Question

Consider a market with a demand curve given (in inverse form) by P(Q)=50−0.25QP(Q)=50−0.25Q, where QQ is total market output and PP is the price of the good. Two firms compete in this market by sequentially choosing quantities q1q1 and q2q2 (where q1+q2=Qq1+q2=Q).

This is an example of:

Choose one:

A. Cournot competition.

B. Bertrand competition.

C. perfect competition.

D. Stackelberg competition.

Part 2(4 pts)

Now suppose the cost of production is constant at $20.00 per unit (and is the same for both firms). If the two firms are maximizing profit, the leader will produce_________ units and the follower will produce ______ units. The total amount of production will be _______ units and the price of the good will be ________ $ . (Give all numerical answers to two decimal places.)

Answer 1

Ans. As the firms compete on quantity which they set simultaneously, so, this is an example of Cournot competition.

b) Assuming firm 1 is the leader.

Demand function, P = 50 - 0.25(q1 +q2)

Total revenue of firm 2, TR2 = P*q2 = 50q2 - 0.25q1q2 - 0.25q22

and

Marginal revenue, MR2 = dTR2/dq2 = 50 - 0.25q1 - 0.5q2

Marginal cost, MC = 20

At equilibrium, MR2 = MC

=> 50 - 0.25q1 - 0.5q2 = 20

=> q2 = 60 - 0.5q1 —> BR2

Substituting BR2 in demand function, we get,

P = 50 - 0.25q1 - 0.25(60 - 0.5q1) = 35 - 0.125q1

Total revenue, TR1 = P*q1 = 35q1 - 0.125q12

=> Marginal revenue, MR1 = dTR1/dq1 = 35 - 0.25q1

At equilibrium, MR1 = MC

=> 35 - 0.25q1 = 20

=> q1 = 60 units

Substituting this value in BR2, we get,

q2 = 30 units

and demand function gives the price, P = $27.5

Profit of firm 1 = TR1 - 20*q1 = $450

Profit of firm 2 = TR2 - 20*q2 = $225

Thus, the leader will produce 60 units and follower will produce 30 units. Total production will be 90 units at price of $27.5 per unit.

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