Theory of the Firm (HL Extension)

Model Answer (a):

Calculations:

• TR (Total Revenue): TR = P × Q
• MR (Marginal Revenue): MR = ΔTR / ΔQ
• MC (Marginal Cost): MC = ΔTC / ΔQ
• Profit: Profit = TR - TC

Completed table:

Q	P ($)	TR ($)	MR ($)	TC ($)	MC ($)	Profit ($)
0	—	0	—	100	—	-100
1	120	120	120	150	50	-30
2	110	220	100	185	35	35
3	100	300	80	210	25	90
4	90	360	60	230	20	130
5	80	400	40	260	30	140
6	70	420	20	310	50	110
7	60	420	0	380	70	40

Example calculation for Q=3: TR = 100 × 3 = $300; MR = (300-220)/(3-2) = $80; MC = (210-185)/(3-2) = $25; Profit = 300 - 210 = $90.

Model Answer (b):

Profit-maximising output and price: The profit-maximising output is Q=5 units at a price of P=$80 per unit, generating a profit of $140.

Reasoning using MC=MR rule: The profit-maximisation condition is where marginal revenue equals marginal cost (MR = MC). Looking at the data:

• At Q=4: MR=$60 and MC=$20. Since MR > MC, the firm should continue producing (each unit adds more to revenue than to cost).
• At Q=5: MR=$40 and MC=$30. MR is still greater than MC, so profit increases. This is the closest point to MR=MC.
• At Q=6: MR=$20 and MC=$50. Now MC > MR, producing the 6th unit reduces profit (cost exceeds revenue benefit).

Price determination: At Q=5, the monopolist reads the price from the demand curve (AR): P = $80. The monopolist is a price maker and charges the maximum price consumers will pay at this output quantity.

Model Answer (c):

Abnormal (Economic) Profit: Abnormal profit is revenue above the level needed to cover all costs, including opportunity costs. It is the profit earned in excess of normal profit. In the monopoly example, the firm earns $140 profit, which exceeds the normal profit (zero economic profit that covers opportunity costs). This abnormal profit reflects the monopoly's market power and ability to restrict output, raising price above marginal cost.

Normal Profit: Normal profit is the minimum profit required to keep factors of production in their current use. It equals the opportunity cost of capital and entrepreneurship. A firm earning normal profit covers all explicit costs (wages, materials, rent) and implicit costs (opportunity cost of owner's time and invested capital), but earns zero economic profit above that. Normal profit reflects competitive returns to risk and effort.

Distinction: Abnormal profit is any return above normal profit. In perfect competition, long-run equilibrium eliminates abnormal profit, leaving only normal profit. In monopoly, barriers to entry allow abnormal profit to persist in the long run, as the monopoly sustains market power. The $140 profit in this case is abnormal because it exceeds the competitive benchmark of normal profit.

Model Answer (d):

Barriers to entry in monopoly: A monopoly sustains abnormal profit in the long run by erecting or maintaining barriers to entry, preventing competitors from entering the market. These barriers include:

• Natural monopoly: Economies of scale are so large that one firm can supply the entire market at lower cost than multiple firms (e.g. utilities, railways).
• Legal barriers: Patents, copyrights, and exclusive licences granted by the government protect the monopoly firm from competition (e.g. pharmaceuticals, broadcast licenses).
• Control of essential resources: The monopoly firm owns or controls key raw materials, technology, or infrastructure (e.g. rare minerals, network effects).
• Brand loyalty and switching costs: High switching costs (retraining, lock-in contracts) and strong brand loyalty make entry unattractive to rivals.

Result: With barriers in place, new firms cannot enter despite abnormal profit. The monopoly faces no competitive pressure to reduce price or increase output, allowing it to maintain the profit-maximising MR=MC output and charge the monopoly price. Abnormal profit persists indefinitely, unlike in perfect competition where entry would eliminate excess profit.

Model Answer (a):

Calculations:

• MC (Marginal Cost): MC = ΔTC / ΔQ
• ATC (Average Total Cost): ATC = TC / Q
• Profit: Profit = (P × Q) - TC = TR - TC, where P = $8

Completed table:

Q	TC ($)	MC ($)	ATC ($)	TR ($)	Profit ($)
0	20	—	—	0	-20
1	26	6	26	8	-18
2	30	4	15	16	-14
3	36	6	12	24	-12
4	46	10	11.50	32	-14
5	62	16	12.40	40	-22
6	84	22	14	48	-36

Profit-maximising output: The firm maximises profit (minimises loss) at Q=3, where profit = -$12. This is where MC is closest to price. At Q=3, MC=$6, which is just below P=$8. For Q=4, MC=$10 exceeds price, so producing further reduces profit. The firm is in loss (price below ATC) but continues producing because P > min(AVC), so it covers variable costs.

Model Answer (b):

Why perfectly competitive firms are price takers:

• Homogeneous product: All firms produce identical products. Consumers see no difference between sellers.
• Many sellers: Each firm is very small relative to the total market. No single firm's output significantly affects market supply or price.
• Perfect information: Buyers know prices and quality everywhere. A firm raising price above the market rate loses all customers to competitors.
• Free entry/exit: No barriers prevent new entrants. Excess profits attract rivals, increasing supply and lowering price back to competitive levels.

As a result, the individual firm faces a perfectly elastic (horizontal) demand curve at the market price. It can sell all it wishes at market price P, but cannot raise price without losing customers to rivals or lower price (reducing revenue). The firm accepts the market price as given—it is a price taker.

Model Answer (c):

Long-run adjustment to normal profit in perfect competition:

Short-run abnormal profit: If market price is high relative to costs, existing firms earn abnormal profit. The market attracts new entrants because profit exceeds the opportunity cost of capital.

Entry process: New firms enter the industry, increasing market supply. The increase in supply shifts the market supply curve rightward, lowering the market price. This process continues as long as abnormal profit exists.

Long-run equilibrium: Entry stops when price falls to equal minimum long-run average total cost (LRATC). At this point, P = LRAC, and firms earn exactly normal profit (zero economic profit).

If abnormal loss: Conversely, if price falls below ATC, firms incur losses. Existing firms exit the industry, reducing supply and raising price until it returns to equal minimum LRAC and normal profit is restored.

Outcome: Only in the long run, when P = minimum LRAC, do firms earn normal profit. This reflects the long-run nature of free entry/exit: it eliminates both abnormal profits and losses, allocating resources efficiently. Individual firm profit maximises at P = MC (short-run condition), but competitive pressure ensures P = ATC (long-run condition), yielding zero abnormal profit.

Model Answer (d):

Shut-down price: The firm shuts down when price falls below the minimum average variable cost (AVC). First, calculate AVC at each output:

• Q=1: TVC = 26 - 20 = 6; AVC = 6 / 1 = $6
• Q=2: TVC = 30 - 20 = 10; AVC = 10 / 2 = $5
• Q=3: TVC = 36 - 20 = 16; AVC = 16 / 3 = $5.33
• Q=4: TVC = 46 - 20 = 26; AVC = 26 / 4 = $6.50

Minimum AVC: The lowest AVC is $5 at Q=2 units. The shut-down price is P = $5.

Explanation: In the short run, fixed costs must be paid regardless of output. The firm can cover variable costs by producing if P ≥ min(AVC). If P < min(AVC), revenue cannot even cover variable costs, making losses worse by producing than by shutting down. At P ≥ min(AVC), the firm continues producing (even at a loss) to minimise total loss. Below P = $5, this firm ceases production in the short run.

Model Answer (a):

Dominant strategy analysis: A dominant strategy is one that yields the highest payoff for a firm regardless of what the rival does.

For Firm A:

• If Firm B chooses High Price: Firm A gets $50m (High) vs. $60m (Low). Low Price is better.
• If Firm B chooses Low Price: Firm A gets $10m (High) vs. $25m (Low). Low Price is better.
• Dominant strategy for A: Low Price (gives $60m or $25m, always better than High Price's $50m or $10m).

For Firm B:

• If Firm A chooses High Price: Firm B gets $50m (High) vs. $60m (Low). Low Price is better.
• If Firm A chooses Low Price: Firm B gets $10m (High) vs. $25m (Low). Low Price is better.
• Dominant strategy for B: Low Price (gives $60m or $25m, always better than High Price's $50m or $10m).

Conclusion: Both firms have a dominant strategy to charge Low Price, regardless of the rival's choice. This dominant strategy arises from each firm's incentive to undercut competitors and gain market share, a common feature in oligopoly.

Model Answer (b):

Nash equilibrium: A Nash equilibrium is where each firm's strategy is optimal given the rival's strategy. No firm wants to unilaterally deviate.

Since both firms have a dominant strategy to choose Low Price, the Nash equilibrium is:

• Outcome: (Low Price, Low Price)
• Firm A earns $25m, Firm B earns $25m

At this outcome, neither firm benefits from unilateral deviation: if A switches to High Price while B stays at Low, A drops to $10m (worse). If B switches while A stays at Low, B drops to $10m. Each firm is playing its best response to the rival's choice.

Pareto efficiency: An outcome is Pareto efficient if no one can be made better off without making someone worse off.

The Nash equilibrium (Low, Low) yielding ($25m, $25m) is NOT Pareto efficient. Consider the alternative (High Price, High Price), which yields ($50m, $50m). Both firms are better off: A gains $25m more, B gains $25m more. No one is worse off. This proves the Nash equilibrium is not Pareto efficient—a Pareto improvement exists.

Explanation: This illustrates the Prisoners' Dilemma in oligopoly. Mutual cooperation (high prices) benefits both, but individual incentives to cheat (undercut and capture market share) drive the equilibrium to lower payoffs. Without collusion enforcement mechanisms, competitive pressure forces firms into an inefficient Nash equilibrium.

Model Answer (c):

Why firms engage in collusion: Collusion (agreement to coordinate pricing or output) moves firms away from the Nash equilibrium toward the Pareto-efficient outcome. In the payoff matrix above, collusion to maintain High Prices yields ($50m, $50m)—higher joint profit than the Nash equilibrium ($25m, $25m).

• Firms gain $25m extra each compared to competitive outcome.
• Higher prices reduce output, raising profit per unit.
• Firms behave as a monopoly, restricting supply and raising price above marginal cost.

Why collusion breaks down: Despite higher joint profit, collusion is unstable due to individual incentive to cheat:

• Cheating incentive: If B agrees to maintain High Price, A can secretly lower price to Low, capturing B's customers and earning $60m (vs. $50m under cooperation). B earns only $10m.
• Defection gain: The cheater gains $10m relative to cooperation; the cheated firm loses $40m.
• Mutual defection: B, anticipating this incentive, also cheats preemptively. Both drop to Low Price, and profit collapses to $25m each.
• Detection and punishment difficulty: In real markets, hidden price cuts (secret discounts, bundling) are hard to detect, encouraging cheating.
• Legal risk: In many jurisdictions, explicit collusion is illegal (antitrust laws), adding enforcement costs and risk of prosecution.

Thus, collusion breaks down because individual firms have stronger incentive to defect than cooperate. Without enforceable agreements and costly detection, collusive arrangements are inherently unstable.

Model Answer (d):

Kinked demand curve model: The kinked demand curve explains why oligopoly prices are sticky (rigid) and slow to change.

The kink: Each oligopolist's demand curve has a kink at the current price level. The kink arises from asymmetric rival reactions:

• Above current price (elastic segment): If the firm raises price, rivals do not follow. The firm loses significant market share to competitors. Demand is elastic (price-sensitive).
• Below current price (inelastic segment): If the firm lowers price, rivals immediately match (price war). All firms cut price; demand falls less than the price cut. Demand is inelastic (quantity doesn't rise proportionally).

Price rigidity: The kink creates a discontinuous marginal revenue curve. The MR curve jumps down at the current output level. This large gap in MR means moderate cost changes (shifts in MC) do not intersect the new MR point—the profit-maximising output and price remain unchanged. The firm maintains current price despite cost fluctuations.

Result: Prices in oligopoly become rigid and sticky. Firms are reluctant to change prices because raising price loses volume, and lowering price triggers costly rivals' responses. Only large cost or demand shocks justify price adjustment, explaining the observed stability of oligopoly prices in reality.

Model Answer (a):

Two characteristics of monopolistic competition:

1. Product differentiation: Each coffee shop differentiates its product from rivals through branding, location, decor, quality, and menu variety. A shop's unique atmosphere and specialty drinks create customer loyalty, making it not a perfect substitute for other cafes. This differentiation gives each firm some price-setting power; it can raise price without losing all customers. However, close substitutes exist, limiting price increases.

2. Many competitors with free entry and exit: The cafe market has numerous competing firms but low barriers to entry—modest capital investment in a small shop, no licensing restrictions. If existing cafes earn abnormal profit, new competitors enter, increasing supply and reducing profit. Conversely, if losses occur, unprofitable cafes exit. This free entry/exit discipline firm behaviour and ensure long-run normal profit.

Alternative characteristics: Other valid explanations include (a) each firm faces a downward-sloping demand curve due to product differentiation (unlike perfect competition's horizontal demand), or (b) there is non-price competition: cafes compete through quality, location, advertising, and service, not just price.

Model Answer (b):

Short-run abnormal profit: In the short run, if a coffee shop successfully differentiates and attracts customers, it earns abnormal profit. Diagrammatically:

• Downward-sloping demand curve D₁ (differentiated product gives price-setting power).
• Downward-sloping MR curve below demand.
• Profit-maximising point: MR = MC at output Q₁.
• Price P₁ read from demand curve at Q₁.
• ATC₁ is below P₁, creating abnormal profit = (P₁ - ATC₁) × Q₁ (shaded rectangle).

Long-run adjustment to normal profit: The abnormal profit attracts new entrants. New cafes enter, competing for customers and reducing the market share of existing firms. The original firm's demand curve shifts leftward to D₂ (fewer customers at each price due to new competition).

• The demand curve D₂ also rotates to become more elastic (closer to horizontal) because substitutes increase as competitors enter.
• New equilibrium: MR₂ = MC at output Q₂ (lower than Q₁).
• Price P₂ (lower than P₁) is read from new demand D₂ at Q₂.
• ATC rises (due to lower output and smaller scale in the short run, or fixed costs spread over fewer sales).
• Long-run result: P₂ = ATC₂. The firm earns zero abnormal profit (normal profit only).

Long-run equilibrium characteristics: Unlike perfect competition's tangency (D is horizontal), the monopolistically competitive firm's demand curve is still downward-sloping, so it touches ATC from above at the profit-maximising point. The firm produces where D = ATC and MR = MC. Price exceeds MC (P > MC), indicating some allocative inefficiency, but free entry drives profit to zero.

Model Answer (c):

Advantage of monopolistic competition: Product variety and innovation. Because firms differentiate through variety, quality improvements, and branding, monopolistic competition encourages innovation and consumer choice. Consumers benefit from diverse products tailored to different preferences. Cafes offer unique atmospheres, specialty drinks, and service levels. In contrast, perfect competition produces homogeneous goods with minimal innovation incentive.

Disadvantage of monopolistic competition: Allocative inefficiency. In long-run equilibrium, P > MC, meaning the price exceeds the marginal cost of production. This creates deadweight loss: consumers who value a coffee at more than MC but less than P do not purchase, even though serving them would increase social welfare. In perfect competition, P = MC achieves allocative efficiency. Monopolistic competition's differentiation and price-setting power create this inefficiency.

Alternative answers: Other valid points: (Advantage) ability to earn short-run abnormal profit encourages entry and competition; (Disadvantage) excess capacity: each firm operates below minimum ATC, wasting productive resources compared to larger-scale perfect competitors.