A monopolistic firm produces a single good and has the cost function C(q) = 6q.

Question

A monopolistic firm produces a single good and has the cost function C(q) = 6q. The market demand is given by the inverse demand function P(q) = 50 q.

(a) Determine the profit-maximizing output and price of the monopolist. Represent the profit-maximization decision of the monopolist graphically.

(b) Calculate the profit of the monopolist and the consumer surplus. Is it possible to achieve a better result in terms of welfare maximization? Why or why not?

A monopolistic firm produces a single good and has the cost function C(q)-60. The market demand is given by the inverse demand function P(q) = 50-q. #4 Determine the profit-maximizing output and price of the monopolist. Represent the profit-maximization decision of the monopolist graphically.

Explanation / Answer

Answer for a)

P = 50- q and C =6q

for a monopolist firm Profit maximization happens when MR =MC

R =P*q & C =6q

MC=dc/cq=6

MR =(50/q-2)*q =50-2q =6

q=22

now P =50-22 =28

Answer for B

Profit can be calculated as below

Profit = TR-TC =P*Q-6*Q =(P-6)*22=22*22 =484

Consumer Surplus can be calculated as below

CS = (50-28)*1/2*22=242

If this firm to produce with respect to perfectly competitive enviornment

P=MC

50-q =6

q=44

then CS will be =0.5*(44)*44=968

Hence increase in CS is 968-242=726

Hence there is good scope to improve social welfare by not producing with constraint at MR=MC which is to reduce Dead Weight Loss

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