Question: What are the equilibrium strategies of the incumbent and potential entrant if the investment cost is not sunk?

1. The profits of an incumbent monopolist, currently £20m, are threatened by a potential entrant. If there is entry, and the incumbent and entrant decide to share the market, the incumbent will earn profits of £12m and the entrant will earn £8m. However, if there is entry, and the incumbent and entrant decide to engage in a price war, the incumbent will earn profits of £6m and the entrant will earn £3m. Prior to entry, the incumbent can invest in extra productive capacity to improve its competitive position in the event there is entry and a price war. The cost is £4m, but it will raise the incumbent’s profits in a price war by £7m to £13m, before the investment cost is deducted, and lower the entrant’s profits to a loss of £2m. Assume that the potential entrant earns zero profits if it decides not to enter and that the incumbent’s decision to invest is visible to the potential entrant.

1. 1. What are the equilibrium strategies of the incumbent and potential entrant if the investment cost is sunk? Comment on the welfare implications to society of your solution.

(25 marks)

1. 2. What are the equilibrium strategies of the incumbent and potential entrant if the investment cost is not sunk?

1. 3. Critically discuss the role sunk costs play in business strategy.

2. There are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4.

1. 1. Making clear your assumptions and calculations, work out the optimal prices the shops should charge for the product, and their profits in terms of N. How does your result relate to the so-called Bertrand Paradox?

(30 marks)

1. 2. Explain why it is optimal for the shops to locate at opposite ends of the city.

(7 marks)

1. 3. Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. Calculate the optimal prices for the shops, and their profits in terms of N.

(13 marks)

3. A monopolist has two geographically segmented markets. The demand curves for these market segments are:

𝑞₁ = 500 − 3𝑝₁

𝑞₂ = 800 − 4𝑝₂

where 𝑞_𝑖 and 𝑝_𝑖, 𝑖 = 1,2, are the outputs and prices for segments 1 and 2 respectively. Suppose the firm has a constant marginal cost for each segment of 50 per unit and no fixed costs.

1. 1. What are the profit-maximising prices and outputs in the two market segments, and hence the firm’s profits?

(13 marks)

1. 2. If the monopolist is forced by regulators to charge the same price in both market segments, what is the profit-maximising price and the firm’s profit level?

(10 marks)

1. 3. Tabulate the welfare of consumers in the two market segments and for the monopolist. Hence, describe who is better off and who is worse off under uniform pricing.

(12 marks)

1. 4. Referring to your answers above, discuss the pros and cons of making price discrimination illegal on grounds of competition.

(15 marks)

4. The inverse demand curve for a product is 𝑝 = 20 − 𝑄, where 𝑄 is the total volume brought to the

market. At present two firms serve this market. Firm 1 has constant marginal costs of 5, while Firm 2 has constant marginal costs of 2. Both firms have fixed costs of 100.

1. Assuming the fixed costs are sunk, calculate the equilibrium quantities, price and profits for the two firms.

(20 marks)

2. Now assuming the fixed costs are not sunk, calculate the equilibrium quantities, price and profits for the two firms.

3. Discuss any competition issues raised by your answer in part b).