Question

In a country, there exists 10,000 firms that are producing cars. Their production function
is: f(K,L)=K 1/3 L 2/3 and all of them have input prices for labor equaling $1 and for capital
equaling $256.
a) Find the long run marginal cost and average costs for each of these firms.
b) Find the long run supply for the whole industry.
c) Assume that these cars are only consumed in the country with demand function
x(p)=36000/p. Using the market supply you found in part (b), find the competitive
equilibrium price and quantity of cars, each firm’s output, and each firm’s profits.
d) If the demand for cars in this country changes to x(p)=24000/p, do we see a change in
results? If yes, how?

Answer 1

A)

LRMC=∆TC/∆Q=12

LRAC=TC/Q=12

B)Long run supply curve will be horizontal at p=12( minimum average cost)

C) Long run Equilibrium price Equal to Minimum average cost =12

Quantity=36000/12=3000

Each firm output=3000/10,000=0.3

Profit=0

D) new Equilibrium price=12 ( same)

Quantity=24000/12=2000

Each firm output=2000/10000=0.2

Profit=0