quiz

Individual Problems 17-2

You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. You believe you have a 25% chance of answering the question correctly.

Ignoring your current winnings, your expected payoff from playing the final round of the game show is

. Given that this is    , you    play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.)

The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is    . (Hint: At what probability does playing the final round yield an expected value of zero?)

Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $350,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $400,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of $450,000, there is a 0.2 chance you will be able to sell the machine. If you commit to a price of $500,000, there is a 0.15 chance you will be able to sell the machine. These probabilities are summarized in the following table.

For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.)

Posted Price	Probability of Sale	Expected Value
($)		($)
$500,000	0.15
$450,000	0.2
$400,000	0.5

Assume you must commit to one posted price.

In order to maximize the expected profit of the potential sale, which posted price would you commit to in order to maximize the expected value of the potential sale of the machine?

$400,000

$500,000

$450,000

The HR department is trying to fill a vacant position for a job with a small talent pool. Valid applications arrive every week or so, and the applicants all seem to bring different levels of expertise. For each applicant, the HR manager gathers information by trying to verify various claims on the candidate's résumé, but some doubt about “fit” always lingers when a decision to hire or not is to be made.

Suppose that hiring an employee who is a bad fit for the company results in an error cost of $200, but failing to hire a good employee results in an error cost of $300 to the company. Although it is impossible to tell in advance whether an employee is a good fit, assume that the probability that an applicant is a “good fit” is 0.65, while the probability that an applicant is a “bad fit” is 1−0.65=0.351−0.65=0.35. Hiring an applicant who is a good fit, as well as not hiring an applicant who is a bad fit, results in no error cost to the company.

For each decision in the following table, calculate and enter the expected error cost of that decision.

Decision	Reality	Expected Error Cost
	Good Fit	Bad Fit
	p=0.65	p=0.35
Hire	Cost: 0	Cost: $200
Do Not Hire	Cost: $300	Cost: 0

Suppose an otherwise qualified applicant applies for a job.

In order to minimize expected error costs, the HR department should    the applicant.

In the late 1990s, car leasing was very popular in the United States. A customer would lease a car from the manufacturer for a set term, usually two years, and then have the option of keeping the car. If the customer decided to keep the car, the customer would pay a price to the manufacturer, the “residual value,” computed as 60% of the new car price. The manufacturer would then sell the returned cars at auction. In 1999, manufacturers lost an average of $480 on each returned car (the auction price was, on average, $480 less than the residual value).

Suppose two customers have leased cars from a manufacturer. Their lease agreements are up, and they are considering whether to keep (and purchase at 60% of the new car price) their cars or return their cars. Two years ago, Paolo leased a car valued new at $14,500. If he returns the car, the manufacturer could likely get $10,150 at auction for the car. Valerie also leased a car, valued new at $19,000, two years ago. If she returns the car, the manufacturer could likely get $9,690 at auction for the car.

Use the following table to indicate whether each buyer is more likely to purchase or return the car.

Buyer	Keep and Purchase Car	Return Car
Paolo
Valerie

The manufacturer will lose money (at auction, relative to the residual value of the car) ifPaolo   returns the car instead of keeping and purchasing it.

True or False: Setting a more accurate residual price of each car would help attenuate the problems of adverse selection.

True

False

Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 10% chance of actually realizing that cost reduction and a 90% chance of realizing no cost reduction.

Assume the customer has an initial total cost of $200.

According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is

.

Suppose the sales representative initially offers the accounting system to the customer for a price of $11.00.

The information asymmetry stems from the fact that the    has less information about the efficacy of the accounting system than does the    . At this price, the customer    purchase the accounting system, since the expected value of the accounting system is    than the price.

Instead of naming a price, suppose the sales representative offers to give the customer the product in exchange for 50% of the cost savings. If there is no reduction in cost for the customer, then the customer does not have to pay.

True or False: This pricing scheme worsens the problem of information asymmetry in this scenario.

True

False

You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them:

Employee Value	Probability
$50,000	0.1
$59,000	0.1
$68,000	0.1
$77,000	0.1
$86,000	0.1
$95,000	0.1
$104,000	0.1
$113,000	0.1
$122,000	0.1
$131,000	0.1

The expected value of hiring one employee is

.

Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value.

The expected value of an employee who would apply for the position, at this salary, is

.

Given this adverse selection, your most reasonable salary offer (that ensures you do not lose money) is    .

Suppose that every driver faces a 1% probability of an automobile accident every year. An accident will, on average, cost each driver $12,000. Suppose there are two types of individuals: those with $96,000.00 in the bank and those with $3,000.00 in the bank. Assume that individuals with $3,000.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse.

In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is

.

Assume that the price of insurance is set at the actuarially fair price.

At this price, drivers with $3,000.00 in the bank likely    buy insurance, and those with $96,000.00 in the bank likely    buy insurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.)

Suppose a state law has been passed forcing all individuals to purchase insurance at the actuarially fair price.

True or False: The law will affect the behavior of both types of drivers.

False

True