1. The demand and cost curves for a monopoly firm are as follows: Q = 750 - 5P T

ID: 1187424 • Letter: 1

Question

1. The demand and cost curves for a monopoly firm are as follows:

Q = 750 - 5P

TC = 2000 + 70Q

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(a) At what output and price will the firm maximize total revenue?

(b) At what output and price will the firm maximize total profit?

(c) Compare the maximum profit obtainable with the profit that the firm would have if it chose a revenue-maximizing strategy.

a) Q = 750 - 5P

P = 150 - 0.2Q

Total Revenue = P*Q = 150Q - 0.2Q^2

to max TR = dTR/dQ = 0

150 - 0.4Q = 0

Q = 150/0.4 = 375

P = 150 - .2*375 = 75

b) TC = 2000 + 70Q

for profit max, d(TR-TC)/dQ = 0

or MC=MR

MR = 150 - 0.4Q

MC = dTC/dQ = 70

150 - 0.4Q = 70

Q = 80/0.4 = 200

P = 150 - 0.2*200 = 110

c) profit max strategy

Profit = P*Q - TC

= 110*200 - (2000 + 70*200)

= 6000

revenue max strategy

Profit = P*Q - TC

= 75*375 - (2000 + 70*375)

= -125

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