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Chapter 20: Problem 15

You have \(\$ 1,000\) that you can invest. If you buy General Motors stock, then, in one year's time: with a probability of 0.4 you will get \(\$ 1,600\); with a probability of 0.4 you will get \(\$ 1,100\); and with a probability of 0.2 you will get \(\$ 800\). 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 General Motors stock? b. Suppose you prefer putting your money into the bank to investing it in General Motors stock. What does that tell us about your attitude to risk?

Short Answer

Expert verified
Answer: The expected value of earnings from investing in General Motors stock is $1,240. If the student prefers putting their money in the bank to investing it in General Motors stock (despite the higher expected value), it indicates that they have a risk-averse attitude.

Step by step solution

01

List the possible outcomes and their probabilities

We have 3 possible outcomes from investing in General Motors stock: 1. With a probability of 0.4, you will get \(\$ 1,600\). 2. With a probability of 0.4, you will get \(\$ 1,100\). 3. With a probability of 0.2, you will get \(\$ 800\).
02

Calculate the expected value

To find the expected value of your earnings from investing in General Motors stock, we will multiply the amount of each outcome by its respective probability and add them together: Expected value = (0.4 * 1,600) + (0.4 * 1,100) + (0.2 * 800)
03

Simplify the expression

Now, let's simplify the expression to find the expected value: Expected value = (640) + (440) + (160) Expected value = \(\$ 1,240\) The expected value of your earnings from investing in General Motors stock is \(\$ 1,240\). #b. Analyzing your attitude towards risk#
04

Compare the expected value with the guaranteed return

We will now compare the expected value from investing in General Motors stock (\(\$ 1,240\)) with the guaranteed return from putting the money in the bank (\(\$ 1,100\)).
05

Analyze the decision-making process

If you prefer putting your money into the bank instead of investing it in General Motors stock, even though the expected value from the stock is higher, it means that you are risk-averse. To conclude, the expected value of your earnings from investing in General Motors stock is \(\$ 1,240\), and if you prefer putting your money in the bank to investing it in General Motors stock, it suggests that you have a risk-averse attitude.

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Most popular questions from this chapter

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?

From 1990 to 2013,1 in approximately every 277 cars produced in the United States was stolen. Beth owns a car worth \(\$ 20,000\) and is considering purchasing an insurance policy to protect herself from car theft. For the following questions, assume that the chance of car theft is the same in all regions and across all car models. a. What should the premium for a fair insurance policy have been in 2013 for a policy that replaces Beth's car if it is stolen? b. Suppose an insurance company charges \(0.6 \%\) of the car's value for a policy that pays for replacing a stolen car. How much will the policy cost Beth? c. Will Beth purchase the insurance in part b if she is risk-neutral? d. Discuss a possible moral hazard problem facing Beth's insurance company if she purchases the insurance.

You own a company that produces chairs, and you are thinking about hiring one more employee. Each chair produced gives you revenue of \(\$ 10\). There are two potential employees, Fred Ast and Sylvia Low. Fred is a fast worker who produces ten chairs per day, creating revenue for you of \(\$ 100\). Fred knows that he is fast and so will work for you only if you pay him more than \(\$ 80\) per day. Sylvia is a slow worker who produces only five chairs per day, creating revenue for you of \(\$ 50 .\) Sylvia knows that she is slow and so will work for you if you pay her more than \$ 40 per day. Although Sylvia knows she is slow and Fred knows he is fast, you do not know who is fast and who is slow. So this is a situation of adverse selection. a. Since you do not know which type of worker you will get, you think about what the expected value of your revenue will be if you hire one of the two. What is that expected value? b. Suppose you offered to pay a daily wage equal to the expected revenue you calculated in part a. Whom would you be able to hire: Fred, or Sylvia, or both, or neither? c. If you know whether a worker is fast or slow, which one would you prefer to hire and why? Can you devise a compensation scheme to guarantee that you employ only the type of worker you prefer?

For each of the following situations, do the following: first describe whether it is a situation of moral hazard or of adverse selection. Then explain what inefficiency can arise from this situation and explain how the proposed solution reduces the inefficiency. a. When you buy a second-hand car, you do not know whether it is a lemon (low quality) or a plum (high quality), but the seller knows. A solution is for sellers to offer a warranty with the car that pays for repair costs. b. Some people are prone to see doctors unnecessarily for minor complaints like headaches, and health maintenance organizations do not know how urgently you need a doctor. A solution is for insurees to have to make a co-payment of a certain dollar amount (for example, \(\$ 10\) ) each time they visit a health care provider. All insurees are risk-averse. c. When airlines sell tickets, they do not know whether a buyer is a business traveler (who is willing to pay a lot for a seat) or a leisure traveler (who has a low willingness to pay). A solution for a profit-maximizing airline is to offer an expensive ticket that is very flexible (it allows date and route changes) and a cheap ticket that is very inflexible (it has to be booked in advance and cannot be changed). d. A company does not know whether workers on an assembly line work hard or whether they slack off. A solution is to pay the workers "piece rates," that is, pay them according to how much they have produced each day. All workers are risk-averse, but the company is not risk-neutral. e. When making a decision about hiring you, prospective employers do not know whether you are a productive or unproductive worker. A solution is for productive workers to provide potential employers with references from previous employers.

Suppose you have \(\$ 1,000\) that you can invest in Ted and Larry's Ice Cream Parlor and/or Ethel's House of Cocoa. The price of a share of stock in either company is \(\$ 100\). The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry's stock rises to \(\$ 150\) but the value of Ethel's stock falls to \$60. When it is cold, the value of Ethel's stock rises to \(\$ 150\) but the value of Ted and Larry's stock falls to \(\$ 60\). There is an equal chance of the weather being warm or cold. a. If you invest all your money in Ted and Larry's, what is your expected stock value? What if you invest all your money in Ethel's? b. Suppose you diversify and invest half of your \(\$ 1,000\) in each company. How much will your total stock be worth if the weather is warm? What if it is cold? c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry's, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning.
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