Answer to Question #279168 in Economics of Enterprise for munna

Question

In a perfectly competitive and constant cost industry, all firms are identical. If the market demand function is: QD = 600P, a typical firm's cost function is: TC = 9³ - 20q² + 120q.

a. In the long run, what is the firm's equilibrium production decision?

b. In the long run, what is the market equilibrium price and quantity? What is the industry's long-run supply curve?

c. In the long run, how many firms will stay in the industry?

d. If the government decide to impost a $7 tax per unit, what is the new long-run equilibrium market price and quantity?

e. How many firms are producing after the tax?

Answer 1

a. In the long run the firm's equilibrium production decision is:

P = ATC = MC,

$ATC = TC/q = q^2 - 20q + 120,$

$MC = TC'(q) = 3q^2 - 40q + 120,$

$q^2 - 20q + 120 = 3q^2 - 40q + 120,$

$2q^2 - 20q = 0,$

q(q - 10) = 0,

q = 0 doesn't satisfy, so q = 10 units.

b. In the long run the market equilibrium price is P = Q/600 and quantity Q = q×N depend on the total quantity of firms N. The industry's long-run supply curve is the increasing part of its long run marginal cost curve above the minimum of its long run average cost.

c. In the long run the amount of N firms will stay in the industry.

d. If the government decide to impose a $7 tax per unit, the new long-run equilibrium market price will increase and quantity will decrease.

e. Less firms are still producing after the tax.