FE486A: Law and Economics
Homework 1
Due January 29th
Please indicate the students that you worked on this homework assignment with, if any.
1. (10 points) What is the marginal rate of substitution (MRS) for the following utilites?
a) U(X,Y) = X1/2 Y1/2
The indifference curves have a “classic” convex shape. The marginal rate of substitution is
equal to – y/x.
b) U(X,Y) = X1/2 + Y1/2
The indifference curves have a convex shape. The marginal rate of substitution is equal to –
y1/2/x1/2.
2. (10 points) Are the following games Prisoner Dilemma Games? Explain.
a)
X
Y
X
4,4
-1,5
Y
5,-1
0,0
Nash Equilibrium (NE) is (Y,Y) is a Prisoner Dilemma game because NE is not Pareto
optimal
b)
X
Y
X
4,4
5,-1
Y
-1,5
0,0
Nash Equilibrium (NE) is (X,X) is NOT a Prisoner Dilemma game because NE is Pareto
optimal
3. (15 points) From the textbook, Question 3.1: If you still haven’t purchased the textbook,
find the case of Butterfield v. Forrester, 11 East 60 (K.B., 1809).
a) What is the plaintiff? What is he asking the court to do?
Butterfield, the plaintiff, asked to be compensated for injuries he incurred when he rode his
horse into a pole put across the street by Forrester, the defendant. Butterfield
claimed that Forrester was negligent in leaving the pole across the street.
b) Is there a statute in this dispute?
The judge stated the law and the jury determined the facts. The law was that a person who
exercised reasonable care could collect damages caused by the negligent behavior of
others.
c) Who won?
The jury determined that the plaintiff did not exhibit reasonable care and found in favor of
the defendant.
4. (15 points) From the textbook (p. 77 – hopefully you have it). Facts: Arthur alleges that
Betty borrowed a valuable kettle and broke it, so he sues to recover its value, which is
$300. The facts are very confusing. Betty contends that she did not borrow a kettle from
Arthur; even if it is proved that she borrowed a kettle from Arthur, she contends it is not
broken; even if it is proved that she borrowed a kettle from Arthur and that it is broken,
she contends that she did not break it.
Assume that because the facts in the case are so unclear, Arthur and Betty independently
believe that the chances of either side’s winning in court are an even 50 percent. Further
assume that litigation in small claims court will cost each party $50 and that the cost of
settling out of court are $0. So, cooperation in this case is a matter of settling out of court
and saving the cost of a trial. Noncooperation in this case means trying the dispute.
a) What are Arthur and Betty’s threat values (two numbers)?
Arthur’s threat value is his expected net gain from trial. Because the value of the
kettle is $300, because he has a 50 percent probability of winning, and because the
trial will cost him $50, the expected net value of a trial is $300(0.5) - $50 = $100.
Betty’s threat value is her expected loss from trial. Because the value of the kettle is
$300, because she has a 50 percent probability of losing, and because the trial will
cost her $50, the value to her of a trial is -$300(0.5) - $50 = -$150 - $50 = -$200.
b) If Arthur and Betty cooperate in settling their disagreement, what is the net cost of
resolving the dispute?
The cost to Arthur and Betty of cooperatively resolving their dispute without trial is
$0 because the transaction costs of settling are, by assumption, zero.
c) What is the cooperative surplus?
The surplus from cooperating (i.e., from settling the dispute rather than litigating) is
$100, which is the sum of the two parties’ costs of litigating.
5. (10 points) Distinguish between the Pareto criterion for evaluating social change in
which there are gainers and losers and the Kaldor-Hicks (or potential Pareto criterion).
What is the difference in the initial distribution of resources in both criterion?
Pareto efficiency: when no one can be made better off without making someone else worse
off.
Klador-Hicks: when there exists a possibility (in theory) to make someone better off (even
if the compensation doesn’t occur).
6. (20 points) A rancher and a farmer live next door to one another. Although the
boundaries of their properties are well defined, there is no fence or natural break that
clearly demarcates the boundaries. As a result, from time to time the rancher’s cattle stray
onto the farmer’s property.
Assume that if the rancher’s cattle stray onto the farmer’s property, the farmer loses $60 in profits
per year; that the annual cost to the rancher of building and maintaining a fence between his
property and the farmer’s is $120; and that the annual cost to the farmer of building and
maintaining a fence between his property and the rancher’s is $95. Assume that the transaction
costs between the rancher and the farmer are zero.
Compare the efficiency of these three legal regimes: Be sure to indicate, 1) if a fence is built and
2) if so, who pays and if not, how an efficient outcome is reached
a.
farmers’ rights: the farmer has a legally-enforceable right to be free from invasion; in the
event of invasion, he is entitled to compensation in the form of his lost profits.
No fence; rancher pays $60 to farmer
b.
ranchers’ rights: the rancher bears no liability for any damage that his cattle may do to
someone else’s property.
No fence; farmer loses $60 (which is better than losing $95)
c.
farmers’ super-rights: the farmer has a legally-enforceable right to be free from invasion;
in the event of invasion, he is entitled to ten times his lost profits.
Note that if the Coase Theorem holds, the outcome under the three different legal regimes
should be the same (or, to be completely accurate, equally efficient—although in this
instance, the outcomes are, in fact, identical).
Under farmers’ super-rights there will be no fence, even though the farmer might receive ten
times his actual losses ($600) in the event of an invasion. The rancher can induce the farmer
to do better by accepting a payment of between $60 and $95. Why will the farmer accept
that? Because if he does not, the rancher will build a fence, in which case the farmer will
receive only $60 in additional profits.
7. (20 points) Use the theory of transaction costs to justify protecting rights by injunction or
damages:
Should we protection the following interests by an injunction or damages?:
a) A landowner’s right to exclude from his property a neighbor’s gas line.
An injunction. There are two parties involved, so, presumably, the transaction costs
between them to negotiate an easement for the neighbor’s gas line should be small.
b) A new car owner’s right to have her care’s defective transmission replaced by the seller.
This is actually a subtle question. Normally, one would say that the car owner ought to have
the right to have his defective transmission replaced—that is, he or she ought to have the
equivalent of a property rule running in his favor. If, then, the seller wanted to try to
bargain ought of this obligation, that would be fine because the seller would have to offer
the car owner enough compensation to make him or her indifferent between having the
transmission replaced or not. But it is possible that the seller, if required to replace the
transmission, might misbehave in some way that would require someone – perhaps a court
– to supervise what he or she was doing to the car. If those supervisory costs are sufficiently
high, then it might be better to have the seller pay the buyer compensatory money damages.
c) A homeowner’s right to be free from air pollution by a nearby factory.
The transaction costs between a single homeowner and the factory might be low, but there
may be lots of homeowners who are affected by the pollution. If so, then the total
transaction costs of internalizing the external costs that the pollution imposes may be so
high as to argue in favor of compensatory money damages instead of an injunction. You
might also talk about the possibility that a regulatory solution—having an administrative
agency set pollution limits on the factory and then monitor compliance—might be superior
to a private law solution (in which the homeowners bring a nuisance action against the
factory.).
d) A spouse’s right to half the house on divorce.
This situation illustrates a situation first articulated in Ian Ayres & Eric Talley, “Solomonic
Bargaining: Dividing an Entitlement to Facilitate Coasean Bargaining,” 104 Yale L.J. 1027
(1995). The title comes, of course, from the famous story in the Bible of King Solomon’s
sitting in judgment of two prostitutes, who came before him to ask him to determine which
of them was the mother of a baby. The evidence was ambiguous as to which of the women
was the true mother. Solomon, renowned for his wisdom, suggested taking his sword and
dividing the baby in half. That suggestion induced the true mother to give up her claim to
the lying mother so as to assure her baby’s survival. The true mother so revealed, Solomon
awarded the baby to her.
The proposal to divide the house in two should induce the spouses to negotiate about its
value. Half a house is, typically, a useless commodity and, therefore, has no particular
value, while the whole house may have a significant market value. Unless the two parties
can agree on a means of dividing up the asset’s value, they will each get nothing (or close to
it). This illustrates Ayres’ and Talley’s proposition that sometimes the best way to induce
bargaining is to compel the parties to do so by making the ownership of the entitlement
unclear or divided between them.