Mike Shields
Economics 405
Economics of the Public Sector
Fall 2012
Homework #2
Due: Friday, September 21, 2012
Possible Points: 20
1. Many governments through their income tax laws offer significant subsidies to people
who own their principal place of residence. These subsides take several forms,
including:
 A taxpayer can reduce his/her tax liability by deducting from their taxable income
the property taxes paid on their home.
 Unlike other interest expenses an individual may incur (say on credit cards), a
taxpayer can further reduce his/her tax liability by deducting mortgage interest.
 “Imputed income” from home ownership escapes taxation altogether. That is,
homeowners essentially rent their homes to themselves. Yet since no market
transaction takes place and no cash is exchanged, the value of the housing
services escape taxation.
a. Identify the circumstances under which this subsidy will NOT promote efficient
resource allocation. Use a graph to supplement your discussion and show the
efficiency loss on the graph. [Note: You do not need to address individually any of
the three tax law provisions discussed above. They are listed here to demonstrate that
the tax subsidy for homeownership is quite large.] [4 points]
b. Could the large subsidy for homeownership ever be justified on efficiency grounds?
On other grounds? Carefully explain the basis for your answer. [6 points]
a)This subsidy will not promote efficient resource allocations if the subsidy given to
home owners exceeds the Marginal Benefit accruing to the community (third
parties) for home ownership. Evidence exists that home ownership does provide
some social benefit. For example, neighborhoods in which residents are
predominantly home owners, not renters, tend to see lower crime rates and higher
home overall home values. Thus, some subsidy may be justified on efficiency
grounds. This is shown on the graph, attached. However, in our case, the subsidy to
home owners exceeds the Marginal Social Benefit of home ownership. The loss of
efficiency resulting from this is shown as the purple triangle on the graph.
b)A subsidy of this size cannot be justified on efficiency grounds because the amount
exceeds the Marginal Social Benefit. An efficient subsidy would equal the marginal
social benefit. This is shown on the graph at Qd+Mb. However, a case might be
made in favor of this type of subsidy on equity grounds. A subsidy of this
magnitude makes home ownership possible for individuals and families who would
not have the ability to own a home without it. In this case, efficiency and equity are
a trade-off, and there is no clear economic standard by which we might determine
which is more important. (Actually, if we want to achieve more access to home
ownership, this is likely not the most efficient way to do it, because these tax
deductions are not structured in an egalitarian way: they disproportionately favor
those who purchase expensive homes, whom we may infer could have bought a
home without them. A more egalitarian solution might be a phased out deduction,
or simply a progressive income tax structure that left more money to low wage
earners). We could attempt to internalize equity by accounting for egalitarian tastes
and preferences as a marginal social benefit. Then we might shift our Qd+Mb curve
out to coincide with our Qd+Subsidy curve. However, viewing the situation thus
puts us on shaky ethical foundations, because it effectively assumes that what is fair
or just is a simple matter of what society deems to be so. Ultimately, we can say that
in this model, either egalitarian preferences are not accounted for as a marginal
benefit, or this subsidy is not efficient.
2. The supply of paper is described by the following equation:
Qs = 5000 P
where Qs is tons supplied per year and P is the price per ton. The demand is described by
Qd = 400,000 – 1,000 P,
where Qd is tons demanded per year. Because of the pollution associated with apper
production, marginal external costs of $20 are associated with each ton of paper.
Assuming that paper is sold in a competitive market , what is the market price? How
many tons of paper will be produced per year at that price? What is the efficient annual
output of paper? How can a corrective tax achieve efficiency?
[5 points]
400,000 - 1000P = 5000P
400,000 = 6000P
P=$66.67
Qd=333,333
Qs=333,333
P + MD =66.67 + 20 = 86.87
Qd’=313,333
In a competitive market, 333,330 tons of paper will be sold at a price of $66.67 per
ton. The efficient output is 313,333. This can be achieved through the use of a
Pigouvian tax in the amount of $20 per ton. The effect of this tax would be to
internalize the marginal damage caused by paper production. It would effectively
shift the supply curve to the left, adding an additional cost of $20 to each unit
produced, and bringing the Price including the tax to $86.87. The demand curve
would be unchanged, and the new equilibrium quantity given this higher price
would be 313,333, for an efficient outcome.
3. The EPA wants to reduce emissions of sulfur dioxides from electric power-generating
plants by 20 percent during the next year. To achieve this goal, the EPA will require
each power-generating plat in the nation to reduce emissions by 100 tons per year.
Suppose five power plants emit sulfur dioxides and serve a given metropolitan area. The
following table shows the cost per ton of reducing emissions for each of the five plants.
Cost Per Ton of Plant
Emissions Reduction
1
$600
2
500
3
500
4
400
5
200
Assuming that the cost per ton of emissions reduction is constant and that the
improvement in the air for the metropolitan area is the same no matter wich plant reduces
emissions, calculate the following:
a. Cost of meeting EPA regulations [2 points]
b. Least-cost method of achieving the EPA goal of reducing emissions of sulfur
dioxides from power plants in the metropolitan area. [3 points]
(600 + 500 + 500 +400 + 200) x 100 = $220,000
a)The Cost of meeting the EPA regulations is $220,000.
200 x 500 = 100,000
220,000 – 100,000 = 120,000
b)The least cost method of achieving the required overall emissions reduction would
be to implement a tradable permit system. In that case, firm 5 would reduce
emissions by 500 tons, while the other firms would not reduce emissions at all. (500
tons is equivalent to 100% of this firm’s emissions. This is only feasible in this
model because it assumes a constant, rather than increasing cost of emissions
reduction). This method would result in a savings of $120,000 to be split some way
between firms, providing an incentive for firms to reach agreements on reductions
wherein firms with higher marginal cost of reduction would effectively pay the firm
with the least cost to reduce emissions for them.
Graph: Question 1