Law and Economics
ONLY A SELECTION OF QUESTIONS AND PARTS OF QUESTIONS WILL BE GRADED. ANSWER CONCISELY.
1. Different Legal Rules
Chapter 5 of the book discusses the outcomes of four different legal rules applied to the case of sparks generated by a single railroad's trains causing fires beside its rail line, by considering numerical examples. In my lecture notes, "Notes on Chapter 5 of the Book", for the case in which all the land beside the rail line is farmed by a single farmer and in which bargaining is prohibitively expensive, I generalized the analysis to treat any combination of costs.
Consider the following combination of costs:
f = 50, s = 25, r = 10
a. Indicate the efficient outcome, and whether application of each of legal rules 1, 2, and 4 yields the efficient outcome.
b. Consider one situation in which application of one of the legal rules gives rise to inefficiency. Explain the source of the inefficiency.
c. Repeat parts a) and b) but with the following combination of costs:
f = 25, s = 50, r = 10.
2. The Coase Theorem
(This is a modified version of the James Meade example referred to in the book.) A beekeeper and the owner of an orange orchard have a synergistic relationship. The beekeeper benefits from putting his beehives in the orchard since his bees make honey from the orange blossom pollen. The orchard owner benefits from having the beehives in his orchard since the bees pollinate his trees. There is a reciprocal positive externality.
The table below gives the profit of the beekeeper and the orchard owner as a function of the number of beehives that the beekeeper places in the orchard, before any transfer between them.
|
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
beekeeper
|
0
|
4
|
8
|
11
|
10.5
|
7
|
3
|
-1
|
|
orchard
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
sum
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0
|
5
|
10
|
14
|
14.5
|
12
|
9
|
6
|
a. What is the efficient number of beehives to have in the orchard?
Assume that the above table is common knowledge to both the orchard and beekeeper, that bargaining is costless, and that there are no other orchards or beehive owners.
b. Suppose that the orchard owner has property rights to his orchard, so that the beekeeper has to obtain the orchard owner's permission to put his beehives in the orchard. What is the equilibrium number of beehives in the orchard? How much will the orchard owner charge to have the beehives in his orchard? Is the equilibrium efficient?
c. Suppose that the beekeeper has the property right to place his beehives in the orchard. What is the equilibrium number of beehives in the orchard? How much will the orchard owner pay the beekeeper? Is the equilibrium efficient?
d. State the Coase Theorem.
e. Are the outcomes of the above example consistent with the Theorem?
3. Principal-agent problem
This question relates to the form of employment contract between a real estate agent and her real estate agency (like Coldwell-Banker or Century 21). The agency provides the agent with a desk, secretarial and paralegal services, and its reputation for honest dealing.
Susan is a real estate agent. Since she is a single mother, she is concerned with the uncertainty associated with her volume of sales. The brokerage contract between the seller (of a home that has been put on the market for sale) and the real estate agent specifies a commission of 6% (payable upon sale). The listing agency presents Susan with two options. She can split her commission earnings 50-50 with the agency or pay an annual franchise fee of $60,000 to the agency and receive the entire commission.
The question has two parts. In part A, there is no moral hazard. In part B, there is moral hazard.
A. Her expected sales are $3,000,000 with a probability of 0.5 and $1,333,333 with a probability of 0.5. Her utility function is u = y1/2, where y is her employment income.
a. Calculate her expected income, expected utility, certainty-equivalent income, and risk premium under the 50% of commission earnings contract.
b. Calculate her expected income, expected utility, certainty-equivalnet income, and risk premium under the franchise contract.
c. Would she prefer receiving 50% of the commission income or paying the annual franchise fee and receiving the entire commission?
B. We now take into account that Susan can decide how hard she will work. If she works hard, her expected sales are $3,000,000 with a probability of 0.75 and $1,333,333 with a probability of 0.25, and her utility function is u = 0.9y1/2. If she does not put in the extra effort, her expected sales are $3,000,000 with a probability of 0.25 and $1,333,333 with a probability of 0.75, and her utility function is u = 1.1y1/2.
d. Under the commission contract, would she or would she not choose to work hard?
Show the calculations.
e. Under the franchise contract, would she or would she not choose to work hard? Show the calculations.
f. Would she prefer the commission contract or the franchise contract?
4. A game
Kermit and Miss Piggy are separately deciding which of two bars to go to, Bar A or Bar B. Miss Piggy would like to go the bar that Kermit goes to. Kermit would like to go to the bar that Miss Piggy does not go to.
a. Depict the normal (box) form of the game, where each of the cells gives the payoff of first Kermit and then Miss Piggy.
b. Are there pure strategy Nash equilibria of the game? If there are, what are they? If there are not, explain why.
5. Fatal Worksite Accident Damage Award
Jim was a construction worker who died in a worksite accident. At the time of his death at 40, he was earning $85,000 a year. The average worker in his occupation and at his age works to the age of 60. In his occupation, earnings after the age of 40 stay constant in nominal terms (since older construction workers are less productive than younger construction workers). The (nominal) discount rate, r, is 5%. The courts have awarded John's wife and children the present (at the time of his death) value of his future earnings as damages, to be paid by the construction company.
a. Set up an expression for the present value of John's future earnings.
b. Calculate the dollar amount of the award.
(The calculations are easier if you use continuous discounting. If you work with discrete discounting, make use of the following hints: i) The value of $Y received at the end of every year forever is $Y/r; and ii) the value of $Y received at the end of every year for twenty years equals the value today of $Y received at the end of every year forever minus the value today of $Y received every year forever, discounted by twenty periods.)
c. Should the courts have awarded additional damages for the emotional suffering John's wife and children have experienced as a result of John's death? Briefly give onereason why and one reason why not.