Question

In a duopoly market with two identical firms, the market demand curve is: P=95-5Q And the marginal cost and average cost of each firm is constant: AC=MC=5 If each firm sets quantity at the same time:

Now assume that firm 1 in this market gets to act first (Stackelberg model).

A) How much will firm 1 produce?

B) How much will firm 2 produce?

C) What will be the total Q and market P for this market?

D) What is the profit for each firm?

Answer #1

**A)** The market demand would be
, and the demand would be
or
.

The MR of firm 2 would be or , and the firm 2 would produce where or or or . This is the reaction function of firm 2.

Supposing that firm 1 in this market gets to act first, they know the reaction function of firm 2, and employ it in the demand as or or . In this case the MR of firm1 would be or . The firm would produce at where or or or units. Hence, firm 1 will produce 9 units.

**B)** Firm 2 would produce according to their
response function as
or
units.

**C)** The total quantity in the market would be
or
. The price would be
or
dollars.

**D)** Since AC for both firm is 5, we have for
i=1,2 -
or
.

The profit of firm 1 would be dollars.

The profit of firm 2 would be dollars.

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