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Oligopoly

An oligopoly exists with two firms, A and B. The demand function for these oligopolists is Q=1000-40P.

a. If firm A's cost function is TC=3000+7Q, what quantity (Qa) will it produce and price (Pa) will it charge to maximize profits?

b. If firm B's cost function is TC=3000+5Q, what is this firm's profit or loss?

c. Which of these oligopolists is the leader in this industry, and why?

Solution Preview

a. If firm A's cost function is TC=3000+7Q, what quantity (Qa) will it produce and price (Pa) will it charge to maximize profits?

Write the demand function into: 40P = 1000-Q, or P = 25 - 0.025Q
When firm A makes decision first, it will produce at its monopoly output level.
Then the revenue function is TR = P*Q = (25 - 0.025Q)*Q = 25Q - 0.025Q^2
Marginal revenue = dTR/dQ = 25 - 0.05 Q
To max its profit, A will produce where MR = MC
25 - 0.05 Q = dTC/Q = 7
0.05Q = 18
Qa = 360
Pa = 25 - 0.025Q = 25-0.025*360 = $16

(Note: if firm B moves next, it can simply lower the price to below $16 to attract all consumers.
Firm B's monopoly price:
MR = ...

Solution Summary

The solution answers the question below.

$2.19