Question

Consider an asymmetric duopoly. The market demand is p = 1 − Q. Firm 1 has zero cost while Firm 2 has constant marginal cost c distributed over the interval 0, 1/2.

a. Find the equilibrium when firms compete in quantities.

b. Suppose a regulator can marginally decrease c. Will this change
increase social welfare and why? Give your answer in terms of the
market share of Firm 2.

c. Suppose now that firms compete in prices. Find the Bertrand equilibrium (assume that firms do not play weakly dominated strategies).

d. Answer question (b) under competition in prices.

Answer #1

b) A marginal decrease in c would increase the market hare of firm 2, leading to an increase in firm 2's quantity. The increase in quantity would reflect a decline in prices and thus increase social welfare.

c) When firms compete in prices, the only bertrand equilibrium is when P= 0 since firm 1 has zero marginal cost. If firm 2 charges a price higher than 0, firm 1 will serve the whole market. If firm 2 charges a price lower than 0 (undercuts firm 1) it'll go into losses. Therefore the only nash equilibrium is p=MC=0

d) Under price competition a decrease in marginal cost c would not affect social welfare since the best response for each firm is to charge a price equal to zero. A marginal decrease in costs would not change the market share of firm 2.

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