ECON 6006 Market structure and Strategic behaviour Mid-semester Test Practice
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Market structure and Strategic behaviour
ECON 6006
Mid-semester Test
Practice
Section A: Answer all short answer questions in the booklet provided. Please be sure to show your working and explain your reasoning where appropriate. (Total 40 marks)
1. The demand for good A is given by Q(P) = 75 - 0.5P, where Q is the market quantity, and P is the
market price. Production of good A involves costs of C(q) = 400 +30q, where q is firm output.
(a) Suppose a single firm operates in the market. Find the profit-maximising price and quantity of the monopolist. [4 marks]
(b) Suppose two firms operate in the market. The firms engage in simultaneous quantity compe- tition in a single period.
i. Find the reaction function for each firm. [4 marks]
ii. Find the Nash equilibrium outputs of both firms. [3 marks]
(c) Suppose that two firms operate in the market. The firms engage in Stackelberg competition. Firm 1 chooses its output first, then Firm 2 chooses it’s output. Find the output of each firm.
[4 marks]
2. Consider the following game. Firm 1 and Firm 2 have three strategies available, A, B, and C. The first entry in each cell contains the payoffs for Firm 1 and the second entry contains the payoffs for Firm 2. Both firms have the common discount factor, δ, where 0 < δ < 1.
Firm 2
A B C
0 0 |
6 -1 |
2 -2 |
-1 6 |
4 4 |
2 2 |
-2 2 |
2 2 |
3 3 |
(a) Suppose the game above is played once. Identify any Nash equilibria. Explain briefly.
[4 marks]
(b) Suppose the game above is played twice. Consider the following strategy:
● in period 1: play B;
● in period 2: play C if both played B in period 1; otherwise play A.
For what value of δ (if any) is there a subgame perfect Nash equilibria in which both players play the above strategy? [6 marks]
3. Two firms compete in the market for a homogeneous product. Each firm has a capacity of 200
units. Market demand is given by
Q(p) = 500 - 10p ﹐
where Q = q1 +q2 . Each firm has a constant marginal cost and no fixed costs: C(q) = 10q.
The firms compete by choosing price. The lowest priced firm captures the whole market (up to their capacity constraints), while the higher priced firm serves any residual demand. The firms interact sequentially in a single period. First, Firm 1 chooses a price p1 . Then, after observing p1 , Firm 2 chooses a price p2 .
(a) Solve for the reaction function for Firm 2.
(b) Solve for a subgame perfect Nash equilibrium to this game. Explain.
[8 marks] [7 marks]
2022-05-31