Question

37. In a perfectly competitive and constant-cost industry demand is given by Q = 2000 - 2P. The short total cost function at the scale of production that minimizes long-run costs for each identical firm is TC = 1000 + 100q + 10q2.

A. What will the long-run price be in this industry? How many firms will there be in long-run equilibrium?

B. What is the equation of the short-run supply curve if the industry is in long-run equilibrium?

C. Suppose that demand in this industry increases to: Q = 4000 - 2P. What will the new long run price be in this industry and how many firms will there be?

d. Describe how the industry will adjust to reach the new long-run equilibrium and illustrate your answer by drawing a graph of the firm and a graph of the industry.

Answer 1

a) ATC= MC=P

ATC=$\frac{1000}{q}+ 100+10q$

MC=$100+ 20q$

$\frac{1000}{q}+ 100+10q= 100+ 20q$

$\frac{1000}{q}+10q-20q= 0$

$10q^2= 1000$

$q^2= 100$

q= 10

P= 100+20(10)= 300

Number of firms in the industry

market Quantity (Q*) = 2000- 2(300)= 1400

nq= Q*

n=$\frac{Q*}{q}=\frac {1400}{10}= 140$

b) minLRATC=LR supply

c) New Price

Q* 4000- 2(300)= 2400

n= $\frac{2400}{10}= 240$

d)