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SUPPLY AND DEMAND: TAXES
2S.1 Taxes
Supply and demand analysis is a very useful tool for analyzing the effects of various
taxes. In this Web supplement, we consider a constant tax per unit of output. How will
the equilibrium price and quantity of a product be affected if a tax of T $10/unit is
levied on each unit sold by the producer? There are two equivalent ways to approach
this question. The first is to suppose that the tax is levied on the seller. In Figure 2S-1,
the line SS denotes the original supply schedule. At a price of P0 $25/unit, sellers
were willing to supply Q0 units of output. When a tax T 10 is levied on sellers, the
market price would have to be P0 10 $35/unit for them to get the same net payment
that they used to receive when the price was P0 $25/unit. At a price of $35/unit, then,
suppliers will offer the same amount of output they used to offer at a price of $25/unit.
The resulting after-tax supply schedule is the original supply schedule shifted upward
by T 10.
In Figure 2S-2, DD represents the demand curve facing the sellers who have been
taxed T $10 per unit of output. The effect of the tax is to cause the equilibrium quantity to fall from Q* to Q*1. The price paid by the buyer rises from P* to P*1, and the price,
net of the tax, received by the seller falls to P*1 10.
Note in Figure 2S-2 that even though the seller pays a tax of T on each product purchased, the total amount the seller receives per unit lies less than T below the old
equilibrium price. Note also that even though the tax is collected from the seller, its
effect is to increase the price paid by buyers. The burden of the tax is thus divided
between the buyer and the seller.
Algebraically, the seller’s share of the tax, denoted ts, is the reduction in the price the
seller receives, divided by the tax:
ts P* 1P*1 T2
(2S.1)
T
2S.1 TAXES
2S-1
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FIGURE 2S-1
A Tax of T $10/Unit
Levied on the Seller Shifts
the Supply Schedule
Upward by T Units
The original supply
schedule tells us what
price suppliers must
charge in order to cover
their costs at any given
level of output. From the
seller’s perspective, a tax
of T $10/unit is the
same as a unit-cost
increase of $10. So the
new supply curve lies
$10/unit above the
old one.
FIGURE 2S-2
Equilibrium Prices and
Quantities When a Tax of
T $10/Unit Is Levied
on the Seller
The tax causes a
reduction in equilibrium
quantity from Q* to Q*1 .
The new price paid by
the buyer rises from P* to
P*1 . The new price
received by the seller falls
from P* to P*1 10.
Price ($/unit)
S'
S
T = 10
35 = P0 + T
25 = P0
S'
S
Quantity (units)
Q0
Price ($/unit)
S'
D
T = 10
S
P *1
P*
P *1 – 10
S'
D
S
Q *1
Quantity (units)
Q*
Similarly, the buyer’s share of the tax, tb, is the increase in price (including tax)
divided by the tax:
tb P*1 P*
T
(2S.2)
EXERCISE 2S-1
Verify that ts tb 1.
In general, tb and ts depend on the shapes of the supply and demand schedules. If, for
example, supply is highly unresponsive to changes in price, tb will be close to zero, and
ts will be close to 1. Conversely, if demand is highly unresponsive to price, tb will be
close to 1, and ts will be close to zero. These claims amount to a statement that a tax
tends to fall most heavily on the side of the market that can least escape it. If buyers
have no substitute products to which they are prepared to turn, the lion’s share of the
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tax will be passed on to them by suppliers. But if suppliers have no alternative other
than to go on supplying a product, most of the burden of a tax will fall on them. As long
as the supply curve is positively sloped and the demand curve is negatively sloped,
however, both ts and tb will be positive.
The second way of analyzing the effect of a tax of T $10 per unit of output is to imagine that the tax is collected directly from the buyer and to analyze how that would affect
the demand curve for the product. In Figure 2S-3, the demand curve before the imposition
of the tax is denoted by the line DD. At a price of P1, buyers would demand a quantity of
Q1. After the imposition of the tax, the total amount that buyers have to pay if the product
price is P1 will be P1 10. Accordingly, the quantity the buyers demand falls from Q1 to
Q2. In like fashion, we can calculate the quantity demanded at any other price after imposition of the tax. The resulting after-tax demand curve will be the line DD in Figure 2S-3.
It is simply the original demand curve translated downward by $10/unit.
If line SS in Figure 2S-4 denotes the supply schedule for this market, we can easily trace
the effects of the tax on the equilibrium price and quantity. The equilibrium quantity falls
FIGURE 2S-3
The Effect of a Tax of T $10/Unit Levied on the
Buyer
Before the tax, buyers
would buy Q1 units at a
price of P1. After the tax,
a price of P1 becomes
P1 10, which means
buyers will buy only Q2.
The effect of the tax is to
shift the demand curve
downward by $10/unit.
Price ($/unit)
D
P1 + 10
D'
P1
T = 10
D
D'
Q2
FIGURE 2S-4
Equilibrium Prices and
Quantities After
Imposition of a Tax
of T $10/Unit Paid
by the Buyer
The tax causes a
reduction in equilibrium
quantity from Q* to Q*2 .
The new price paid by
the buyer rises from P* to
P*2 10. The new price
received by the seller falls
from P* to P*2.
Quantity (units)
Q1
Price ($/unit)
D
S
D'
P *2 + 10
P*
P *2
T = 10
S
D'
Q *2
Q*
D
Quantity (units)
2S.1 TAXES
2S-3
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from Q* to Q*2, and the equilibrium price falls from P* to P*2. The total price paid by the
buyer after imposition of the tax rises to P*2 10.
Is the effect of a tax on the seller any different from the effect of a tax levied on the
buyer? Not at all. To illustrate, suppose the supply and demand curves for a market are
given by P Qs and P 10 – Qd, respectively, and consider first the effect of a tax of
$2 per unit of output imposed on the seller. Figure 2S-5(a) shows the original supply
and demand curves and the new after-tax supply curve, SS. The original equilibrium
price and quantity are both equal to 5. The new equilibrium price to the buyer (inclusive
of tax) and quantity are $6 per unit and 4 units, respectively. The price received by sellers, net of the tax, is $4 per unit.
Now, consider a tax of $2 per unit of output imposed on the buyers. Figure 2S-5(b)
shows the original supply and demand curves and the new after-tax demand curve,
DD. Note that the effects on price and quantity are exactly the same as in the case of
the tax levied on sellers shown in panel (a).
FIGURE 2S-5
A Tax on the Buyer Leads
to the Same Outcome as
a Tax on the Seller
The price received by
sellers (net of the tax), the
price paid by buyers
(including tax), and the
equilibrium quantity will
all be the same when the
tax is collected from
sellers (panel [a]) as when
it is collected from buyers
(panel [b]).
Price
Price
10 D
10 D
S'
8 D'
S
T=2
6
5
4
S
6
5
4
T=2
2 S'
D
S
4 5
(a)
10
Quantity
S
4 5
(b)
D'
8
D
10
Quantity
EXERCISE 2S-2
Consider a market whose supply and demand curves are given by P 4Qs and P 12 2Qd,
respectively. How will the equilibrium price and quantity in this market be affected if a tax of
$6 per unit of output is imposed on sellers? If the same tax is imposed on buyers?
When tax revenues have to be raised, political leaders may find it expedient to propose a sales tax on corporations because “they can best afford to pay it.” But careful
analysis of the effects of a sales tax shows that its burden will be the same whether it is
imposed on buyers or sellers. The legal incidence of the tax (whether it is imposed on buyers or on sellers) has no effect on the economic incidence of the tax (the respective shares
of the tax burden borne by buyers and sellers). Economically speaking, the entity from
which the tax is actually collected is a matter of complete indifference.
A word of caution: When we say that the economic burden of the tax does not depend
on the party from whom the tax is directly collected, this does not mean that buyers and
sellers always share the burden of taxes equally. Their respective shares may, as noted,
be highly unequal. The independence of legal incidence and economic incidence simply
means that the burden will be shared in the same way no matter where the tax is placed.
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QUESTIONS FOR REVIEW
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political reasons, you want the burden of the tax to
fall mostly on consumers, not firms (who have been
substantial contributors to your campaign fund).
What should you look for when picking a product
to tax?
2S1. The steeper the demand curve for some good relative
to the supply curve for that good, the greater the proportion of a tax on that good that will fall on buyers.
True or false? Explain, using a diagram.
2S2. Suppose you are an elected government member
and need to collect revenue by taxing a product. For
PROBLEMS
2S1. The government, as a revenue-generating measure, imposes a tax of $2/kg on the retail price
of gumdrops. It collects the tax from gumdrop sellers. The original supply and demand schedules for gumdrops are as shown in the following diagram. Show, in the same diagram, how
the short-run equilibrium price and quantity of gumdrops will be affected by the tax. Label all
important points clearly. How much tax revenue does the government receive?
Price ($/kg)
6
S
5
4
3
2
1
D
0
1
2
3
4
5
6
Quantity (tonnes/yr)
2S2. In the market for gumdrops described in Problem 2S1 (with no tax), suppose that a price
floor of $4/kg results in sales of only 2 tonnes/year. If the price floor was removed, describe
a transaction that would make some buyers and sellers better off without harming others.
2S3. Suppose the gumdrop market in Problem 2S1, with a tax of $2/kg, experiences growth in
the demand for gumdrops because of new-found medical uses. The new demand curve is
P 8 Q, where P is in $/kg and Q is in tonnes. Find the change in government tax revenue due to the heightened demand for gumdrops.
2S4. Suppose instead that the gumdrop market in Problem 2S2, with no tax but a price floor at
$4/kg, suffers a reduction in supply. The new supply curve is P 2 Q.
a. How does excess supply change due to the reduction in supply?
b. Is the price floor still binding (does it cause price to be above its equilibrium level)?
2S5. The market for DVDs has supply and demand curves given by P 2Qs and P 42 Qd,
respectively, where P is in $/DVD and Qs and Qd are in DVDs. Construct and label a
diagram.
a. (i) How many units will be traded at a price of $35? (ii) At a price of $14? (iii) Which
participants will be dissatisfied at these prices?
b. What quantity of DVDs at what price will be sold in equilibrium?
c. What is the total revenue from DVD sales? Where is it shown on your diagram?
PROBLEMS
2S-5
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2S6. Suppose that in the market described in Problem 2S5, the government levies a tax of $9 on
each DVD sold, collected from sellers.
a. What quantity of DVDs will be sold in equilibrium?
b. (i) What price do buyers pay? (ii) How much do they spend in total?
c. (i) What after-tax price do sellers now receive? (ii) What is their total after-tax
revenue?
d. How much money goes to the government?
e. Show the above results graphically.
2S7. For the tax described in Problem 2S6, (a) what fraction of the tax do the sellers bear and
(b) what fraction of the tax do the buyers bear?
*2S8. The Frug, a subcompact car, is produced only in the small country of Leutonia. The Canadian government, concerned by high levels of Frug imports, negotiates a “voluntary”
import quota on Frugs with Leutonian Frug exporters. Some Canadian economic advisers
recommend using an import tax (or tariff) instead. If the tariff (at $T per Frug) was set to
produce the same reduction in imports as the quota,
a. How will the prices paid for Frugs by Canadian consumers compare under the two
policies?
b. How much revenue will Frug exporters receive?
c. How much import tariff revenue will the Canadian government receive under each
policy?
Show your results in a diagram.
*2S9. Because of concerns that barbecuing meat using charcoal may cause cancer, the government decides to impose a 100 percent tax at the retail level on charcoal briquettes. Suppose
the daily demand for charcoal was P 120 2Q and the supply was P 30 Q, where P
is in dollars and Q is the number of 10-kg bags of charcoal sold daily.
a. Give the before-tax charcoal price and quantity exchanged.
b. Give the after-tax charcoal price to buyers, the quantity exchanged, and total tax
revenues.
c. How is the tax divided among sellers and buyers?
2S10. In the Gizmo market, supply is given by the equation P 4Q, while demand is given by
P 20, where P is price in dollars per unit and Q is quantity in units per week.
a. Find the equilibrium price and quantity (using both algebra and a graph).
b. If sellers must pay a tax of T $4 per unit, what happens to the quantity exchanged,
the price buyers pay, and the price sellers receive (net of the tax)?
c. How is the burden of the tax distributed across buyers and sellers and why?
2S11. Repeat Problem 2S10, but instead suppose the buyer pays the tax, demand is P 28 Q,
and supply is P 20.
2S12. Suppose the supply of a good is given by the equation P Q and demand is fixed at Q 12 units per week, with P in dollars per unit.
a. Find the equilibrium price and quantity.
b. Suppose the government levies a tax equal to $4 per unit on sellers of the good. Find
the equilibrium quantity, price paid by buyers, and price received by the sellers (net
of taxes).
c. How is the tax burden distributed and why?
*Problems marked with an asterisk are more difficult.
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ANSWERS TO IN-SUPPLEMENT EXERCISES
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2S-1. ts tb [(P* P*1 T) (P*1 P*)]/T T/T 1.
2S-2. The original price and quantity are given by P* $8/unit and Q* 2 units, respectively.
The supply curve with the tax is given by P 6 4Qs. Letting P and Q denote the new
equilibrium values of price and quantity, we now have 6 4Q 12 2Q, which yields
Q 1 unit. P $10/unit, where P is the price paid by buyers. P 6 $4/unit is the
price received by sellers. Alternatively, the demand curve with a tax of $6/unit levied on
buyers is given by P 6 2Qd, and we have 4Q 6 2Q, which again yields Q 1 unit.
P $4/unit, where P is the price received by sellers. P T P 6 $10/unit is the
price paid by buyers, including the tax.
ANSWERS TO IN-SUPPLEMENT EXERCISES
2S-7