Question 1 (25 marks)
a) Outline the Random Growth Hypothesis and explain the implications of Girbat’s Law for the long-run trend in seller concentration. [10 marks]
b) Suppose in period 0 an industry comprises 8 equal-sized firms, each with sales of £12 millions. The assumed random growth process is as follows: in any subsequent year, each firm has an equal chance of either doubling or halving its sales. Show the validity of Gibrat’s law, using both CR4 and HHI indices after 3 periods [15 marks]
Question 2 (25 marks)
A market has a demand curve given by 𝑄 = 80 − 2𝑃. All suppliers have identical marginal cost, 𝑀𝐶 = 16, there are no fixed costs, and produce homogeneous goods.
a) For each of the following market structures, compute the output produced by each firm (if possible), the total industry output, the market price and each firms’ (if possible) profit.
i) There is only one firm in the industry (Monopoly) [2 marks]
ii) There are many small firms in the market (Perfect Competition) [2 marks]
iii) There are two firms in the industry (Firm A and Firm B), compete in quantities, and choose quantities simultaneously (Cournot duopoly) [2 marks]
iv) There are two firms in the industry (Firm A and Firm B), compete in quantities, and firm A moves first. (Stackelberg duopoly) [2 marks]
v) There are two firms in the industry (Firm A and Firm B), compete in prices, and choose prices simultaneously (Bertrand duopoly) [2 marks]
b) How the solutions would change in (iii), (iv) and (v) if 𝑀𝐶! = 16 and 𝑀𝐶” = 20?
[8 marks]
c) How the solutions would change in (iii) and (iv) if there are three firms with 𝑀𝐶! =
16and𝑀𝐶” =20and𝑀𝐶# =16? [7 marks]
Question 3 (25 marks)
Two Firms, Mac Havant’s and Fratton Burger must decide whether to put one of their restaurants in University Campus. The strategies are to “Enter” or “Don’t Enter”. If either firm plays “Don’t Enter”, it earns £0 profits. If one firm plays “Enter” and the other plays “Don’t Enter”, the firm that plays “Enter” earns £200,000 per year in profits and the firm that plays “Don’t enter” always yields £0 profits”. If both firms choose to play “Enter”, both lose £50,000 per year as there is not enough demand for two restaurants to make positive profits.
a) Construct the pay-off matrix [5 marks]
b) Is there a dominant strategy for any of the firms? [5 marks]
c) Is there a Nash equilibrium in pure strategies? If yes which one(s). [8 marks]
d) Find all Nash equilibria and draw best response graph for each of the firm. [7 marks]
Question 4 (20 marks)
Gosport Electric Ltd is an electricity supplier that faces domestic and commercial customers (these are denoted ‘𝑑’ and ‘𝑐’ respectively. The two sets of customers have the following demand curves:
𝑃 =30−𝑄 $$
𝑃 =60−𝑄 %%
Additionally, Gosport Electric Ltd total cost curve is given by 𝑇𝐶 = 5𝑄
a) Initially Gosport Electric Ltd cannot easily separate these two types of customers so it sets price on the basis of the total market demand curve (i.e. the horizontal aggregation of the two demand curves above). Calculate the single price that Gosport Electric Ltd will charge, the number it sells and the profit it makes. Draw the outcome on a diagram. [7 marks]
b) Now Gosport Electric Ltd can separate these two markets so it is able to price discriminate. Find the prices it sets in both markets, the sales in each and its overall level of profit. Compare your answer with that in Part (a). [7 marks]
c) If you are now advising the government on whether to prevent Gosport Electric Ltd from using price-discrimination, what would your advice be, and why? [6 marks]
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