Q = Q_{MES}$There is no excess capacity in this specific case. For excess capacity to arise, the demand curve must be tangent to AC at a point where $Q < Q_{MES}$.

Problem 6. Two duopolists, Firm A and Firm B, face market demand $P = 100 - Q_A - Q_B$. Both Have $MC = 10$. Assuming Cournot competition (each firm chooses output taking the other’s output as Given), find the Nash equilibrium outputs, price, and profit for each firm.

Hint

Firm A's reaction function: $\pi_A = (100 - Q_A - Q_B)Q_A - 10Q_A$. FOC: $100 - 2Q_A - Q_B - 10 = 0 \Rightarrow Q_A = 45 - Q_B/2$. By symmetry: $Q_B = 45 - Q_A/2$. Solving: $Q_A = 45 - (45 - Q_A/2)/2 = 45 - 22.5 + Q_A/4 \Rightarrow 3Q_A/4 = 22.5 \Rightarrow Q_A = 30$$Q_B = 30$. $P = 40$. $\pi_A = \pi_B = 30 \times 30 = 900$. Compare with collusion: $Q = 45$$P = 55$Profit each = $55 \times 22.5 - 10 \times 22.5 = 1012.5$.

Problem 7. A natural monopoly has total cost $TC = 200 + 20Q$ and faces demand $P = 100 - Q$. (a) Find the profit-maximising outcome. (b) Find the allocatively efficient outcome. (c) Find the Outcome under average cost pricing. (d) Evaluate the trade-offs.

Hint

(a) Monopoly: $MR = 100 - 2Q = MC = 20 \Rightarrow Q_m = 40$$P_m = 60$. Profit $= 2400 - 1000 = 1400$. (b) Allocative efficiency: $P = MC \Rightarrow 100 - Q = 20 \Rightarrow Q = 80$$P = 20$. Loss $= 1600 - 1800 = -200$ (subsidy needed). (c) AC pricing: $P = AC \Rightarrow 100 - Q = 200/Q + 20 \Rightarrow Q(80 - Q) = 200 \Rightarrow 80Q - Q^2 - 200 = 0 \Rightarrow Q \approx 2.56$ or $Q \approx 77.4$. Valid: $Q \approx 77.4$$P \approx 22.6$. Zero profit. (d) Trade-off: monopoly maximises profit but has DWL; MC pricing is efficient but requires subsidy; AC pricing is a compromise.

Problem 8. “Monopolies are always harmful to consumer welfare.” Evaluate this statement with Reference to (a) natural monopolies, (b) innovation incentives, and (c) price discrimination.

Hint

(a) Natural monopolies: LRAC falls over relevant range, so a competitive market with many small firms would have *higher* costs. Regulation (price caps) can capture some monopoly benefits. (b) Schumpeterian argument: monopoly profits fund R&D; patent monopolies incentivise innovation. Counter: monopolies may also be complacent. (c) First-degree price discrimination increases output to competitive level (allocative efficiency), but all surplus goes to producer. Third-degree discrimination increases total output compared to single-price monopoly.

Problem 9. Explain why the kinked demand curve model predicts price rigidity but cannot explain How the initial price is determined. How does game theory provide a more complete analysis of Oligopoly pricing?

Hint

The kinked demand curve takes the current price as given and analyses reactions to price changes. It doesn't explain the level of that initial price. Game theory provides a more complete framework: the initial price may be set by historical factors, collusion, or a focal point. Repeated games show that collusion can be sustained as a Nash equilibrium if the discount factor is high enough (the threat of future punishment deters cheating).

Problem 10. “The theory of perfect competition is irrelevant because no real market satisfies All its assumptions.” Discuss this criticism.

Hint

For: perfect competition is an idealised model — no market has infinitely many firms, perfect information, or zero transaction costs. Against: the model provides a benchmark for efficiency, helps identify sources of market failure, and many markets approximate perfect competition (agricultural commodities, foreign exchange). The value of a model is not realism of assumptions but predictive power and explanatory insight (Friedman's methodology).

Problem 11. A firm in monopolistic competition spends £50,000 on advertising. This shifts demand From $P = 50 - Q$ to $P = 60 - Q$ without changing costs ($TC = 200 + 10Q + Q^2$). Is advertising Profitable? What are the welfare implications?

Hint

Without advertising: $MR = 50 - 2Q = 10 + 2Q \Rightarrow Q = 10$$P = 40$. Profit $= 400 - 400 = 0$ (LR equilibrium). With advertising: $MR = 60 - 2Q = 10 + 2Q \Rightarrow Q = 12.5$$P = 47.5$. Profit $= 593.75 - 456.25 - 50 = 87.5$. Advertising is profitable. Welfare: output increases from 10 to 12.5 (closer to social optimum), but consumers face higher price. The advertising itself may be a wasteful arms race (if all firms advertise, demand shifts back).

Problem 12. Evaluate the argument that “the best policy towards monopoly is to break it up into Many small competing firms.” Under what circumstances might this policy be counterproductive?

Hint

Counterproductive for natural monopolies: breaking up would destroy economies of scale, raising costs for consumers. Also problematic where monopoly arises from innovation (patents): breaking up reduces R&D incentives. May be appropriate where monopoly stems from anti-competitive behaviour (mergers, predatory pricing) rather than natural cost advantages. Consider contestable markets as an alternative: maintain single firm but eliminate entry barriers.

Problem 13. A tech platform operates as a two-sided market: it connects app developers with Smartphone users. The platform charges developers a commission of 30% on each sale but charges users GBP 0 to download the app. Explain this pricing strategy using the concept of cross-subsidy. Why Might regulators be concerned about this business model?

Hint

This is an example of third-degree price discrimination combined with **network effects**. Users have highly elastic demand (many free alternatives), so the platform charges them nothing to maximise the user base. Developers have inelastic demand (they need access to the platform's users), so the platform extracts surplus via commissions. The cross-subsidy means users are subsidised by developers. Regulators (e.g., the European Commission under the Digital Markets Act) are concerned because: (a) the 30% commission may be excessive (monopoly pricing), (b) developers cannot pass the full cost to consumers, (c) the platform's control over app distribution creates barriers to entry for competing platforms. Evaluation: the commission also funds platform security, app review, and infrastructure — it is not pure surplus extraction.

Problem 14. Two firms in a duopoly can choose to invest in R&D or not. The payoffs (profit in Millions of GBP) are shown below. Identify the Nash equilibrium and discuss why the outcome may Differ in a repeated game.

	B: Invest in R&D	B: No R&D
A: Invest	A: 8, B: 8	A: 15, B: 2
A: No R&D	A: 2, B: 15	A: 10, B: 10

Hint

Nash equilibrium: (Invest, Invest) — this is the **only** Nash equilibrium. If A invests, B's best response is to invest (8 > 2). If B invests, A's best response is to invest (8 > 2). (No R&D, No R&D) is NOT a Nash equilibrium because either firm can deviate to Invest and earn 15. This is an inverted prisoner's dilemma — cooperation (both investing) is also the dominant strategy, unlike the pricing prisoner's dilemma where defection is dominant. In a repeated game, the outcome is even more likely to be (Invest, Invest) because firms that fail to invest will lose market share permanently. Evaluation: in practice, firms may underinvest in R&D if they cannot appropriate the full returns (knowledge spillovers), which is a justification for government R&D subsidies.

Problem 15. The UK supermarket industry has seen significant merger activity. The CMA blocked The proposed merger between Sainsbury’s and Asda in 2019. Using game theory and the concept of Contestable markets, evaluate the CMA’s decision.

Hint

The CMA's rationale: the merger would have reduced the number of "big four" supermarkets from four to three, reducing competitive pressure and potentially raising prices. The Herfindahl-Hirschman Index (HHI) would have increased significantly. Game theory supports this: fewer firms means the temptation to collude (tacitly) increases, and monitoring cheating becomes easier. Contestable market theory provides a counter-argument: the threat of entry from Aldi, Lidl, and online grocery (Ocado, Amazon Fresh) constrains pricing behaviour even with fewer incumbents. The CMA ultimately concluded that Aldi and Lidl were not yet close enough substitutes (different product ranges, store locations) to fully offset the loss of competition. Evaluation: the CMA's decision may need revisiting as Aldi and Lidl continue to expand their product ranges and market share.

Problem 16. A monopolist has the option to engage in limit pricing (charging a price below the Short-run profit-maximising level to deter entry). The firm faces potential entry from a competitor With identical costs. Using the concept of contestable markets, analyse under what conditions limit Pricing is a rational strategy. Why might limit pricing fail in practice?

Hint

Limit pricing is rational when: (a) the long-run gain from maintaining monopoly power (higher future profits) exceeds the short-run sacrifice (lower current profits from charging below the monopoly price), (b) the incumbent has a cost advantage or better information than the potential entrant (asymmetric information about demand or costs), (c) there are significant sunk costs for the entrant, making hit-and-run entry difficult. Limit pricing may fail because: (a) the entrant may interpret the low price as a sign of weak demand rather than a threat, (b) the incumbent cannot credibly commit to maintaining the low price if the entrant does enter (the incumbent would rationally raise prices after the entrant's sunk costs are sunk), (c) predatory pricing (limit pricing pushed below average variable cost) is illegal under UK and EU competition law. Evaluation: contestable market theory suggests that if there are no sunk costs, the mere *threat* of entry achieves the same outcome as limit pricing without the incumbent needing to actually lower its price.

• Market Failure covers externalities and government intervention that constrain firm behaviour and market outcomes.
• Labour Markets applies the monopsony and minimum wage models that extend the theory of the firm to factor markets.
• The Financial Sector explains how interest rates and monetary policy affect firms’ cost of borrowing and investment decisions.
• Demand, Supply and Equilibrium provides the demand and cost foundations used throughout the theory of the firm analysis.