Suppose that all firms in a constant-cost industry have the following

Suppose that all firms in a constant-cost industry have the following long-run cost curve:

c(q) = 4q2 + 100q + 100
The demand in this market is given by QD = 1280 – 2p. Suppose the number of firms in the market is restricted to 80
a. Derive the supply curve with this restriction. Find the market equilibrium price and quantity with the restriction.
b. If firms are allowed to buy and sell these permits in an open market, what will be the rental price of permits? Will firm’s that own permits make profit? Briefly explain.
c. How much deadweight loss is generated by the permit system? Provide a graph showing the region of this deadweight loss.
d. Suppose the government abandons the permit system and simply imposes a fixed fee on firms in the market. If the fee is set equal to the permit price you found in c., what will be the equilibrium price, quantity, number of firms and deadweight loss?

ANSWER

a. Each firm sets p = MC:
p = 8q + 100
The individual firm’s supply is then
q = (p – 100 )/8
80 identical firms yields the market supply
Q = 80q = 10p – 1000
Equate to demand:
10p – 1000 = 1280 – 2p
12p = 2280
p = 190, Q = 900
b. Firm’s will earn not profits but RENTS. The rent will equate the firm’s profits to zero:
Rent = 406.25
This will be the permit price.
c. Without the permits, the market price will fall to the breakeven price:
AC = 4q + 100 + 100/q = 8q + 100 = MC
4q = 100/q
q = 5, p* = 140
The market quantity is Q* = 1000
The Supply curve with the restriction will intersect the supply without the restriction at a quantity of Q = 400.
Thus, DWL = .5(1000 – 400 )(190 – 140 ) = 15,000
d. The resulting price, quantity and number of firms will equal the outcome with the restriction. Thus, the DWL will remain 15,000. The rent firm’s earned from permits will now be collected in fees by the government.