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.