ANSWER FOR PART B. DONT COPY THE ANSWER AND PROVIDE ME THE ANSWER C=-440 OR 440,

Question

ANSWER FOR PART B. DONT COPY THE ANSWER AND PROVIDE ME THE ANSWER C=-440 OR 440, BECAUSE C HAS TO BE LESS THAN 20

Consider a Stackelberg game of quantity competition between two firms. Firm 1 is the leader and firm 2 is the follower. Market demand is described by the inverse demand function P = 1000 4Q. Each firm has a constant unit cost of production equal to 20.

a. Solve for Nash equilibrium outcome.

b. Suppose firm 2’s unit cost of production is c < 20. What value would c have so that in the Nash equilibrium the two firms, leader and follower, had the same market share?

Explanation / Answer

The first step here is to derive firm 2’s reaction function:

Profit for firm 2 = 1,000Q2-4Q1Q2-4Q2^2-20Q2
This implies the first order condition:
1,000-4Q1-8Q2-20=0, so firm 2’s reaction function is:

Q2=(980-4Q1)/8=122.5-.5Q1

Firm 1 anticipates Firm 2’s reaction function, so its profit is:
1,000Q1-4Q1^2-4Q1(122.5-.5Q1)-20Q1

This implies the first order condition:
1,000-8Q1-490+4Q1-20=490-4Q1=0,
Which implies that firm 1 produces
Q1=490/4=122.5 units.

Firm 2, then, produces
Q2=122.5-.5(122.5)=61.25 units.

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