rev_20externalities_new - Externalities Chapter 20 1 Two...

Externalities
Chapter 20
1. Two firms are located on adjacent properties. The first firm generates smoke as a byproduct
of its production process. The smoke imposes cost on the other firm. The first firm produces
X according to the cost function: C
X
=0.5X
2
+7X+1845. The second firm produces y
according to the cost function C
Y
=0.038Y
2
+12X. Both firms sell their products in perfectly
competitive markets with P
X
=70 and P
Y
=14.06.
a) Find the optimal X and Y if the firms act independently. What are the profits for each
firm?
b) Find the optimal X and Y if the firms merge. What are the profits for the joint firm?
Explain why profits are different in part a and part b.
c) Find the Pigouvian tax that will lead the socially efficient amount of X. Discuss the
strengths and weaknesses of the tax approach for dealing with externalities.
Answer:
a) X=63, Y=185, profit for first firm is 139.5 and for second is 544.55.
b) X=51, Y=185, profit for joint=67.5+688.55. When the firms are separate, the first firm
does not account for the costs that it imposes on the second. With the merger, the
externality is internalized.
c) tax is $12 per unit of X on firm 1's output. The tax does lead to the efficient level of
output, but the government may not be able to estimate the true cost of the externality
and firm 2 had an incentive to overstate its losses to the government. Also, the
government may respond more to political incentive than economic costs.
2. Two firms are located on adjacent properties. The first firm generates smoke as a byproduct
of its production process. The smoke imposes cost on the other firm. The first firm produces
X according to the cost function: C
X
=0.125X
2
+25X+2300. The second firm produces Y
according to the cost function C
Y
=0.2Y
2
+10Y+350+15X. Both firms sell their products in
perfectly competitive markets with P
X
=69 and P
Y
=62.
a) Find the optimal X and Y if the firms act independently. What are the profits for each
firm?
b) Find the optimal X and Y if the firms merge. What are the profits for the joint firm?
Explain why profits are different in part a and part b.
c) Find the Pigouvian tax that will lead the socially efficient amount of X. Discuss the
strengths and weaknesses of the tax approach for dealing with externalities.
d) Discuss how a property-rights approach could be used to reach an efficient solution to
this type of externality.
Answer:
a) X=176, Y=130, profit for first firm is 1572 and for second is 390.
b) X=116, Y=130, profit for joint=1122+1290=2412 as compared with 1962 before
merger. When the firms are separate, the first firm does not account for the costs that
it imposes on the second. With the merger, the externality is internalized.
c) tax is $15 per unit of X on firm 1's output. The tax does lead to the efficient level of
output, but the government may not be able to estimate the true cost of the externality
and firm 2 had an incentive to overstate its losses to the government. Also, the
government may respond more to political incentive than economic costs.