The inverse demand curve for widgets is P = 1302Q. There are two firms, A and B,
ID: 1168742 • Letter: T
Question
The inverse demand curve for widgets is P = 1302Q. There are two firms, A and B, who produce wid- gets. Each firm has a constant marginal and average cost of producing the good that equals 10. Firms compete in quantities and they make their quantity choices simultaneously (Cournot competition). Firms can choose any quantity to produce.
(a) Write down the profit function of each firm.
(b) Suppose there are three firms (instead of two). Each firm still has constant marginal and average cost equals 10 and they compete in quantities. What is the Cournot-Nash equilibrium in this case? To solve for the NE you need to re-do the first two questions of this problem, now with three firms.
(c) Suppose again that there are only two firms, but now firms have different costs. In particular, firm A has constant marginal and average cost equals 10, whereas firm B has constant marginal and average cost equals 34. What is the Cournot-Nash equilibrium in this case? Note that, as we did in class, when firms have different marginal costs, the only way to solve for the NE is to replace one best-response in the other.
Explanation / Answer
Profit function will be Profit = P – 10
P = 130 – 2Q Hence Marginal Revenue = 130 – 4Q
At profit maximization, Marginal Revenue = Marginal Cost = 10
Therefore, 130 – 4Q = 10
4Q = 120
Q = 30
Nash Equilibrium for each firm is 30 units
Profit maximization for 2nd firm
130 – 4Q = 34
4Q = 96
Q = 24
Hence Nash equilibrium for both the firms with different marginal cost will be 30 units.
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