Question Page 1 of 1 Department of Economics, University of California, Davis

04 Jun Question Page 1 of 1 Department of Economics, University of California, Davis

Question
Page 1 of 1

Department of Economics, University of California, Davis

Ecn 103 ? Uncertainty and Information

HOMEWORK # 3 (for due date see the web page)

Nobody can blame Art for being upset: he went to the hospital to have a liposuction and

instead they removed his appendix, although there was nothing wrong with it! So Art is now

talking to his lawyer, Mr Litigon. Mr Litigon explains to Art that there has never been a case

like this before and that he can only try to estimate what the judgment will be. He thinks that

there are four possible outcomes, expressed in terms of the sum of money that the hospital

will have to pay Art for damages. Mr Litigon thinks that the amounts and probabilities are as

follows:

$12,000 $36,000 $48,000 $72,000

1 5 2 4

12 12 12 12

? ? ? ?

? ?

. Art’s current wealth is $9,000 and his

utility-of-money function is U m m ( ) ln( ) ? . Mr Litigon is risk-neutral. He suggests one of

two contracts. Contract A involves a payment of $6,000 from Art to the lawyer, if the

judgment is less than 40,000, and a payment of $18,000 from Art to the lawyer, if the

judgment is more than 40,000. Contract B involves a payment to the lawyer equal to 25% of

the actual judgment.

(a) Write the expression that gives Art’s expected utility from contract A. [No need to

compute it.]

(b) Write the expression that gives Art’s expected utility from contract B. [No need to

compute it.]

(c) What is Mr Litigon’s expected utility from contract A?

(d) What is Mr Litigon’s expected utility from contract B?

The following day, Mr. Litigon calls Art and tells him that he did some more research and

he now thinks that the judgment will not be $12,000, nor will it be $48,000. He thinks that it

is going to be one of the other two amounts with probabilities

$36,000 $72,000

5 4

9 9

? ? ? ?

? ?

.

(e) What is Art’s expected utility from contract A?

(f) What is Art’s expected utility from contract B?

(g) What is Mr Litigon’s expected utility from contract A?

(h) What is Mr Litigon’s expected utility from contract B?

(i) Does one of the two contracts Pareto dominate the other? Explain why.

(j) Is contract A Pareto efficient? Explain why.

(k) Is contract B Pareto efficient? Explain why.

(l) Find a Pareto efficient contract which is as good as contract B from the point of view

of Art, but better for Mr Litigon. You don’t need to compute the contract: it is

sufficient to write an equation whose solution gives the contract. Describe the contract

in words.

(m) Suppose now that Mr Litigon’s utility-of-money function is V m m ( ) ? and his

initial wealth is $0 (zero). Show that contract B is not Pareto efficient.