Answer to Question #70201 in Microeconomics for Mida

Question

A monopolist faces a demand curve Q = A – P and has a cost function C(Q) = cQ. Derive
the optimal monopoly price and its total profit.

Answer 1

Maximizing profit:
MR=MC.
MC = C’(Q) = (CQ)’ = C.
Demand function:
Q=A-P
P=A-Q.
TR=AQ-Q^2
MR=A-2Q
A-2Q=C
-2Q=C- A
Q=1/2(A-C) – optimal quantity.
P=A-1/2(A- C) = A-1/2A+1/2C=1/2(A+C)
Total profit is:
TP=(P-AC)*Q
AC=cQ/Q=C.
TP=(1/2A+1/2C-C)*(1/2A- 1/2C)= (1/2A-1/2C)^2