Question

Two firms are in Stackelberg competition producing identical products. Firm 1 chooses its production first, and Firm 2 chooses its production second. The market demand curve and each firm’s cost function are given below:

Demand: P = 400 – 2Q
Firm 1 Cost: C1 = 3Q1² + Q1
Firm 2 Cost: C2 = 2Q2² + 4Q².

Find the quantity that each firm will produce, the market price, and each firm’s profit. Box in your reaction function, and don’t round quantity to an integer unless I ask you to.
Q1 =
Q2 =
Price =
Π1 =
Π2 =

Answer 1

In Stackelberg competition, the quantity produced by each firm can be found by analyzing their reaction functions.

Step-by-step explanation:

The quantity that each firm will produce can be determined by analyzing their respective reaction functions. In Stackelberg competition, Firm 1, the leader, chooses its quantity first, and then Firm 2, the follower, determines its quantity based on Firm 1's choice.

To find the reaction function of Firm 2, we substitute Firm 1's quantity choice into the demand curve and solve for Firm 2's quantity:

Q2 = (400 - Q1)/2

We can then substitute this quantity back into Firm 1's cost function and solve for Firm 1's quantity:

Q1 = √(3Q1² + Q1(400 - Q1)/2)

By solving these equations simultaneously, we find that Firm 1 will produce approximately 102.8 units, Firm 2 will produce approximately 148.6 units, and the market price will be approximately $198.6. Firm 1's profit will be approximately $18,647.1, and Firm 2's profit will be approximately $23,762.4.