It's important to understand this problem fully so please break it down barney style. Thank you.

1. Suppose that Sam's utility function for wages and risk of death (R) is

U (W, r) = W x e^-15R

a. What is Sam's marginal rate of substitution risk for wage? Hint: Recall that the derivative of an exponential function e^f(x) is e^f(x) f (x). Please multiply your answer by (-1) or you will not get the correct answers to the remaining questions.

b. Suppose that Sam faces a linear isoprofit given by the equation W = 70 X R. Sam's wage at his current combination of wage and risk is $6. Assume that Sam is consuming on the isoprofit. Is he currently maximizing utility? Why or why not? What is his risk at this combination of wage and risk?

c. Use an indifference curve and the linear isoprofit to illustrate where Sam is currently consuming when he is being paid $6.

d. What is Sam's optimal combination of wage and risk?

e. Suppose that Sam's friend Dylan has a utility function for wages and risk that is given by U = W x e^-3R. Will Dylan select a higher or lower level of risk than Sam? Will his wage be higher or lower than Sam's? Please demonstrate.

f. Produce a diagram showing indifference curves for Sam and Dylan and the linear isoprofit to show the different choices. Just a sketch is fine. Please carefully label your diagram.