Question

1 Production Externality A barbecue restaurant on Monroe Street has a (private) marginal cost function given by MC = 8 + 0.10%, where QⓇ is the quantity supplied, and MC is measured in dollars. The inverse demand function for the product is given by P = 25 -0.52", where Q" is the quantity demanded and P is the price. Production at the restaurant spreads a barbecue odor through the neighborhood, and the marginal external cost is estimated to be constant at $2. 1. What is the equilibrium amount of food sold by the restaurant? 2. What is the equilibrium price in this market? 3. What is the socially-optimal quantity in this setting? 4. What is the socially-optimal price?

Answer 1

1. The firm in consideration is a monopoly firm. The equilibrium amount of food sold would be where given marginal private cost is equal to marginal revenue
1 R = (TR} = (PQ) = (250 - 0.52}
or
MR= 25-0
, which would be where or
8+0.10 = 25-0
or
1.10 = 17
or
W = 15.45
units. This would be the monopoly output.

2. The equilibrium price would be as
p. = 25 -0.50 W
or
pl = 25 -0.5 * 15.45
or
pW = 17.27
dollars.

3. The marginal social cost would be as , for MEC be the marginal external cost. We have
MSC = 8 +0.10 + 2
or
MSC = 10+ 0.10
. The socially optimal setting would be where MSC would be equal to marginal social benefit of
MSB = 25 -0.50
(the MSB is the demand curve itself, as there is no consumption externality). This would be where or
10+ 0.10 = 25 -0.50
or
0.6Q = 15
or
Q = 25
units.

4. The socially optimal price would be
pe= 25 -0.500
or
po = 25 -0.5*25
or
pe = 12.5
dollars.