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Oct. 17th, 2005 10:14 pmMore fun from the brother in graduate school. I have no fucking idea what a Utility Function is. Never seen one before today.
Risky work. This problem requires you to calculate through the decision-making process of tow employees and an employer concerned with the tradeoff between risky jobs and wages.
Suppose that Naomi has a utility function Un(W,L). The means her utility depends on her wealth W in millions of dollars and on a binary variable , L, which tells if Naomi is alive (1) or dead (0). In particular suppose Naomi's utility function is as follows: Un (W, L) = L - e^-w Her initial wealth is finite, she lives a risk free life and places no value on her time.
a. Naomi is offered a job carrying a one time risk one percent risk of death. What is the minimum compensation (C) that Naomi would require to run this risk. Think of C as a lump sum increase in Naomi's wealth. Is it possible she would refuse this job for any compensation, no matter the size? Explain why or why not.
b. A second job is available, but its risk is uncertain. Naomi believes there is a one percent chance the job is very risky (50% chance of death), a 50% chance the job is moderately risky (1% chance of death), and a 49% chance the job is absolutely safe with zero risk. What is the minimum compensation she would require for this job?
c. The potential employer is also uncertain about the risks in part b. He has the same subjective distribution as Naomi. At no cost he can discover if the job is very risky, moderately risky, or safe. If he finds out he must tell Naomi. If his only goal is to minimize the expected value of hte risk premium he pays to Naomi to induce her to take the job, should he obtain the information? Why or why not.
d. Return to a and assume the answer you obtained is that Naomi will demand at least $C to take the job. OSHA frowns on paying of risk premiums for work so her employer offers her a life insurance policy of 100$C, which provides her with the same expected financial return as wage $C. Will Naomi accept the insurance in lieu of the risk premium? (note that she receives nothing from the insurance if she lives where as in A she got the wages regardless of being alive or dead)
e. John, a friend of Naomi, has the following utility function Uj( W,L) = L *1n(1+W) He is a bachelor with no dependents. His initial wealth is also W. The employer in part A is willing to pay a wage premium, pay an insurance contract, or provide some other incentive to John. The employer wants to minimize his expected monetary cost. What is the main difference between Un and Uj in terms of how John and Naomi evaluate different levels of wealth and the tradeoff beween money and the risk of dying. Discribe the general nature of the contract he should offer John.
( Playing to win is easier if you get to attend the lectures, have the text, and get someone to do a couple of examples for you... )
Risky work. This problem requires you to calculate through the decision-making process of tow employees and an employer concerned with the tradeoff between risky jobs and wages.
Suppose that Naomi has a utility function Un(W,L). The means her utility depends on her wealth W in millions of dollars and on a binary variable , L, which tells if Naomi is alive (1) or dead (0). In particular suppose Naomi's utility function is as follows: Un (W, L) = L - e^-w Her initial wealth is finite, she lives a risk free life and places no value on her time.
a. Naomi is offered a job carrying a one time risk one percent risk of death. What is the minimum compensation (C) that Naomi would require to run this risk. Think of C as a lump sum increase in Naomi's wealth. Is it possible she would refuse this job for any compensation, no matter the size? Explain why or why not.
b. A second job is available, but its risk is uncertain. Naomi believes there is a one percent chance the job is very risky (50% chance of death), a 50% chance the job is moderately risky (1% chance of death), and a 49% chance the job is absolutely safe with zero risk. What is the minimum compensation she would require for this job?
c. The potential employer is also uncertain about the risks in part b. He has the same subjective distribution as Naomi. At no cost he can discover if the job is very risky, moderately risky, or safe. If he finds out he must tell Naomi. If his only goal is to minimize the expected value of hte risk premium he pays to Naomi to induce her to take the job, should he obtain the information? Why or why not.
d. Return to a and assume the answer you obtained is that Naomi will demand at least $C to take the job. OSHA frowns on paying of risk premiums for work so her employer offers her a life insurance policy of 100$C, which provides her with the same expected financial return as wage $C. Will Naomi accept the insurance in lieu of the risk premium? (note that she receives nothing from the insurance if she lives where as in A she got the wages regardless of being alive or dead)
e. John, a friend of Naomi, has the following utility function Uj( W,L) = L *1n(1+W) He is a bachelor with no dependents. His initial wealth is also W. The employer in part A is willing to pay a wage premium, pay an insurance contract, or provide some other incentive to John. The employer wants to minimize his expected monetary cost. What is the main difference between Un and Uj in terms of how John and Naomi evaluate different levels of wealth and the tradeoff beween money and the risk of dying. Discribe the general nature of the contract he should offer John.
( Playing to win is easier if you get to attend the lectures, have the text, and get someone to do a couple of examples for you... )
