Question

Suppose Firm X is a dominant firm in a market where the market demand is Q = 1200 -2p. Once Firm X sets its price, those small competitors set their prices a little lower so that they can always sell up to their capacity. Assume the small firms’ combined capacity is 100 units. Further assume Firm X’s marginal cost is 50. Answer the following questions.

a. Let QD be the quantity produced by the dominant firm. Write down the residual demand function faced by Firm X. (Hint: Think about how Q and QD are related.) b. Find Firm X’s profit-maximizing price.

Answer #1

a) It is given that market demand is Q = 1200 - 2P and small firms who compete with the dominant firm set a price

at which they are able to sell 100 units which is their combined capacity. Hence the Residual demand is the

difference between market demand and firms' combined supply. This gives residual demand QD = 1200 - 2P - 100

or **QD = 1100 - 2P.**
Inverse demand is P = 1100/2 - QD/2 or P = 550 - 0.5QD

b) Profit is maximized when MR = MC. MR has same intercept but twice the slope. Hence MR = 550 - QD. This

gives 550 - QD = 50 or QD = 500
units. The profit maximizing price is 550 - 500*0.5 =
**$300**.

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