A monopoly's demand function is Q = 80 - P/6

Economics May 19, 2021

A monopoly's demand function is Q = 80 - P/6. The interval marginal cost is 7Q and the external marginal cost is 3Q. What is the socially efficient output for the firm,
a) 30
b) None of these answers listed is correct

c) 24
d) 12
e) 40

Expert Solution

Computation of the social efficient output for the firm:-

Social MC included Internal MC and External MC.

Social marginal cost = 7Q + 3Q = 10Q

At social optimal point. Price = marginal cost

Q = 80 - P/6

P = 10Q

Q = 80 - (10Q/6)

Q = ((80*6) - 10Q) / 6

6 * Q = 480 - 10Q

6Q + 10Q = 480

16Q = 480

Q = 480 / 16

= 30

Hence, the correct option is a) 30

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