3) Consider a monopolist with total cost curve given by TC = 45 + 5Q + Q2 6 and

Question

3) Consider a monopolist with total cost curve given by TC = 45 + 5Q + Q2 6 and marginal cost given by MC = 5 + Q 3 . The market demand curve takes the form Q = 202 - 2P.

A) What quantity will the monopoly choose to produce and what price will they charge?

B) Calculate the magnitude of profit that the monopoly will earn.

C) Calculate the price elasticity of demand at the the firms profit maximizing price and quantity.

D) Suppose that a change in wages causes the firms marginal cost to increase to MC = 7 + Q 3 . What quantity will the monopoly choose to produce and what price will they charge?

E) Calculate the magnitude of profit that the monopoly will earn.

F) Suppose that the firms marginal cost stays at MC = 7 + Q 3 and the demand curve that the firm faces falls to Q = 150 - 2P. What quantity will the monopoly choose to produce and what price will they charge?

G) Calculate the magnitude of profit that the monopoly will earn.

H) Calculate consumer and producer surplus in the market.

I) Calculate the deadweight loss created by the monopoly

Explanation / Answer

A)

Q = 202 - 2P

P=101 - Q/2

TR(total revenue) = P*Q = 101Q - Q2/2

MR(marginal revenue) = 101-Q

Profit maximization condition MR=MC

101-Q=5+Q/3

Q=72, P=65

B)

TR= 72*65=4680

TC= TC = 45 + 5Q + Q2/6 = 1269

profit= TR-TC = 3411.

C) IF Q= 74, P=64

Price elasticity of demand = Change in Q/Change in P * P/Q = 2/1 * 65/72 = -1.8

D) IF, MC= 7+Q/3

then, 101-Q=7+Q/3, Q=70.5 or 71 and P=65.5

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