Reference no: EM133199430

Assignment:

1. Table below presented calculations of fixed and declining discount rate present values using a 5 percent discount rate. Fill in the following table using a 10 percent discount rate. Is the difference for future years greater or equal to those using the 5 percent rate?

2. Jayne is playing a simple game with a fair 20-sided cube. There are 9 blue sides, 9 red sides, 1 green side, and 1 black side. If the chance cube lands with a blue side up, Jayne will win 5 points, if it lands with a red side up, she'll lose 10 points. Similarly, if it lands with the green side up, she will win 30 points and if the black side is facing up, then she will lose 20 points. Based on this information, answer the following questions.

A. What is the probability that the chance cube will land with a blue face up on any given turn? What are the chances of winning this game each time it is played?

B. What is the expected value of each roll of the chance cube?

C. Suppose it costs Jayne 1 point each time she rolls the cube. How much does this change the expected value?

D. Suppose Jayne is risk averse, with an initial wealth of 400 points and a utility function of √Wealth . Should she continue to play the game, or should she cash in her points for toys (a no risk proposition)?

E. Zoe is more adventurous than Jayne. Zoe has a utility function U = W2, where W = wealth. If her initial wealth is 500 points, should she play the game?

3. Your Turn 9-6 (p. 258) analyzed a simple expected utility problem based on the 2005 proposal to reform Social Security. Let's consider this problem with different values, and see how sensitive an individual's choice is to those values. Assume that the current system would pay a retirement benefit of $25,600 per year with no risk. Also assume that the private account would provide the following possible benefits: a ¼ chance of receiving $14,400, a ½ chance of receiving $27,225, and a ¼ chance of receiving $36,100.

A. Draw the decision tree for this problem.

B. Calculate the expected value of the private account. For a person with no risk aversion, which retirement program should be chosen?

C. For a risk averse person with a utility function of U =√I and no initial wealth, find the expected utility of the private account. Would the person prefer this result to the certain $25,600 payoff?

4. Suppose that the government decides to require all school children to wear helmets when playing dodge ball. Assume that 40 million school children play dodge ball and that 50% more children wear helmets now than had previously done so. Given this information, answer the following questions:

A. If 4/5 of the 50% increase is due to the enactment of the law, how many children would now be wearing helmets because of the law?

B. If 3,500 nosebleeds are prevented per year, what is the change in the annual risk of nosebleeds caused by the new law?

C. Assume the implicit value of a nosebleed is $100. What are the total benefits of the law?

D. If a dodge-ball helmet costs $10, what is the total cost of the program? Do the costs outweigh the benefits?