Question

An industry consists of an incumbent (firm 1) and a potential entrant (firm 2). Each firm can produce output at a constant marginal cost of $3 per unit. The incumbent has already incurred a sunk cost F but the potential entrant must pay it if it enters. The inverse demand curve is P(Y ) = 12 − Y , where Y is total output. The firms compete in quantities. Firm 1 choose its quantity q1 first. Firm 2 observes q1 and then decides whether or not to enter, the quantity it supplies is q2. (a) Suppose firm 2 enters. What is the best reply to firm 1’s choice of q1. (b) Suppose F = 0. Determine the equilibrium prices, quantities, and profits. (c) How big would F need to be for firm 1 to profitably deter firm 2’s entry?

Answer 1

Solution:-

Given that

An industry consists of an incumbent (firm 1) and a potential entrant (firm 2). Each firm can produce output at a constant marginal cost of $3 per unit. The incumbent has already incurred a sunk cost F but the potential entrant must pay it if it enters. The inverse demand curve is P(Y ) = 12 − Y , where Y is total output.

q1 = quantity supplied by firm 1

q2 = quantity supplied by firm 2 if it enters into the market.

a)

Firm 2 enters the market,

Total cost for firm 2

Revenue of firm 2

Profit of firm 2:

Firm's 2's objective is to maximise profit .

FOC:

Best reply to firm 1's choice of q1 is

........(1)

eqn (1) represents the best response of firm 2 for the given choice of firm 1.

b)

F = 0

Both the firms compete in quantities

Firm 1 = leader

Firm 2 = Follower (because firm 2 observes q1 and then decides whether or not to enter)

Firm 1's profit function.

Firm 1 chooses q1 to maximises .

Note: Firm 1 chooses q1 knowing that firm 2 will react to it in the 2nd period according to its reaction function .

Therefore,

From (1)

put into the profit function of firm 1

FOC:

optimal quantity supplied by firm 1

Put the value of q1 unto the best response of firm 2

and

optimal quantity supplied by firm 2

Profit of firm 1:

  

Profit of firm 2: at FCO

  

c)

If firm 2 enters the industry it can make maximum profit equal to .

Therefore, to profitability data entry of firm 2, F should be greater than or equal to .

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