NPTEL-Economics-Public Economics
Lecture 40
Topics
Assignment
1
Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
Module
Lecture 40
Topics
1. The country of C has two citizens, A and B. A has a private legal business. He earns 50
per hour. At a tax rate of 0%, A works 20 hours. At a 25% tax rate he works only 16
hours, and at a 40% tax rate he works only 8 hours per week. B works a manufacturing
job. He works 20 hours per week and earns 6 per hour, regardless of the tax rate. The
government is considering imposing an income tax of either 25% or 40% on A and using
the revenues to make transfer payments to B. The accompanying table summarizes the
three possible policies. Does either tax policy raise social welfare? Is either of the
policies less than optimal? Explain your answers.
Effects of Redistributive Policies in C
0%
A’s pretax income
1000
A’s taxes
0
A’s net income
1000
B’s pretax income
120
B’s transfer payment 0
B’s net income
120
25%
800
200
600
120
200
320
40%
400
160
240
120
160
280
Solution:
Whether or not the policies raise social welfare depends on the society’s taste for
redistribution. Indeed, either of the policies makes Ted better off and makes Bill worse
off than the status quo of no taxes, so if society deems it sufficiently important to
redistribute to Ted, then either policy would raise social welfare. If society cares about
only the “size of the pie,” however, then both policies would lower social welfare.
Whenever society deems that improving Ted’s income by $200 improves social welfare
more than reducing Bill’s income by $400 harms social welfare, the 25% tax policy
raises social welfare and is the optimal policy. The 40% tax policy can never be optimal,
since the 25% tax policy makes both Bill and Ted better off than the 40% tax policy.
2. For the example below, answer the following:
Buying a car with added safety features that prevent the drivers’/passengers’ deaths in the
event of an accident
a) Does an externality exist? If so, explain and classify the externality as
positive/negative (or both).
2
Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
b) If an externality exists, determine whether the Coase theorem applies (i.e. is it
possible/reasonably feasible to assign property rights and solve the problem?)
c) If an externality exists and the Coase theorem does not apply, argue which of the
government’s tools are best suited to address the issue: quantity regulation,
taxes/subsidies, tradeable permits, or something else.
Solution:
a. Depends; if people drive more recklessly as a result of having a safer car, then buying
the safety feature imposes a negative externality on other drivers. If having a safety
feature does not change the likelihood of an accident or the impact on the other cars and
then there is no externality.
b. The coase theorem does not apply: It would be incredibly difficult to write a contract
with those with whom you may eventually be engaged in a car accident.
c. Quantity regulation (e.g. regulating the safety feature, or preventing it), or taxation
would correct the externality (Yes, that’s right, we’d theoretically want to tax the safety
feature if it causes people to drive more recklessly).
3. Suppose that demand for a product is Q = 1,200 – 4P and supply is Q = –200 + 2P.
Furthermore, suppose that the marginal external damage associated with the consumption
of this product is $8 per unit. How many more units of this product will the free market
produce and consume than is socially optimal? Calculate the deadweight loss associated
with the externality
Solution:
First consider what the free market would do by setting demand equal to supply:
1,200 – 4P = –200 + 2P, or 1,400 = 6P.
P =233.33, so, QFree Market = 1,200 – 4(233.33) =266.67.
The socially optimal level occurs when the marginal external cost is included in the
calculation.
Suppose the $8 externality were added to the price each consumer had to pay. Then
demand would be: Q = 1,200 – 4(P + 8).
Solving for P, 1,200 – 4(P + 8) = –200 + 2P, or P = 228.
Solving for Q, 1,200 – 4(228 + 8) = 1,200 – 944.
QSocial Opt = 256, 102/3 units less than provided by the free market.
Deadweight loss is the area of a triangle of height 8 and width 102/3: ½ (8 *102/3) =
42.67.
3
Indian Institute Of Technology, Kanpur
NPTEL-Economics-Public Economics
4. A, B, and C live in IIT-Kanpur. A’s demand for a flyover bypassing the GT road, a
public good, is given by Q = 12 – 2P. B’s demand is Q = 18 – P and C’s is Q = 8 – P/3,
(where Q is the length of the flyover).The marginal cost of building a flyover is MC = 21.
The city’s government decides to use the following procedure for deciding how long a
flyover to build. It asks each resident how long a flyover they want, and it builds the
longest one asked for by any resident. To pay for the construction, it then taxes A, B, and
C the prices a, b and c per km, respectively, where a + b + c = MC. (The residents know
these tax rates before stating how long a flyover they want.)
i.
If the taxes are set so that each resident shares the cost evenly (a = b = c), how
long a flyover will get built?
ii.
Show that the government can achieve the social optimum by setting the
correct tax prices a, b and c. What prices should it set?
Solution:
a. If the taxes are set so that each resident shares the cost evenly (a = b = c), how
many paths will get built?
When taxes are set at a = b = c = MC/3 = 7, each resident faces an individual marginal
cost of 7 per km.
At this marginal cost, Andrew wants no stretch, Beth wants 11km, and Cathy wants 2.67.
The government therefore builds 11 kms.
b. Show that the government can achieve the social optimum by setting the correct
tax prices a, b, and c. What prices should it set?
The social optimum can be computed by re-expressing the demand curves for the three
residents as P = 6 – Q/2, P = 18 – Q, and P = 24 – 3Q, respectively, and summing them
to get marginal social benefit MSB = 48 – 4.5 Q.
Setting MSB = MC and solving for Q gives Q = 6.
We need to tax prices so that nobody will want more than 6 km (and someone will want
exactly 6 units).
Looking at Andrew’s inverted demand curve, we see that he will want exactly 6 units at
a = 3 (since then a = 6 – 6/2).
Beth will want exactly 6 units at b = 12.
And at c = 6, Cathy will want exactly 6 units.
Since 3 + 12 + 6 = 21, these tax rates are just enough to cover MC, and the social
optimum is achieved.
Note that with this tax system in place, the three residents are unanimous in the length of
the flyover they desire.
4
Indian Institute Of Technology, Kanpur