Economics and the Environment
Homework #1: Answers
1. Do the following using the various tools
suggested in the question:
a. Using supply and demand, explain
how the Brazilian government exemption of agriculture from taxation contributes
to deforestation of the Amazon rainforest. (Note: Exemption of
agriculture from taxation means that there will be an increase in demand by
non-farmers for regular agricultural land. Farmers will move off regular
agricultural lands and go to the rainforest where agricultural land is cheaper.
Why is it cheaper? Because government taxes unimproved land
in the Amazon at a higher rate than improved land. This gives settlers
an incentive to cut down the trees to lower their taxes.)
The key here is to notice that land
in the Amazon and regular agricultural lands outside the Amazon are rather poor
substitutes, but substitutes nonetheless. An increase in demand for regular
agricultural lands by businessmen seeking tax shelters means that the price of
these lands has declined considerably for businessmen (but has risen
considerably for farmers). That can be seen by the movement along the original
demand curve in the graph which establishes the price PB and the
shift in the demand curve yielding the price PF for farmers. Since
the price of regular agricultural land has risen for farmers many of them will
seek out a cheaper substitute, land in the Amazon. The demand for land in the
Amazon increases as a result of the government’s tax exemption policy for
agriculture.
b. Suppose that (1) investment
projects in the Amazon are eligible for a 75% tax credit by the Brazilian
government; (2) a particular project develops land for 100 farms with the cost
of clearing the land and building roads of $1,000 per farm; and (3) each farm
would generate a net revenue stream whose present value is $400. Explain
whether this project would be built in the absence of the tax credit and how
the introduction of the tax credit affects this decision. Then show a
supply-demand graph which illustrates this situation.
These data indicate that the cost of
developing farmland in the Amazon is $100,000 while the benefits
of developing such land is $40,000. This project would not be undertaken
in the absence of the tax credit since it would impose net costs of $60,000 on
the owners. But the tax credit lowers the costs to private parties to $25,000
(the developers are NOT bearing the full costs of their actions) and makes the
project feasible by generating $15,000 in net benefits for the developers.
The graph with the original supply
and demand (D and S0) indicates that the land in the Amazon would
not be developed. But the tax credit (read subsidy) to developers (who are
suppliers of land) will shift the supply curve to S1 thereby making
it feasible to develop.
c. Suppose a cement plant emits dust
which settles on nearby properties and causes various amounts of damage. Use a
supply and demand framework to show the following:
(1) Show what kind of tax must be
imposed to eliminate the externality. What kind of welfare loss is associated
with such a tax? Show and explain.
A tax that drives output to zero
will eliminate the pollution. Such a tax will shift the supply curve to the
left as shown on the graph above. Since output is significantly below its
optimal level, there is a welfare loss associated with the tax. That is, the
tax has driven resources out of the current market into their next best
alternative uses–which are a lower valued use than their current use. Note that
it is not worthwhile to eliminate pollution in this case because of the welfare
loss; what such a result tells us is that eliminating pollution yields
declining benefits while we must incur increasing costs to eliminate a given
amount of pollution. At some point the gain in environmental value is not worth
the sacrifice of other goods. (NOTE: Can you illustrate the case where it is
worthwhile to eliminate the pollution?)
2.
Using information from the Stroup and
Shaw article and the in-class discussion of subsidies do the following:
a. Stroup
and Shaw argue that farm subsidies are one of the major reasons why wetlands
are converted to farmlands. Show and explain how this occurs and why a welfare
loss occurs.
Assume
agricultural markets are in equilibrium at price P0 and quantity Q0.
Then farm subsidies are introduced in the form of direct payments or target
pricing so that farmers receive the price PTAR, consumers pay the
price PCON, and farmers are paid a subsidy of (PTAR - PCON)Q1.
This means that farmers are willing to produce more than they did in
equilibrium (Q1 – Q0). To produce more farmers must use more
marginal lands (as they move up the supply curve land cultivated becomes
more marginal—that is it is more difficult and costly to grow crops on) such as
wetlands (which ordinarily would not make good farmland). Such subsidies
produce a welfare loss because the extra resources used to produce (Q1
– Q0) have a higher value elsewhere. The subsidy, in effect, diverts
resources into a lower valued use. Another way to see this would be to realize
that the resources used in agriculture because of the subsidy would be in some
other (higher valued) use in the absence of the subsidy. In this way subsidies
to agriculture act as a tax on the rest of the economy and cause the
destruction of wetlands.
b.
Be sure you can explain how the combination of farm subsidies and acreage
restrictions can lead to excessive pollution of streams and groundwater.
See Stroup
and Shaw article, pp. 55-56.
c. Stroup
and Shaw argue that water subsidies to farmers in
Cotton and
rice are typically grown in warm moist environments (such as the
d. People
who build on coastal barriers where destructive storms frequently occur receive
numerous subsidies that allow them to rebuild in the same place as often as
they want. Show how this results in excessive development in such dangerous
areas and how a welfare loss occurs (otherwise called a major misallocation of
resources).
Before
subsidies are introduced housing on coastal barriers has a higher price because
of higher insurance costs or extra construction measures needed to make homes
more storm-proof. This is reflected in the price difference P2 – P1.
Now introduce a subsidy for homeowners who build on coastal barriers (in
the form of subsidized flood insurance or post-disaster aid that reduces the
costs of rebuilding in the same place again and again). This reduces the price
they must pay from P2 to P1. The size of the subsidy they
receive is P3 – P1. This subsidy increases the
amount of development in storm-prone areas by shifting the demand curve to the
right (the subsidy goes to the homeowner) and getting suppliers (developers) to
increase the quantity of housing there. Resources are thus diverted from
building in safer areas into a lower valued use on coastal barriers (causing
the supply curve of housing in safe areas to shift to the left and prices of
homes in safer areas to increase).
3. Use
the Coase Theorem to solve the following problems and
explain your answer.
a. Suppose a
cement factory and a laundry are located near one another. The paper mill (PM)
has initial profits of $300,000 and the downstream farmer (F) $100,000 when
neither has taken action to clean up the water. The farmer incurs damages from
the water pollution of $25,000, the farmer’s costs of cleaning the water are
$15,000, and the paper mill’s costs of installing pollution control equipment
are $35,000. Fill in the table and then show the results of applying the two
property rules: Rule #1-the property rights to pollute the river belong to the
PM; Rule #2-the farmer has property rights to the river and may sue to recover
damages.
|
|
Not Clean Water (F) |
Clean Water (F) |
|
Not Clean Water (PM) |
F = $100,000 PM = $300,000 |
F = $110,000 PM = $300,000 |
|
Clean Water (PM) |
F = $125,000 PM = $265,000 |
NOT RELEVANT |
Rule #1: The Farmer knows he will lose if
he goes to court so he simply cleans up the water himself. We have arrived at
the efficient solution where the low cost avoider has acted and the profits are
jointly maximized at $410,000.
Rule #2: The Paper Mill knows it will lose
if the farmer takes it to court so it negotiates an out of court settlement. The maximum price the PM is willing to pay is
$25,000 while the minimum price the farmer is willing to accept is $15,000.
They negotiate a settlement whereby the PM pays F $20,000 for the right to
pollute. Note that this solves the pollution problem since F has sold the
property right to pollute to the PM. Profits for PM = $300,000 - $20,000 =
$280,000; profits for F = $100,000 - $15,000 + $25,000 + $20,000 = $130,000.
Once again the efficient result has been achieved with F acting (the low cost
avoider) and joint profits maximized at $410,000.
Both rules produce the efficient outcome so
the Coase Theorem is satisfied.
b. Suppose the initial data on profits from
part a. is the same but the paper mill drastically increases its pollution. The
farmer incurs damages from the water pollution of $50,000, the farmer’s costs
of cleaning the water are now $40,000, and the paper mill’s costs of installing
pollution control equipment are still $35,000. Fill in the table and then show
the results of applying the two property rules: Rule #1-the property rights to
pollute the river belong to the PM; Rule #2-the farmer has property rights to
the river and may sue to recover damages.
|
|
Not Clean Water (F) |
Clean Water (F) |
|
Not Clean Water (PM) |
F = $100,000 PM = $300,000 |
F = $110,000 PM = $300,000 |
|
Clean Water (PM) |
F = $150,000 PM = $265,000 |
NOT RELEVANT |
Rule #1: The Farmer knows he will lose if
he goes to court so he makes the following deal with the PM. The maximum he is
willing to pay the PM is $40,000 (why?) and the minimum the PM will accept is
$35,000 (why?). They bargain and reach agreement at $37,500 where both parties
are better off. F = $100,000 - $37,500 + $50,000 = $112,500 and PM = $300,000 +
$37,500 - $35,000 = $302,500. Joint Profits are maximized and low cost avoider
(PM) acts.
Rule #2: The Paper Mill knows it will lose
if the farmer takes it to court so it simply installs the pollution control
equipment. F = $150,000 and PM = $265,000. Joint profits are maximized and low
cost avoider (PM) acts.
Both rules produce the efficient outcome so
the Coase Theorem is satisfied.
4. Using
the concept of marginal user cost developed in class do the following: In a
three period model, suppose that U1 = $10, U2 = $12, U3
= $13, and r = 10%. Explain what must be done to
achieve a dynamically efficient allocation of a resource over three time
periods. Show your work.
The condition for dynamic efficiency
is
U1 U2
U0 = ──────
= ──────
1 + r (1 + r)2
But
U1
──────── = $10.91
1 + r
And
U2
─────────
= $10.74
(1 + r)2
This state of affairs implies that
reducing current production of the resource will raise U0;
increasing production of the resource in periods two and three will lower U1
and U2 (noting that proportionately more resources should be shifted
to period two than period three as the user cost in this period has farther to
decrease).