Question

The inverse demand function a monopoly faces is P = 100 − Q. The firm’s cost curve isTC(Q) = 10 + 5Q

(f) (4 points) For what value of fixed costs, does the monopolist break even?

(g) (4 points) For what value of fixed costs, would be monopolist find it optimal to shut down in the short-run?

(h) (4 points) For what value of fixed costs, would be monopolist find it optimal to shut down in the long-run?

(i) (4 points) What is the value of Lerner Index at the profit maximizing level of output?

Answer 1

f) at break even, TR = TC

(100-Q)Q =10+5Q

Q² -95Q+10=0

This equation is solved at Q=0 or Q =95

TC at Q=0 is 10 and TC at Q=95 is 485.

g) for shut down in the short run, the TR must cover the variable costs only hence

100-Q= 5

Q =95 The cost will be 485

h) for shut down in long run, revenue must cover all costs therefore TR=TC, Q= 0/95

TC= 10/495