LAW AND ECONOMICS
HOMEWORK #1: ANSWERS

1. Using the example of the cement company (C) and the laundry (L), explain what outcomes result when the cost of installing filters (for L) is $20,000, the pollution damage from the cement dust is $15,000, and the cost of new precipitator technology (for C) is $10,000. Consider all three rules for assigning property rights.

                                                                                             LAUNDRY (L)

                                                                       NO FILTER                                FILTER

                               NO                                  L: $25,000                                 L: $20,000
                               PRECIPITATOR            C: $100,000                               C: $100,000

CEMENT
FACTORY (C)
                                PRECIPITATOR            L: $40,000                                     NOT
                                                                       C: $90,000                                RELEVANT
 

Rule 1: C has the right to pollute.

Since L can raise his profits by $15,000 when C installs the precipitator at a cost of $10,000, L must bribe C to put in the precipitator by offering him a side payment of more than $10,000 but less than $15,000 (say $12,500). Why? Because both L and C can be better off (i.e. have higher profits) when they voluntarily negotiate this solution.

Rule 2: L has the right to be paid compensatory damages.

C will voluntarily install the precipitator in order to avoid the payment of damages.

Rule 3: L has the right to petition for an injunction against C to cease and desist polluting.

C will be indifferent between voluntarily installing the precipitator and going to court and being forced to install the precipitator (if court costs are positive this will induce C to voluntarily install the precipitator)

Notice several things: (1) the efficient solution has been reached in all three cases; (2) C is the low cost avoider of pollution and installs the precipitator in all cases.


 
 

                                                               Non-Co-operative                                    Co-operative
                                                                      Solution                                                Solution
                       Rule                                    L                C           Surplus                    L              C

                         1                                   $25K          $100K         $5K                   $27.5K   $102.5K

                         2                                   $40K             $90K        $0K                   $40K         $90K

                         3                                   $40K             $90K        $0K                   $40K          $90K

2. Using the notions of property rights and present values, explain how the following policies would affect the deforestation of the Amazon:

a. Suppose that there are no land taxes and a nature lover X wants to establish a wildlife sanctuary in the Amazon. After careful study X purchases a choice plot of land for $500. This piece of land will yield $100 a year from visitors for 10 years when the interest rate is 10%. Is it worthwhile for X to purchase this land?
C = Cost of Land = $500

PV = $100(AF[n=10, i= 10%]) where AF = Annuity Factor
      = $100(6.145)
      = $614.50

PV > C so it is worthwhile to purchase this land as long as the owner has full property rights to the land and can enforce them. (This means he will be able to collect and keep the full $100 each year.) The rainforest will be protected in this case.

(1) Now assume that X must pay a 10% tax on the value of the land every year because it is unimproved. Will X purchase this land now?

Tax = $500(0.1) = $50/Year

C = Cost of Land = $500

PV = $50[6.145] = $307.25

PV < C so it is not worthwhile for nature lover X to purchase this land.

(2) Now assume a farmer Y is willing to purchase the land for $350 after figuring that he will be able to earn $100 a year for 5 years when the interest rate is 10%. He knows that his taxes on the value of the land will be reduced to 1% (a 90% reduction). Will farmer Y be willing to purchase and develop this land?

Tax = $350(0.01) = $3.50

C = Cost of Land = $350

PV = $96.50(AF[n=5, i=10%])
      = $96.5(3,791)
      = $365.73

PV > C so it is worthwhile for the farmer to purchase this land and clear it. But he will move on after 5 years because nutrients in the soil will be exhausted after 5 years and he will seek another site to develop.

Result: Deforestation of the rainforest. Note that this land would not have been developed in the absence of the tax break for developed land. Note that the land is being used in a lower valued use because the tax discourages the higher valued activity (because it leaves the forest in an undeveloped condition). The example here is taken from real life. See "How Brazil Subsidizes the Destruction of the Amazon" The Economist, March 18, 1989, p. 69 for further details.

b. Assume a farmer is contemplating the purchase of some farm land in the Amazon rainforest which is very cheap. He knows that he can get $50 a year in crops for five years. If the interest rate is 10% what price will he be willing to pay for this land?
PV = $50(AF[n=5, i=10%]) = $50(3.791) = $189.55
c. Suppose the farmer knows that property rights are not very secure in the Amazon rainforest and that he will really only be able to get $20 a year in crops (the other $30 will be stolen). What price will he offer for the land now?
PV = $20[3.791] = $75.82
d. Daniel Benjamin writes that "the absence of secure property rights threatens forests by deterring investments in irrigation, terracing, and soil enrichment." Explain why this leads to the clearing of more land in the Amazon rainforest. (Hint: What happens to agricultural yields?)
If the farmer faces insecure property rights (as in part c.) he will not be able to reap the full benefits of his investment in the land (others will free-ride on his investment by stealing) so he will under-invest (and in the extreme case not invest at all) in the maintenance of the productivity of the land. As a result of this under-investment, the productivity of his land will rapidly diminish (yields will fall), causing him to abandon the land and move on to another site to develop.
e. A rancher is tempted to buy some land and raise some cows on it in the Amazon rainforest. He knows that annual revenues from ranching would be $1,000 a year for 5 years when the interest rate is 10% and that initial setup costs will be $3,000 plus annual costs of $300 for 5 years.
(1) Will this rancher go ahead with this project?

C = Cost of the Land = $3,000

PV = $700(3.791) = $2,653.70

PV < C so the rancher will not buy this land.

(2) Suppose the government grants the rancher a 75% tax credit on all his costs. (Note: This effectively lowers the rancher's costs by 3/4.) Will he set his ranch up in the Amazon now?

C = $750

PV = $700(3.791) = $2,653.70

PV > C so the rancher will buy this l;and for cattle grazing and clear it. Result: Deforestation.

Note: Deforestation would not have occurred in the absence of the subsidy because the cost of ranching in the Amazon is too high to make it economical. It is the subsidy that makes it economical.

3. Explain why the clear-cutting of trees (cutting down all the trees) is a practice often used on public lands but very rarely on private lands. Under what circumstances would clear-cutting be a rational strategy?
Using property rights concepts, we can reason as follows: public lands are not owned by anyone so that they will be treated as commons. This means that any trees that one company does not cut down (to allow them to grow into more mature and profitable trees) will be cut down by another company. In this situation, it makes sense for all companies to cut down all the trees they can as fast as they can. The result is clear-cutting. Such methods are unnecessary on private lands because the owner can exclude non-owners from cutting down his trees. This implies that an owner can postpone cutting down some trees to allow them to mature and will replace any trees that are cut down. Such results are possible when the owner can reap the future stream of benefits from the maturing and newly planted trees.

Basic Note On The Economics of Trees

When young trees are growing, they grow very rapidly. Assume that such trees add 10% of their biomass per year. That means that a young tree is adding 10% of its value per year. If the interest rate is 7.5% then it does not pay to cut the tree down and put the money in the bank. However as trees mature they grow at a slower rate. Suppose that in 10 years, the tree is growing at a rate of 5% per year. Now it does pay to cut the tree down because the foregone value of the uncut tree is higher than the rate at which the tree gains in value.

4. The following questions concern the issue of takings:
a. Is the optimal dollar-value of takings positive or zero?

The text would argue that the optimal amount of takings is positive. The text's argument is based on the idea that a taking can be efficiency enhancing (i.e. there are net benefits from exercising the taking power). For the complete argument see the text and the argument developed in lecture.

b. Does your approach to the problem of takings depend on how many public goods there are? (That is, is the number of public goods large, small, or zero?)

The positive view of takings depends on the conclusion that public goods will be under-produced by private providers as a result of free-riders. If there are private methods of solving the free-rider problem as suggested in lecture, then there are no public purposes for which the taking power must be exercised.