Finance 462

Problem Set #1

1)      Suppose that, each year, you have a 2% chance of being involved in a car accident.  The damages from a car accident are $10,000.

a)      Assuming that you donít purchase insurance, calculate the expected value of your losses.  Calculate the standard deviation of your losses.

b)      Now, suppose that you by insurance.  How much should an insurance policy cost (Assuming everybody has a 2% accident rate)? What happens to the expected value and standard deviation of your losses?

c)      Now, suppose that there are two types of drivers.  Safe drivers have a 2% accident rate, while unsafe drivers have a 4% accident rate.  Assume that there are an equal number of safe and unsafe drivers, but the insurance company canít distinguish between the two types.  How does your answer to (b) change? 

Suppose that apples and oranges are the only two goods available in the economy, and that they are sold in the quantities and prices indicated in the following table

 

Apples

 

Oranges

 

Year

Quantity

Price

Quantity

Price

1970

30

$1

70

$1

2000

40

$4

60

$2

2)      Suppose the assuming that the average household spends 30% of its income on apples and 70% of its income on oranges each year, calculate the CPI for 1970 and 2000.  What is the average annual inflation rate?

3)      Using 1970 as the base year, calculate real and nominal GDP for 2000. What is the implied annual inflation rate?

4)      Over the past 30 years, we have seen a shift in consumer patterns in the US .  In 1970, the average household spent 30% if its income on services while in 2000, the average household spent 40% on services (hmmÖ..these numbers sound familiar!).  Further, services have higher rates of inflation than goods (some goods.  What does this information tell us about the accuracy of the CPI?

5)      Consider an economy with 100 people in the labor force.  At the beginning of every month, 5 people lose their jobs and remain unemployed for exactly one month; one month later, they find new jobs and become employed.  In addition, on January 1 of each year, 2 people lose their job and remain unemployed for 6 months.  Finally, on July 1 of each year, 1 person loses his job and remains unemployed for 1 year.

a)      What is the unemployment rate in this economy in a typical month?

b)      What is the average duration of unemployment?