N U M E R I C A L P R O B L E M S
1. Joe Higgins is thinking about how much time to spend studying for a biology exam tomorrow. Using “utility units” he measures the benefits and costs of study; his calculations are shown in the following
table.
a. Fill in the fourth row for net benefit in the table. Use the midpoint convention to emphasize that the net benefit is a marginal value showing the gain as hours spent increase by one-hour increments.
b. Using a graph similar to Panel (a) of Figure 6.1 show the marginal benefit curve and verify that the area under the curve at 3 hours of study corresponds to the total benefit of that much study.
(Hint: Remember that marginal values are plotted at the midpoints of the corresponding intervals
on the horizontal axis.)
c. Use a graph similar to Panel (b) of Figure 6.1 to show the marginal cost curve and verify that the
area under the curve at 3 hours of study corresponds to the total cost of that much study.
d. Use a graph similar to Panel (a) of Figure 6.6 to combine the marginal benefit and marginal cost
curves you drew in parts (a) and (b).
e. Based on the marginal decision rule, how many hours should Joe spend studying for his biology
exam?
2. Now suppose some friends of Joe’s call to say they are having a party tonight. Joe calculates that the party
is now his best alternative to study, and he increases his estimate of the cost of each hour of study. One
hour of study now costs 70; two hours cost 140; three hours 210, four hours 280; five hours 350; and six
hours 470.
a. Draw the new marginal benefit and marginal cost curves as in Problem 1, part (d):
b. Based on the marginal decision rule, identify the new solution that maximizes the net benefit of
study time.
3. The local gasoline market in a particular city has demand and supply curves given by the following data.
(All quantities are in millions of gallons per month.)
Price per gallon $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00
Quantity demanded 6 5 4 3 2 1 0
Quantity supplied 0 1 2 3 4 5 6
a. Plot the demand and supply curves, and determine the equilibrium price and quantity.
b. Show the areas of consumer and producer surplus.
c. Now suppose that the community determines that each gallon of gasoline consumed imposes
$0.50 in pollution costs. Accordingly, a $0.50-per-gallon tax is imposed. The tax is imposed on
sellers of gasoline, and it has the effect of increasing by $0.50 the price required to induce the
quantities supplied in the table. For example, a price of $2.00 is now required for a quantity of 1
million gallons to be supplied each month. Plot the new supply curve.
d. Approximate the new equilibrium price and output.
e. Does the price increase by the full amount of the tax? If not, explain why.
f. Would your answer be different if the demand for gasoline were perfectly inelastic?
4. The flu vaccination market has the demand and supply curves given by the following data. (All quantities
are in thousands.)
Price per vaccination $10 $15 $20 $25 $30
Quantity demanded 90 80 70 60 50
Quantity supplied 50 60 70 80 90
a. Plot the demand and supply curves, and determine the equilibrium price and quantity.
b. Show the areas of consumer and producer surplus.
CHAPTER 6 MARKETS, MAXIMIZERS, AND EFFICIENCY 163
c. Now suppose that each vaccination given generates an external benefit, as those who do not get
vaccinated are less likely to get the flu when others do get vaccinated. As a result, suppliers
receive a $10 subsidy from the government for each vaccine. For example, if consumers pay $10
per vaccination, suppliers receive $20, so only $10 from consumers is required to induce suppliers
to offer 70,000 vaccinations per month. Plot the new supply curve.
d. Determine the new equilibrium price and quantity.
e. Does the price fall by the full amount of the subsidy? If not, explain why.
f. What is the total amount that consumers now pay for the new equilibrium quantity of
vaccinations?
g. What is the total subsidy that suppliers receive from the government at the new equilibrium
quantity of vaccinations?
5. Given the following information about the supply of and demand for apples:
Price perpound Quantity demanded (pounds permonth) Quantity Supplied (pounds permonth
$0.50 12,000 0
0.75 10,000 2,000
1.00 8,000 4,000
1.25 6,000 6,000
1.50 4,000 8,000
1.75 2,000 10,000
2.00 0 12,000
a. Draw a graph similar to Figure 6.12
b. Assuming the market for apples meets the efficiency condition, show the equilibrium price and
quantity that maximizes net benefit to society.
c. Identify the area of consumer surplus and the area of producer
