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714 CHAPTER 17 EXTERNALITIES AND PUBLIC GOODS

MSB = MPB + MEB

Supply (MC)
A

Price B Supply – subsidy
per unit
1
MSB at Q
H
E
s N
P
J
M Optimal subsidy
F
per unit = P – P*
s
T
P 1
P* G K L
MPB = market demand
R
U
MEB
V W
Q*
Q 1
Market quantity
Difference in Benefits
Social Optimum between Social
Equilibrium (equilibrium Optimum and Equilibrium
(no subsidy) with subsidy) with No Subsidy
Private consumer B E F B E F G K L G K L
surplus
Producer surplus G R F G R J M F J M
Benefit from externality A H J A H J M N T M N T
Government cost zero F G J K F G J K
from subsidy L M T L M T

Net social benefits A B E F A B E F G M N
(private consumer G H J R H J M N R
surplus producer surplus
benefit from externality
government cost)

FIGURE 17.6 Optimal Subsidy with a Positive Externality
With a positive externality, the marginal social benefit MSB equals the marginal private benefit MPB
plus the marginal external benefit MEB. In a competitive market with no correction for the exter-
nality, the equilibrium is determined by the intersection of the demand curve (i.e., the marginal
private benefit curve MPB) and the supply curve. The equilibrium price is P 1 and the quantity is Q 1 .
The socially optimal output is Q*, determined by the intersection of the supply curve and
the marginal social benefit curve. The externality leads the market to underproduce by the
amount (Q* Q 1 ). The social optimum can be reached with a government subsidy. The optimal
s
subsidy per unit is the difference between the price received by producers P and the price paid
by consumers P* at the efficient quantity Q*. The optimal subsidy eliminates the deadweight
loss (area M N) that would arise without the subsidy.