Question

1. Consider a firm whose demand curve is given by Q = 300 – 2P and whose marginal cost is given

by   MC = 70 + 3Q .

a. determine the profit-maximizing output.   

b. determine the profit-maximizing price.   

c. suppose that demand increases to Q = 500 – 2P , while marginal cost remains the same.
    what happens to the firm’s profit-maximizing price and output? (show your work)

d. is this result similar to what would happen to price and quantity in a perfectly competitive
    market? Explain briefly.

Answer 1

1.
a.
Q=300-2P
2P=300-Q
P=150-0.5Q
TR=PQ=(150-0.5Q)Q
MR=dTR/dQ=150-Q
MC=70+3Q
For profit maximization MC=MR
70+3Q=150-Q
3Q+Q=150-70
4Q=80
Q=20
b.
P=150-0.5(20)=140
c.
if Q=500-2P
2P=500-Q
P=250-0.5Q
TR=PQ=(250-0.5Q)Q
MR=dTR/dQ
MR=250-Q
MC=70+3Q
Mc=MR
250-Q=70+3Q
4Q=180
Q=45
P=250-0.5(45)=227.5
d.
No, the outcomes will not be same.For a perfectly competitive firm, the profit is maximized when P=MC and the demand curve for a perfectly competitive firm is a horizontal line given by P=MR=AR not a downward sloping curve.A perfectly competitive firm achieved both productive and allocative efficiency.It would have a lower price and higher quantity.