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394 CHAPTER 10 COMPETITIVE MARKETS: APPLICATIONS
Problem the demand equation, we find that the equilibrium
d
quantity Q 10 0.5(8) 6 million units.
(a) With no tax, what are the equilibrium price and
quantity? (b) With a $6 excise tax, there are two conditions that
must be satisfied:
(b) Suppose the government imposes an excise tax of (i) P P 6: there is a tax wedge between the
d
s
$6 per unit. What will the new equilibrium quantity market price P consumers pay and the net after-tax
d
be? What price will buyers pay? What price will sellers price P that sellers receive.
s
receive? (ii) Also, the market clears, so that Q Q , or
d
s
d
s
10 0.5P 2 P .
Solution
s
s
Thus 10 0.5(P 6) 2 P , so the price pro-
s
(a) With no tax, two conditions must be satisfied: ducers receive P $6 per unit. The price consumers
d
s
s
d
(i) P P (there is no tax wedge). Since there is only pay P P $6 $12 per unit. The equilibrium
d
one price in the market, let’s call it P*. quantity can be found by substituting P $12 into the
s
d
d
d
(ii) Also, the market clears, so that Q Q . demand equation: Q 10 0.5P 10 0.5(12)
Together these conditions require that 10 0.5P* 4 million units. (Alternatively, we could have substituted
s
2 P*, so the equilibrium price P* $8 per unit. The P $6 into the supply equation.)
equilibrium quantity can be found by substituting P*
$8 into either the supply or demand equation. If we use Similar Problems: 10.2, 10.6, 10.10, 10.17, 10.21
INCIDENCE OF A TAX
In a market with an upward-sloping supply curve and a downward-sloping demand curve,
an excise tax will increase the market price that consumers pay but will decrease the net
after-tax price that sellers receive. Which price will change more as a result of the tax: the
market price paid by buyers or the net, after-tax price received by sellers? In Learning-
By-Doing Exercise 10.1, the price consumers pay increases by $4 (rising from $8 to $12).
incidence of a tax A The price producers receive falls by $2 (decreasing from $8 to $6). The incidence of
measure of the effect of a a tax is the effect that the tax has on the prices consumers pay and sellers receive in a
tax on the prices consumers market. The incidence, or burden, of the tax is shared by both consumers and produc-
pay and sellers receive in a ers (in Learning-By-Doing Exercise 10.1, the larger share is borne by consumers).
market.
The incidence of a tax depends on the shapes of the supply and demand curves.
Figure 10.4 illustrates two cases. In both cases the equilibrium price with no tax is $30
per unit. However, the effects of a tax of $10 are quite different in the two markets.
In Case 1 the demand curve is relatively inelastic, and the supply curve is quite
elastic. The tax increases the amount consumers pay by $8 and reduces the amount
producers receive by $2. The price change resulting from the tax is larger for con-
sumers because demand is comparatively inelastic.
In Case 2 the supply curve is relatively inelastic, while the demand curve is com-
paratively elastic. Therefore, the tax has a larger impact on producers, decreasing the
price they receive by $8, while increasing the price consumers pay by only $2.
As shown in these two cases, a tax will have a larger impact on consumers if demand
is less elastic than supply at the competitive equilibrium, and a larger impact on produc-
ers if the reverse is true. At least for small price changes, it is reasonable to assume that
the demand and supply curves have approximately constant own-price elasticities, Q ,P
d
s ,
and Q ,P which means we can summarize the quantitative relationship between the in-
cidence of a tax and the price elasticities of supply and demand as follows:
¢P d Q ,P (10.1)
s
¢P s Q ,P
d