UBC
Principles of Microeconomics
Solution to Selected Review Questions #5
1. (moderate) There are three industrial firms in a Happy Valley.
Firm
A
B
C
Initial Pollution Level
70 units
80 units
50 units
Cost of Reducing Pollution by 1 Unit
$20
$25
$10
The government wants to reduce pollution to 120 units so it gives each firm 40
permits.
a. If trade is not allowed what is the total cost of pollution control?
b. If trade is allowed, who sells and who buys permits and how many do they
sell or buy? What is the total cost of pollution control with trade?
a. If the permits could not be traded, then firm A would have to reduce its pollution
by 30 units at a cost of $20 x 30 = $600, firm B would reduce its pollution by 40
units at a cost of $25 x 40 = $1,000, and firm C would reduce its pollution by 10
units at a cost of $10 x 10 = $100. The total cost of pollution reduction would be
$1,700.
b. One permit is worth $25 to firm B, $20 to firm A, and $10 to firm C, since that is
the cost of reducing pollution by one unit. Since firm B faces the highest costs of
reducing pollution, it will keep its own 40 permits and buy 40 permits from the
other firms, so that it can still pollute by 80 units. That leaves 40 permits for
firms A and C. Since firm A values them most highly, it will keep its own 40
permits. So it must be that firm C sells its 40 permits to firm B. Thus firm B does
not reduce its pollution at all, firm A reduces its pollution by 30 units at a cost of
$20 x 30 = $600, and firm C reduces its pollution by 50 units at a cost of $10 x 50
= $500. The total cost of pollution reduction is $1,100. Thus trade saves $600
cost of pollution control (compare with costs in a).
2.
(moderate) It is well known that we can use either Pigouvian Tax or
Tradable Pollution Permits to control pollution. As shown in the
diagram, both the policy instruments lead to the same result.
a. Now suppose there is a sharp improvement in the technology for
pollution control. How will this improvement in technology affect
the level of pollution under the Pigouvian tax?
b. How will this improvement affect the level of pollution under the
Tradable Pollution Permits?
$
Supply of
pollution permits
Pigouvian tax
t
Demand for
pollution rights
Q
Pollution (Q)
An improvement in the technology for controlling pollution would reduce the
demand for pollution rights, shifting the demand curve to the left. In the
figures below, the improvement in technology shifts demand curve for
pollution rights from D1 to D2.
a. With a Pigovian tax, the price of pollution remains unchanged and the
quantity of pollution declines from Q1 to Q2.
b. With pollution permits, the price of pollution permits declines from P1 to P2
and the quantity of pollution is unchanged.
3. (easy) Greater consumption of alcohol leads to more motor vehicle accidents and,
thus imposes costs on people who do not drink and drive.
a. Illustrate the market for alcohol. How will the market equilibrium
level of alcohol consumption differ from that of optimal consumption
level?
b. On your diagram show the deadweight loss caused by overconsumption of alcohol.
c. What is the level of Pigouvian tax that can induce alcohol consumers
to reduce consumption to optimal level?
$
Supply
A
Pm ar ke t
Popt
B
C
Private D
Social D
Qo pt
Qm ar ke t
Alcohol
a.
The social value/demand curve is below the (private) demand curve
because of the negative externality from increased motor vehicle accidents
caused by those who drink and drive. The market equilibrium level of
alcohol consumption is Qmarket and the efficient level is Qopt.
b.
The deadweight loss of the market equilibrium = area ABC.
c.
A Pigouvian tax equal to the Marginal External Harm (at the optimal
level) will shift the private demand curve to the left such that this new
private demand curve after tax will coincide with the social demand curve.
Consequently, the private optimal level of consumption (in the face of
taxation) will be equal to the socially optimal level of consumption.
4. (hard) UBC has $100 million dollars that it can spend for cancer research
or other educational activities. If it gets $10 million grant from the
provincial government for cancer research (Note this $10 million can be
used only for cancer research),
a. How will UBC’s new budget line look like?
b. Show the situation whereby this conditional grant provides UBC with
lower utility than when it gets the grant without any conditions (i.e. it
can use the grant as it wishes).
(This question is for your practice)
5. (moderate) Jennifer divides her income between coffee and croissants.
An early frost in Brazil causes a large increase in the price of coffee in
Canada.
a. Show the effect of the frost on Jennifer’s budget constraint.
b. Show the effect of frost on Jennifer’s optimal consumption assuming
that the substitution effect outweighs the income effect for croissants.
a.
Since the price of coffee rises, her budget constraint swivels from BC1 to
BC2.
b.
If the substitution effect outweighs the income effect for croissants,
Jennifer buys more croissants. In the case of coffee, both substitution and
income effect lead Jennifer to have less coffee. She moves from point A to
point B.
If the income effect outweighs the substitution effect for croissants, Jennifer buys
fewer croissants. However, in the case of coffee, she will consume less coffee due to
both income and substitution effects, moving her from point A to point B.
6.
(tricky) Keyboards and Computers are perfect complements. With the help
of a diagram, show the effect of an increase in the price of Keyboards on the
consumption of both Keyboards and Computers (show both income and
substitution effects).
Since Keyboards and computers are complements, the indifference curves are L
shaped and consumers will always consume them in a fixed proportion (for
example (2, 2) or (1, 1)). With the increase in the price of Keyboards, the
consumption will decrease from say (2, 2) to say (1, 1). Since consumers will not
substitute to computers because of the decrease in the price of Keyboards there is
no substitution effect (or substitution effect is zero). The movement from (2, 2) to
(1, 1) with the decrease in utility from U1 to U2 is purely due to income effects.
Computers
2
U1
1
U2
BL after P
incresase
1
2
BL before Increase
in P of keyboards
Keyboards
7. Jim buys only milk and cookies.
a. In 2004, Jim earns $100, milk costs $2 per litre, and cookies cost $4 per
dozen. Draw Jim’s budget constraint.
b. Now suppose that all prices increase by 10% in 2005 and that Jim’s
salary increase by 10% as well. Draw Jim’s new budget constraint.
How would Jim’s optimal combination of milk and cookies in 2005
compare to his optimal combination in 2004?
a. Figure below shows Jim's budget constraint. The vertical intercept is 50
litres of milk, since if Jim spent all his money on milk he would buy
$100/$2 = 50 litres of it. The horizontal intercept is 25 dozen cookies,
since if Jim spent all his money on cookies he would buy $100/$4 = 25
dozen cookies.
b. If Jim's salary rises by 10 percent to $110 and the prices of milk and
cookies rise by 10 percent to $2.20 and $4.40, Jim's budget constraint
would be unchanged. Note that $110/$2.20 = 50 and $110/$4.40 = 25, so
the intercepts of the new budget constraint would be the same as the
old budget constraint. Since the budget constraint is unchanged, Jim's
optimal consumption is unchanged.
8. Consider your decision about how many hours to work.
a. Draw your budget constraint assuming that you pay no taxes on your
income. On the same diagram, draw another budget constraint assuming
that you pay a 15% tax.
b. Show how the tax might lead to more hours of work, fewer hours, or the
same number of hours. Explain.
a. Budget constraint BC1 shows the budget constraint if you pay no taxes.
Budget constraint BC2 shows the budget constraint with a 15 percent tax.
b. This figure below shows indifference curves for which a person will work
more as a result of the tax because the income effect (less leisure) outweighs the
substitution effect (more leisure), so there is less leisure overall.
Figure below shows a situation in which a person will work fewer hours as a
result of the tax because the income effect (less leisure) is smaller than the
substitution effect (more leisure), so there is more leisure overall.
Figure below shows a situation in which a person will work the same number of
hours after the tax because the income effect (less leisure) equals the substitution
effect (more leisure), so there is the same amount of leisure overall.
9. Suppose you take a job that pays $30,000 and set some of this income aside in a
saving account pays annual interest of 5%. Use a diagram that to show how your
consumption changes in each of the following situation.
a. Your salary increases to $40,000.
b. The interest on your account rises to 8%.
a. Figure below shows the situation in which your salary increases from
$30,000 to $40,000. With numbers shown in thousands of dollars in the
figure, your initial budget constraint, BC1, has a horizontal intercept of 30,
since you could spend all your income when young. The vertical intercept
is 31.5, since if you spent nothing when young and saved all your income,
earning 5 percent interest, you would have $31,500 to spend when old. If
your salary increases to $40,000, your budget constraint shifts out in a
parallel fashion, with intercepts of 40 and 42, respectively. This is an
income effect only, so if consumption when young and old are both
normal goods, you will spend more in both periods.
b. If the interest rate on your bank account rises to 8 %, your budget
constraint rotates. If you spend all your income when young, you will
spend just $30,000, as before. But if you save all your income, your oldage consumption increases to $30,000 x 1.08 = $32,400, compared to
$31,500 before. As Figure bellow, the steeper budget line leads you to
substitute future consumption for current consumption. But the income
effect of the higher return on your saving leads you to want to increase
both future and current consumption if both are normal goods. The result
is that your consumption when old certainly rises and your consumption
when young could increase or decrease, depending on whether the
income or substitution effect dominates.