Question

The A Company and the B Company are the only two firms that produce and sell a particular product. The inverse demand curve for their product is:

P=19-0.5Q

where Q=Q_A+Q_B

The companies have identical cost functions:

TC_A=3+Q_A

TC_B=3+Q_B

a) Suppose that the two companies are owned by Cournot duopolists. Find the output produced by each firm and the market price. Very briefly explain the steps you take in your solution.

b)Instead of the Cournot assumption, assume Company A sets its output before Company B does. Find the output levels of each firm and the market price. Hint: this is the Stackelberg solution. Very briefly explain the steps you take in your solution.

c) How big is the first-mover advantage for Company A in part b) in terms of profits? Very briefly explain and show your work.

Answer 1

a. Firm 1's problem:

Solving:

Firm 1's best response function is:

Firm 2's problem:

Solving:

Firm 2's best response function is:

Solving the two best response functions:

Market price at these quantities is:

Firm 1's profit is:

b. If firm 1 gets to decide its quantity before firm 2, firm 1 acts as a monopolist:

Solving:

Substituting this into firm 2's best response function:

Market price at these quantities is:

Firm 1's profit:

c. Firm 1 earns 7% greater profit when it gets to choose its output before firm 2.