Imperfect comp question?

Question

3. Barbara is a producer in a monopoly industry. Her demand curve, total revenue curve, marginal revenue curve and total cost curve are given as follows:

Q = 120 - 2P TR = 60Q - 0.5Q^2 MR = 60 - Q TC = 4Q

a) How much output will Barbara produce?

b) How much will she charge for her product?

c) How much profit will she make?TR-TC

Answer 1

a)

MR=MC

MC=(TC)'=4

60-Q=4

60-4=Q

Q=56

b)

56=120-2P

2P=120-56

2P=64

P=32

c)

Profit=TR-TC

TR=60*Q-0.5Q^2 = 60*56 - 0.5 * 56 * 56=1792

TC=4*Q=56*4=224

Profit=1792-224 = 1568