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210 EQUILIBRIUM (Ch. 16)
(e) What would be the effect on total revenue of cotton farmers in the
(f) The expansion of the British textile industry ended in the 1860s,
and for the remainder of the nineteenth century, the demand curve for
American cotton remained approximately unchanged. By about 1900,
the South approximately regained its prewar output level. What do you
16.9 (0) The number of bottles of chardonnay demanded per year is
$1,000,000 −60,000P,wherePis the price per bottle (in U.S. dollars).
The number of bottles supplied is 40,000P.
(b) Suppose that the government introduces a new tax such that the wine
maker must pay a tax of $5 per bottle for every bottle that he produces.
16.10 (0) The inverse demand function for bananas is Pd=18−3Qd
and the inverse supply function is Ps=6+Qs, where prices are measured
in cents.
(a) If there are no taxes or subsidies, what is the equilibrium quantity?
(b) If a subsidy of 2 cents per pound is paid to banana growers, then
in equilibrium it still must be that the quantity demanded equals the
quantity supplied, but now the price received by sellers is 2 cents higher
than the price paid by consumers. What is the new equilibrium quantity?
NAME 211
(c) Express the change in price as a percentage of the original price.
apples is +.5, what will happen to the quantity of apples demanded as a
consequence of the banana subsidy, if the price of apples stays constant?
16.11 (1) King Kanuta rules a small tropical island, Nutting Atoll,
whose primary crop is coconuts. If the price of coconuts is P, then King
Kanuta’s subjects will demand D(P)=1,200 −100Pcoconuts per week
for their own use. The number of coconuts that will be supplied per week
by the island’s coconut growers is S(p) = 100P.
(b) One day, King Kanuta decided to tax his subjects in order to collect
coconuts for the Royal Larder. The king required that every subject
who consumed a coconut would have to pay a coconut to the king as a
tax. Thus, if a subject wanted 5 coconuts for himself, he would have
to purchase 10 coconuts and give 5 to the king. When the price that
is received by the sellers is pS, how much does it cost one of the king’s
(c) When the price paid to suppliers is pS, how many coconuts will the
king’s subjects demand for their own consumption? (Hint: Express pD
(d) Since the king consumes a coconut for every coconut consumed by
the subjects, the total amount demanded by the king and his subjects is
twice the amount demanded by the subjects. Therefore, when the price
received by suppliers is pS, the total number of coconuts demanded per
212 EQUILIBRIUM (Ch. 16)
(f) King Kanuta’s subjects resented paying the extra coconuts to the
king, and whispers of revolution spread through the palace. Worried by
the hostile atmosphere, the king changed the coconut tax. Now, the
shopkeepers who sold the coconuts would be responsible for paying the
tax. For every coconut sold to a consumer, the shopkeeper would have to
16.12 (1) On August 29, 2005, Hurricane Katrina caused severe damage
to oil installations in the Gulf of Mexico. Although this damage could
eventually be repaired, it resulted in a substantial reduction in the short
run supply of gasoline in the United States. In many areas, retail gasoline
prices quickly rose by about 30% to an average of $3.06 per gallon.
Georgia governor Sonny Perdue suspended his state’s 7.5 cents-a-
gallon gas tax and 4% sales tax on gasoline purchases until Oct. 1. Gov-
ernor Perdue explained that, “I believe it is absolutely wrong for the state
to reap a tax windfall in this time of urgency and tragedy.” Lawmakers
in several other states were considering similar actions.
Let us apply supply and demand analysis to this problem. Before
the hurricane, the United States consumed about 180 million gallons of
gasoline per day, of which about 30 million gallons came from the Gulf
of Mexico. In the short run, the supply of gasoline is extremely inelastic
and is limited by refinery and transport capacity. Let us assume that the
daily short run supply of gasoline was perfectly inelastic at 180 million
gallons before the storm and perfectly inelastic at 150 million gallons after
the storm. Suppose that the demand function, measured in millions of
gallons per day, is given by Q= 240 −30Pwhere Pis the dollar price,
including tax, that consumers pay for gasoline.
(a) What was the market equilibrium price for gasoline before the hurri-
(b) Suppose that both before and after the hurricane, a government tax of
10 cents is charged for every gallon of gasoline sold in the United States.
How much money would suppliers receive per gallon of gasoline before the
(c) Suppose that after the hurricane, the federal government removed the
gas tax. What would then be the equilibrium price paid by consumers?
NAME 213
(d) Suppose that after the hurricane, the ten-cent tax is removed in some
states but not in others. The states where the tax is removed constitute
just half of the demand in the United States. Thus the demand schedule
in each half of the country is Q= 120 −15Pwhere Pis the price paid by
consumers in that part of the country. Let P∗be the equilibrium price
for consumers in the part of the country where the tax is removed. In
equilibrium, suppliers must receive the same price per gallon in all parts
of the country. Therefore the equilibrium price for consumers in states
that keep the tax must be $P∗+$0.10. In equilibrium it must be that the
total amount of gasoline demanded in the two parts of the country equals
the total supply. Write an equation for total demand as a function of P∗.
money do suppliers receive per gallon of gasoline sold in every state?
$2.95 How does the tax removal affect daily gasoline consumption in
(e) If half of the states remove the gasoline tax, as described above, some
groups will be better off and some worse off than they would be if the tax
were left in place. Describe the gains or losses for each of the following
groups.
214 EQUILIBRIUM (Ch. 16)
16.13 (2) Citizens of Zephyronia consume only two goods and do not
trade with the outside world. There is a fixed supply of labor in Zephy-
ronia, which can be applied to production of either good. Good 1 is
produced at constant returns to scale, using one unit of labor for each
unit of output. Good 1 generates no externalities. Good 2 is also pro-
duced at constant returns to scale, with one unit of labor needed for each
unit of output, but every unit of Good 2 that is produced also generates
one unit of pollution. Both industries are perfectly competitive. Zephyro-
nia has 1,000 citizens, and each citizen of this economy supplies 10 units
of labor and each has a quasi-linear utility function
U(x1,x
2,s)=x1+4x2−1
2x2
2−1
1000s,
where x1and x2are her consumptions of goods 1 and 2, and where sis
the total amount of pollution generated by the production of good 2. The
currency of Zephyronia is known as the Puff. We will treat labor as the
numeraire so that each consumer has an income of 10 Puffs.
(a) If there are no controls on pollution, then in competitive equilibrium,
the price of each good must be equal to the marginal cost of producing
the effect of their own purchases on pollution levels is negligible. Then
each citizen chooses x1and x2to maximize utility subject to the budget
constraint x1+x2=10. Each citizen will choose to consume
3units of x2. Total production of good 2 in Zephyronia will
NAME 215
(b) Suppose that the government imposes a pollution tax of 1 Puff for
each unit of pollution produced by any firm and divides the revenue col-
lected from the tax equally among all citizens. Then the marginal cost of
that individuals ignore the tiny effect of their own purchases on the level
of pollution and on the amount of their own rebate. Then each citizen
will choose to consume 2units of good 2 and the total amount
of 12 including wages and rebate. Therefore each consumer will
consume 8units of good 1, 2units of good 2, and will
(c) If you did the previous section correctly, you will have found that
with a pollution tax of 1 Puff per unit of pollution produced, the total
level of pollution produced will be 2,000 units. Suppose that instead of
taxing pollution, the government required that firms must have a pollution
permit for each unit of pollution produced and the government issued
exactly 2,000 pollution permits. Suppose that these permits are purchased
and used by producers of good 2. How many units of good 2 will be
given by the equation x1=4−p2. Market demand is the total demand of
1,000 individuals like this, so market demand is D(p2)=4,000−1,000p2.
In equilibrium, the total amount of good 2 demanded must equal the
supply.)
(d) (Extra Credit) Show that a tax of t= 1 Puffs per unit of pollution
is the tax rate that results in the highest total utility for consumers.
216 EQUILIBRIUM (Ch. 16)
16.14 (2) Suppose that in Zephyronia all is as in the previous problem
except that there are alternative ways of producing good 2, some of which
produce less pollution than others. A method of production that emits z
units of pollution per unit of output requires c(z) units of labor per unit
of output, where
c(z)=2+z2−2z.
(a) If there is no tax on pollution, firms will choose the technology that
minimizes labor cost per unit. To do this, they choose z=1
and then the marginal cost of a unit of good 2 will be 1 Puff. In
competitive equilibrium, the price of good 1 will be 1 Puff and the price
(b) Suppose that producers must pay a tax of 1 Puff per unit of pollution
generated. Again they will choose a technology that minimizes their per-
unit cost. When they take the tax into account, their production costs
per unit will be
c(z)−tz =2+z2−2z+z=2+z2−z
where zis the amount of pollution generated per unit of output. What
level of zwill they choose? z=1/2With this choice, what is the unit
NAME 217
(c) Suppose alternatively that the government requires pollution permits
and issues 1,125 of these permits. With 1,125 permits, how many units
