CC0311 Semester 2 2014

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CC0311

Semester 2 2014

PART B

SHORT ANSWER QUESTIONS

ANSWERS WITHOUT EXPLANATION RECEIVE ZERO CREDIT

QUESTION 1. (15 marks)

In an industry market demand is given by P = 100 – 5Q, where P is market price and Q is total industry quantity. There are two firms in the market. Initially both firms    have marginal costs of production of $10 per unit.

(a) What is the Cournot equilibrium in the market if firms set their quantities simultaneously? Also derive your answer graphically. (3 marks)

Now, it becomes known to one of the firms, say firm 1, that they can purchase a new technology that will lower their marginal costs of production to $5 per unit.

(b) Determine the new Cournot equilibrium if firm 1 purchases the new technology. Again, show this equilibrium graphically. (3 marks)

(c) Determine how much firm 1 would be willing to pay for this new technology. (3 marks)

Now suppose that the firms are Bertrand competitors. As usual, if the firms set the    same price they split the market 50:50. If, on the other hand, a firm sets a lower price than their competitor they get all of the demand.

(d) What is the equilibrium outcome when both firms have marginal costs of $10 per unit? (3 marks)

(e) What is the equilibrium if firm 1 has marginal costs of $5 per unit? How much is firm 1 willing to pay for the new technology? (3 marks)

QUESTION 2. (15 marks)

The market for pizza is competitive. There are 100 firms currently in the market each facing the cost function Ci(qi) = 25 + qi2, where qi denotes the quantity of pizzas        produced by firm i, for i = 1, … ., 100. Industry demand for pizza is given by:

D(p) = 440 – 5p, where p denotes the price of a pizza.

(a) Find the competitive equilibrium price. (2 marks)

(b) How many pizzas does each firm produce and what are its profits? (3 marks)

(c) Is this a long run competitive equilibrium? If not, what is? (3 marks)

Consider the following model for the remainder of this question. (This model is    unrelated to parts (a) to (c) above.) Two firms compete in a market every period.   There is an infinite number of periods, and both firms discount future payoffs by a discount factor δ per period, where 0 < δ < 1.

(d) Suppose the firms adopt the following trigger strategy: set the monopoly price if   both firms have set the monopoly price in every previous period; if not set the one-      shot Bertrand price. In any period of cooperation each firm gets half the monopoly      profit (πm/2). If a firm cheats in a cooperative period they receive the monopoly profit, πm . In any punishment period (Bertrand pricing) each firm makes zero profit. Find the δ necessary to sustain collusion. Label this value of delta δ*. (3 marks)

(e) Now consider the case when in any punishment period the firms revert to the     Cournot equilibrium, in which they each make πc . (In all other respects the model is the same as in part (d).) What is the δ necessary to sustain collusion in this case?     Label this value of delta δ**. (3 marks)

(f) Which is larger δ * or δ**? Provide some intuition for this result. For example,     relate your answer to the theory on conditions that help to sustain collusion. (1 mark)

QUESTION 3. (15 marks)

The final output for a product is comprised of one unit of input from both a                 wholesaler and a retailer. There is only one wholesaler but there are two retailers. The wholesaler has marginal cost of c. The retailers have marginal costs of 0. Final            demand is given by P = a – bQ. The wholesaler can set a two-part tariff, with a fixed- fee F and a per unit fee w.

(a) If the retailers are Bertrand competitors, what is the fixed-fee and w that will      maximise profits for the wholesaler? How does this compare to the output and price level of a vertically-integrated firm? (3 marks)

(b) Now assume that the retailers are Cournot competitors. Again the wholesaler sets a fixed-fee and a per-unit charge. What is the output level of the retailers, given that the wholesaler has set a per-unit charge of w? What is the maximum fixed fee F that the retailers would be willing to pay? (4 marks)

(c) Write down the wholesaler’s profits in terms of w. What is the w that maximises profits? (4 marks)

(d) Compare the w and F set when with retailers are Bertrand competitors with when they are Cournot duopolists. (4 marks)


















2022-06-13