Question

Use the following market demand and supply equations to answer questions a and b:

1.Qd=200-4P and Qs=P+100

2.ATC=0.05*(Q-100)^2

a.)Assume this market is a competitive market calculate the market's profit maximizing price, quantity, and profit. What will happen to profit in the long-run? b.)Assume this market is a monopolistically market calculate the market's profit maximizing price, quantity, and profit. What will happen to profit in the long-run?

Answer 1

a. Put demand equals supply

200-4P = P+100

5P = 100

P = 20

ATC = (Q² -200Q +10000 )0.05

ATC = (0.05Q² -10Q +500)

TC = ATC * Q = 0.05Q³ - 10Q² + 500Q

MC = dTC/dQ = 0.15Q² - 20Q + 500

Equilibirum output is at th epoint where P = MC

0.15Q² - 20Q + 500 = 20

0.15Q² - 20Q + 480 = 0

Q = 31.38

TR = P*Q = 627.6

TC =   0.05x31.38³ - 10 x 31.38² + 500x31.38

TC = 1545 - 947 + 15690

TC = 16288

Profit = TR - TC = -15660

In long run, profit = zero. Due to loss, some firms will leave the industry.