Question

QUESTION 9 

 Peter has inherited $100,000 from a wealthy uncle who has passed away. Peter is deciding how to invest his money. Peter can invest his money safely where he is guaranteed an increase of S25.000 after five years. He can also invest his money in risky assets where there are three outcomes: he has a 21 percent chance of losing $30,000, a 10 percent chance of gaining $15,000 and a 69 peroent chance of gaining an unknown amount of money. What must the unknown amount of money equal if the expected value is to equal the guaranteed $25,000? Give your answer to the nearest whole dollar (with no decimal points, spaces, S signs, or commas in your answer).

QUESTION 10 

Jennifer is looking to sell her one-person Laser sail boat, which she has kept in excellent condition. Ordinarily this type of sail boat sells second hand for S3,000, but as Jennifer has looked after hers extremely well, she will only want to sell it for S3,500. Tom is looking to buy a second-hand sail boat and is willing to pay up to $3,900 for a boat in excellent condition. Tom has no inexpensive way to determine whether Jennifer's boat is in good condition or not. Answer the following questions: 

a. Thinking like an economist, would Tom definitely buy the sail boat from Jennifer? 

b. What is the DWL, as a result of the inefficiency caused by the asymmetric information, if Tom did not buy the boat at Jennifer's price? 

c. Over the following few months, after many sail boats are put up for sale at the end of a summer sailing season, what is likely to happen to the average quality of used sail boats in the market?

Answer 1

Answer 2

Question 9

Let the unknown amount of money be equal to $X.

It is provided that the expected value of earning from risky assets equals $25,000.

In risky assets, there is 21% chance of losing $30,000, a 10% chance of gaining $15,000, and a 69% chance of gaining an unknown amount of money.

Calculate the expected value of the risky assets -

EV = [0.21 * (-30,000)] + [0.10 * 15,000] + [0.69 * X]

EV = [-6,300] + 1,500 + 0.69X

EV = -4,800 + 0.69X

It is given that,

Expected value of risky assets equals $25,000.

EV = 25,000

-4,800 + 0.69X = 25,000

0.69X = 25,000 + 4,800

0.69X = 29,800

X = 29,800/0.69

X = 43,188

Thus,

The unknown amount of money is $43,188.