1. Maritime Insurance Company offers insurance policies for recreational boats. A typical policy will pay the replacement cost of $25,000 if the boat is a total loss. If the boat is not a total loss but the damage is more than $10,000 the policy pays $5,000. For damage under $10,000, no coverage is offered. The company estimates the probability of no damage to be 0.60, the proof damage between $0 and $10,000 to be 0.25, and the probability of damage between $10,000 and $25,000 to be 0.12. If the company wants to make a profit of $200 above the expected cost, what should be the price of the policy?
2. 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 .25
60,000 .25
70,000 .25
80,000 .25
What is the expected value of employees you hire?
3. Spreadsheet Problem 1. An individual has to choose between investment A and investment B. The individual estimates that the income and probability of the income from each investment are as given in the following table:
Investment A Investment B
Income Probability Income Probability
$4000 .02 $4000 0.3
$5000 .03 $6000 0.4
$6000 .03 $8000 0.3
$7000 0.2
Using Excel’s statistical tools, calculate the standard deviation of the distribution of each investment. (b) Which of the two investments is more risky? (c) Which investment should the individual choose?
4. Spreadsheet 2. An individual is considering two investment projects. Project A will return a zero profit if conditions are poor, a profit of $4 if conditions are good, and a profit of $8 if conditions are excellent. Project B will return a profit of $2 if conditions are poor, a profit of $3 if conditions are good, and a profit of $4 if conditions are excellent. The probability distribution of conditions is as follows:
Conditions: Poor Good Excellent
Probability: 40% 50% 10%
Using Excel, calculate the expected value of each project and identify the preferred project according to this criterion. (b) Assume that the individuals utility function for profit is U(X) = X – 0.05X2. Calculate the expected utility of each project and identify the preferred project according to this criterion. (c) Is this individual risk averse, risk neutral, or risk seeking? Why?
5. Spreadsheet Problem 3: The benefits and costs of an investment project (the purchase of a piece of machinery) are those given in the following table. In excel, calculate net revenue, or the revenue from the investment minus the costs; the present value coefficient for every year; and the present value of the net revenue. Add together column F to get the net present value of the project. Should the firm purchase the machine?
End of Year Investment Revenue NE PV Coefficient 1/(1+0.5)n PVNR
0 1000 ----
1 200 600
2 300 800
3 300 800
4 400 800
4 --- 200 (salvage value)
6. 1.Using a spreadsheet like the following, entering formulas for the total revenue and consumer’s surplus, and given the following demand curve of a consumer for a monopolist’s product Q = 14-2P (a) find the total revenue of the monopolist when it sells 6 units of the commodity without practicing any form of price discrimination. What is the value of the consumers’ surplus? (b) What would be the total revenue of the monopolist if it practiced first degree price discrimination? How much would the consumers surplus be in this case? (c) What if the monopolist charged P = $5.50 for the first 3 units of the commodity and P = $4 for the next 3 units. What type of price discrimination is this?
TR Consumer’s Surplus
Q 6.0 24
P $4
1st Degree Consumer’s Surplus
2 Prices TR Consumer’s Surplus
P1 $5.50
P2 $4.00