/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q9. Draw a utility function over inc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q9. (page 206)

Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk-averse when his income is high. Can you explain why such a utility function might reasonably describe a person鈥檚 preferences?

Short Answer

Expert verified

The utility function is shown below:

The utility function will be S-shaped.

Such a utility function describes people鈥檚 preferences because an individual's risk preferences change with a change in the stock of resources.

Step by step solution

01

Explanation

Suppose an individual needs an I* to sustain. The diagram below shows that after level I*, the individual will experience diminishing marginal utility. Below the income level I*, the individual will be a risk lover. The return will also be high; thus, the individual may take unfavorable gambles to increase the income. Above the income level I*, the individual will be risk averter as the required level of income to sustain life is covered; thus,the individual will take up insurance to cover the losses.

The utility function is shown below:

The utility function will be S-shaped.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are an insurance agent who must write a policy for a new client named Sam. His company, Society for Creative Alternatives to Mayonnaise (SCAM), is working on a low-fat, low-cholesterol mayonnaise substitute for the sandwich-condiment industry. The sandwich industry will pay top dollar to the first inventor to patent such a mayonnaise substitute. Sam鈥檚 SCAM seems like a very risky proposition to you. You have calculated his possible returns table as follows:

Probability
Return
Outcome
.999
-\(1,000,000
(he fails)
.001\)1,000,000,000
(he succeeds and sell his formula)

a. What is the expected return of Sam鈥檚 project? What is the variance?

b. What is the most that Sam is willing to pay for insurance? Assume Sam is risk-neutral.

c. Suppose you found out that the Japanese are on the verge of introducing their own mayonnaise substitute next month. Sam does not know this and has just turned down your final offer of $1000 for the insurance. Assume that Sam tells you SCAM is only six months away from perfecting its mayonnaise substitute and that you know what you know about the Japanese. Would you raise or lower your policy premium on any subsequent proposal to Sam? Based on his information, would Sam accept?

A moderately risk-averse investor has 50 percent of her portfolio invested in stocks and 50 percent in risk-free Treasury bills. Show how each of the following events will affect the investor's budget line and the proportion of stocks in her portfolio:

  1. The standard deviation of the return on the stock market increases, but the expected return on the stock market remains the same.

  2. The expected return on the stock market increases, but the standard deviation of the stock market remains the same.

  3. The return on risk-free Treasury bills increases.

Suppose an investor is concerned about a business choice in which there are three prospects鈥攖he probability and returns are given below:

PROBABILITY
RETURN
4\(100
3\)30
3-$30

What is the expected value of the uncertain investment? What is the variance.

Consider a lottery with three possible outcomes:

鈥� \(125 will be received with probability .2

鈥� \)100 will be received with probability .3

鈥� $50 will be received with probability .5

a. What is the expected value of the lottery?

b. What is the variance of the outcomes?

c. What would a risk-neutral person pay to play the lottery?

A city is considering how much to spend to hire people to monitor its parking meters. The following information is available to the city manager:

  • Hiring each meter-monitor costs \(10,000 per year.

  • With one monitoring person hired, the probability of a driver getting a ticket each time he or she parks illegally is equal to .25.

  • With two monitors, the probability of getting a ticket is .5; with three monitors, the probability is .75; and with four, it's equal to 1.

  • With two monitors hired, the current fine for overtime parking is \)20.

  1. Assume first that all drivers are risk-neutral. What parking fine would you levy, and how many meter monitors would you hire (1, 2, 3, or 4) to achieve the current level of deterrence against illegal parking at the minimum cost?

  2. Now assume that drivers are highly risk-averse. How would your answer to (a) change?

  3. (For discussion) What if drivers could insure themselves against the risk of parking fines? Would it make good public policy to permit such insurance?
See all solutions

Recommended explanations on Economics Textbooks

Taxation Economics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.