1. 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 $200,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $300,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of $400,000, 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 0.1 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 |
0.1 |
$__? |
|
$400,000 |
0.2 |
$__? |
|
$300,000 |
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?
$300,000
$500,000
$400,000
2. Suppose that every driver faces a 5% probability of an automobile accident every year. An accident will, on average, cost each driver $10,000. Suppose there are two types of individuals: those with $80,000.00 in the bank and those with $2,000.00 in the bank. Assume that individuals with $2,000.00 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 $80,000.00 in the bank likely
will/will not?
buy insurance, and those with $2,000.00 in the bank likely
will/will not?
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 only the behavior of drivers with $2,000.00 in the bank.
False
True
