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9708 · 7.8

Differing objectives and policies of firms — practice questions

Practice and worked examples for 9708 Differing objectives and policies of firms. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A monopolist faces P = 40 − Q and TC = 200 + 8Q.

(a) Find output and price for profit maximisation (MC = MR). (b) Find output and price for revenue maximisation (MR = 0). (c) Explain why a manager might prefer (b).

Show solution outline

(a) Profit max: MR = 40 − 2Q, MC = 8 40 − 2Q = 8 → Q = 16, P = 40 − 16 = £24 Profit = (24 × 16) − (200 + 128) = 384 − 328 = £56

(b) Revenue max: MR = 0 → 40 − 2Q = 0 → Q = 20, P = £20 TR = 20 × 20 = £400 (maximum) Profit = 400 − (200 + 160) = £40 (lower than profit max)

(c) Why prefer revenue max?

  • Manager's bonus tied to sales revenue, not profit.
  • Higher output (20 vs 16) means larger market share and greater perceived success.
  • Satisficing: shareholders get adequate profit (£40 > 0) while manager maximises personal reward linked to turnover.
  • Short-run sacrifice of £16 profit may be justified by manager's career incentives.

Worked example 2

A dominant firm, 'MarketLeader', has a demand curve P = 100 - 0.5Q and a constant marginal (and average) cost of $10. A potential entrant has an average cost of $40.

(a) Calculate MarketLeader's profit-maximising price, output, and profit. (b) Calculate MarketLeader's output and profit if it adopts a limit pricing strategy to deter the entrant. (c) Advise MarketLeader on the trade-off it faces.

Show solution outline

(a) Profit Maximisation:

  1. Find MR and MC. TR = P*Q = (100 - 0.5Q)Q = 100Q - 0.5Q². So, MR = d(TR)/dQ = 100 - Q. MC is given as 10.10.
  2. Set MR = MC: 100 - Q = 10 => Q = 90 units.
  3. Find price: P = 100 - 0.5(90) = 100 - 45 = **55∗∗.55**.
  4. Calculate profit: Profit = TR - TC = (P * Q) - (AC * Q) = (55∗90)−(55 * 90) - (10 * 90) = 4950−4950 - 900 = **4050∗∗.4050**.

(b) Limit Pricing:

  1. To deter entry, MarketLeader must set a price just below the entrant's AC of $40. Let's set P = $39.
  2. Find the quantity MarketLeader sells at this price: $39 = 100 - 0.5Q => 0.5Q = 61 => Q = 122 units.
  3. Calculate profit at this price and quantity: Profit = (P - AC) * Q = (39−39 - 10) * 122 = 29∗122=∗∗29 * 122 = **3538**.

(c) Advice and Trade-off: MarketLeader faces a trade-off between short-run profit and long-run market dominance. By choosing limit pricing, it sacrifices $512 in short-run profit ($4050 - $3538). However, this strategy prevents a new competitor from entering the market. If the entrant were to enter, the market would become a duopoly, likely leading to price competition and a significant fall in MarketLeader's long-run profits, which would almost certainly be far below the $3538 earned under limit pricing. Therefore, sacrificing some short-run profit is a rational strategy to secure higher, stable monopoly profits in the long run.

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