Book cover for Economics

Economics

Paul Krugman, Robin Wells

ISBN #9781464143847

4th Edition

458 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the fundamentals of managing uncertainty and risk. It explains how to compute the expected value of a random variable and why risk-averse individuals, due to diminishing marginal utility, value the reduction of risk. Insurance mechanisms, such as fair insurance policies, help transfer risk from those who dislike uncertainty to those more tolerant of risk. Additionally, diversification and pooling are key strategies for reducing risk, while issues like adverse selection and moral hazard highlight the importance of information asymmetry in market transactions and the various strategies implemented (e.g., deductibles, screening) to mitigate these problems.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Aggregate Demand

The total demand for final goods and services in an economy at various price levels during a given period. •

Example Problems

Example 1

For each of the following situations, calculate the expected value. a. Tanisha owns one share of IBM stock, which is currently trading at $\$ 80 .$ There is a $50 \%$ chance that the share price will rise to $\$ 100$ and a $50 \%$ chance that it will fall to $\$ 70$. What is the expected value of the future share price? b. Sharon buys a ticket in a small lottery. There is a probability of 0.7 that she will win nothing, of 0.2 that she will win $\$ 10,$ and of 0.1 that she will win $\$ 50 .$ What is the expected value of Sharon's winnings? c. Aaron is a farmer whose rice crop depends on the weather. If the weather is favorable, he will make a profit of $\$ 100$. If the weather is unfavorable, he will make a profit of $-\$ 20$ (that is, he will lose money). The weather forecast reports that the probability of weather being favorable is 0.9 and the probability of weather being unfavorable is $0.1 .$ What is the expected value of Aaron's profit?

Example 2

Vicky N. Vestor is considering investing some of her money in a startup company. She currently has income of $\$ 4,000,$ and she is considering investing $\$ 2,000$ of that in the company. There is a 0.5 probability that the company will succeed and will pay out $\$ 8,000$ to Vicky (her original investment of $\$ 2,000$ plus $\$ 6,000$ of the company's profits). And there is a 0.5 probability that the company will fail and Vicky will get nothing (and lose her investment). The accompanying table illustrates Vicky's utility function. a. Calculate Vicky's marginal utility of income for each income level. Is Vicky risk-averse? b. Calculate the expected value of Vicky's income if she makes this investment. c. Calculate Vicky's expected utility from making the investment. d. What is Vicky's utility from not making the investment? Will Vicky therefore invest in the company?

Example 3

Vicky N. Vestor's utility function was given in Problem 2 . As in Problem 2, Vicky currently has income of $\$ 4,000$. She is considering investing in a startup company, but the investment now costs $\$ 4,000$ to make. If the company fails, Vicky will get nothing from the company. But if the company succeeds, she will get $\$ 10,000$ from the company (her original investment of $\$ 4,000$ plus $\$ 6,000$ of the company's profits). Each event has a 0.5 probability of occurring. Will Vicky invest in the company?

Example 4

You have $\$ 1,000$ that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get $\$ 1,500$; with a probability of 0.4 you will get $\$ 1,100$; and with a probability of 0.4 you will get $\$ 900 .$ If you put the money into the bank, in one year's time you will get $\$ 1,100$ for certain. a. What is the expected value of your earnings from investing in Ford stock? b. Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?

Example 5

Wilbur is an airline pilot who currently has income of $\$ 60,000 .$ If he gets sick and loses his flight medical certificate, he loses his job and has only $\$ 10,000$ income. His probability of staying healthy is $0.6,$ and his probability of getting sick is 0.4 . Wilbur's utility function is given in the accompanying table. a. What is the expected value of Wilbur's income? b. What is Wilbur's expected utility? Wilbur thinks about buying "loss-of-license" insurance that will compensate him if he loses his flight medical certificate. c. One insurance company offers Wilbur full compensation for his income loss (that is, the insurance company pays Wilbur $\$ 50,000$ if he loses his flight medical certificate), and it charges a premium of $\$ 40,000 .$ That is, regardless of whether he loses his flight medical certificate, Wilbur's income after insurance will be $\$ 20,000$. What is Wilbur's utility? Will he buy the insurance? d. What is the highest premium Wilbur would just be willing to pay for full insurance (insurance that completely compensates him for the income loss)?
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Common Mistakes

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