Question

Assume that a monopolists Sells a product In the short - run with a total cost function - ST. Hoztoat2q² Q70 7 96 Q=0 The market demand curve is given by the equation PCG) = 70-8Q a) Find the marginal cost for the firm b) Find the profit - Maximizing out put and price (PQ) C) what are the mono po lists Profits ? d) Does the monopolist want to stay in businessa

Answer 1

A). Stc = 102+10Q+2Q2

To get MC ,we differentiate stc with respect to Q,

MC=4Q+10

B).The profit maximize condition is ,

MR= MC

AR= 70-8Q

TR=70Q-8Q2

MR=70-16Q

Applying condition,

MR=MC

70-16Q=4Q-+10

Q=3

PUTTING Q INTO DEMAND FUNCTION,

P=70-8*3

P=46

C). PROFIT=TR=TC

=46*3-102-10*3-2*3^2

PROFIT =-12

D). BECAUSE MONOPOLIST IS MAKING LOSS IN SHORT RUN ,HE DOES NOT WANT TO STAY IN BUSINESS IN SHORT RUN BUT IN LONG RUN THERE WILL BE NO FIXED COST FOR FIRM ,AND THE TOTAL COST FUNCTION WOULD CHANGED TO ,

TC(LONG RUN)=2Q2+10Q+6

THEN FIRM WILL MAKE A PROFIT OF +84.

SO FIRM WILL MAKE LONG RUN HUGE PROFITS BUT FOR THAT IT HAVE TO BEAR SMALL LOSSES IN SHORT RUN . IF IT CAN BEAR THAT LOSSES THEN IT WILL REMAIN IN BUSINESS and earn huge in long run.