3. Consider a market of four firms with demand given by P = 200 – Q. Each firm h

Question

3. Consider a market of four firms with demand given by P = 200 – Q. Each firm has a constant marginal cost of $20. Competition is currently characterized by making simultaneous profit-maximizing quantity decisions.

a. What are the expected quantity, price, and profit outcomes in this market?

b. Suppose that two firms merge to form a leader firm who gains the advantage of setting his production levels before the other firms in the market. What are the expected leader/follower quantity, market price, and leader/follower profit outcomes in this market? Was the merger profitable for the firms involved?

c. Our model does not consider the potential for economic costs associated with a merger. If there were costs associated with the merger in part b, at what value would they make the merger unprofitable?

d. Suppose that the two remaining follower firms merged into a second co-leader. What are the expected leader/follower quantity, market price, and leader/follower profit outcomes in this market? Was the merger profitable for the firms involved?

e. What does your answer to part d suggest about future merger activity in this market? Other than economic costs, what other factors not included in our model might limit such activity?

Explanation / Answer

a) In case when 'n' firms simulateneously setting a quantity, generating a Cournot outcome, the individual firm's output is given by q = (a - m)/(b*(1 + n)) where a is the quantity intercept, b is the demand slope and m is the marginal cost. This results in a price p = (a + nm)/(1 + n)

Hence quantity q = (200 - 20)/(5 + 1) = 30 units by each of the five firms and price p = (200 + 5*20)/(1 + 5) = $50 per unit. Firms earn an indivual profit of (P - AC/MC)*Q = (50 - 20)*30 = $900

b) Each firm has no intention to deviate from its current outcome. All are deciding simultaneously so that their expectations about their rivals are same.

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