Question

ONLY ANSWER QUESTION B, C (both c's), F (identifying i, ii, iii) & G. THANK YOU!

dud Jackson has a utility of money function given by U()- y. a) Is Jackson risk averse, risk neutral, or a risk lover? How do you know this? All of Jackson's wealth is in his land and his house; the total value is $1,000,000. With probability 0.4, the house will burn down, and Jackson's remaining wealth will be only the value of the land, which is $28,900. b) What is the expected value of the gamble Jackson faces? c) Write down the equation you would use to calculate the expected utility Jackson receives from this gamble, and briefly explain what expected utility is. c) Sketch Jackson's utility of wealth function, using at least page for your diagram. On the diagram indicate the expected value (EV) and his expected utility (EU). d) Explain what is meant by the "certainty equivalent of the gamble" in this context, and identify it on your diagram. How would you calculate the value of Jackson's certainty equivalent? e) What is the maximum amount Jackson would be willing to pay for full insurance against the tial lost wealth? Identify this amount on your diagram, and explain why this amount is correct. f) Using at least X page for your diagram, sketch Jackson's indifference curve given the situation above. Put income in the good state (no loss) on the horizontal axis. Identify the following in your diagram: i) the expected value of the gamble Jackson faces (EV) ii) Jackson's certainty equivalent of the gamble (y) ill) the amount Jackson would be charged for actuarially fair full insurance. 8) In a separate diagram, repeat the questions in part ( putting income in the good state on the vertical axis.

Answer 1

The utility of money function is given as U(y) = y? Jackson is a risk averse. This is because the utility function is strictly concave and has diminishing marginal utility of money. U(y) = y. U (9) - [(y)= 2y -<o 3 The function has diminishing marginal utility because the first derivative is strictly positive and the second derivate is negative indicating a strictly concave function. The expected value of the gamble is calculated as follows: Expected value=U(Y) 1+U(Y2)(1-1) Expected value= 28900(0.4)+1000000(0.6) Expected value=11560+600000 Expected value = 611560 The expected utility of wealth is determined as follows: Expected wealth =U[(Y,) A+(Y2)(1-1)] Expected wealth =U (611560) Expected wealth =(611560)3 Expected wealth=81.1

The expected value of the utility is calculated as follows: Expected utility = U(Y), A +U(Y)(1-1) Expected utility = (28900) (0.4)+(1000000)} (0.6) Expected utility = (29.6) (0.4)+(100) (0.6) Expected utility = 11.84 +60 Expected utility = 71.84 Utility U(Y) Wealth utility U[(Y).+(Y)(1-)] Expected U(Y) =+U(Y)(1-1) Utility U(Y) 611560 Y 28900 Y2 Income 1000000 Expected Value The certain equivalent of the gamble is the value of income which if Jackson had then it would yield him the same level of utility as he is receiving in the current situation. The expected utility received in this case is 71.84. Thus, the certain equivalent of the gamble is 71.84 Expected utility = U(Y), A +U(Y2)(1-1) Expected utility = (28900)] (0.4)+(1000000 )} (0.6) Expected utility = (29.6) (0.4)+(100) (0.6) Expected utility = 11.84+60 Expected utility = 71.84