Question

tdSDoorstope, INC.(DD is a monopolist in the doorstop industry its total cost function 1s oiven by the quadratic function of output Cla) 100-5Q+. The inverse demand function for doorstops Pis given by the linear function PIQ)-55-2Q. Nte that the margnal cost C'(Q) is not constant. (Also, it happens to be negative for 0 s Q <2

Answer 1

Answer:

Given

A)

Cost function C(Q)=100-5Q+Q^2

MC=dC/dQ=2Q-5

MC=2Q-5

P=55-2Q

TR=P*Q=55Q-2Q^2

So MR=dTR/dQ=55-4Q

So for profit maximization for monopolistic firm

MR=MC
55-4Q=2Q-5

Q=10

P=55-2*10=$35

From Above graph we find that CS=area of triangle ABE=0.5*(55-35)*10=$100

From Above graph we find that PS=area of trapzoid EBCD=(35-15)*10+0.5*(15-(-5)*10=$300

Since at MC=-5 , Qs=0

So TS=CS+PS=100+300=$400

B) MC=2Q-5

for price taker firm profit maximization

P=MC

55-2Q=2Q-5

Q=15 units

C) for Q=15 units

P=55-2*15=$25

TR=P*Q=15*25=$375

C(Q)=100-5*15+15^2=$250

So Profit= 375-250=$125