W 2 Assume you have the following von Neumann-Morgenstern utility function: U(w) = 200 – (12...
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probability %, and 4 with probability %. Calculate my certainty equivalent for this gamble: CE=_ . Calculate my risk premium p for this gamble p=
4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m 2 . She currently has $2025. a. Would she be willing to undertake a gamble that involves a gain $2875 with probability ) and a loss of $1125 with probability Ž ? Show your work and explain your answer. b. Would she be willing to undertake a gamble that involves a gain $2599 with probability { and a loss of $800 with probability — ? Show your work and explain...
Suppose you are selling car insurance. You have a customer with the utility function U(w)=600-200 Where w is the customer's wealth. With probability 0.1, this customer is going to get into an accident while driving. If there is an accident, the customer would have to pay for all the damages and would end up with wealth of $1. The customer has a 0.9 probability of not getting into an accident, and if this were to happen, the individual would get...
2. (20) Suppose your VN-M utility is u(w) = ln w. You are offered to bet on a coin flip which lands heads with probability p. If you bet $x, you win o in case of a head, and lose x in case of a tail. Your initial wealth is w. How much would you bet?
2. (20) Suppose your VN-M utility is u(w) = ln w. You are offered to bet on a coin flip which lands heads with probability p. If you bet $x, you win in case of a head, and lose x in case of a tail. Your initial wealth is wo. How much would you bet?
Ann is risk-averse with a Bernoulli utility function u(w) = 100 + w^1/2 where w is her wealth in dollars. Ann’s current wealth is one million dollars, including her small boat valued at $180, 000. She estimates that with 10% probability the boat will sink and lose its full value; with 15% probability there will be damages and the boat will lose half its value, and with 25% probability the boat will lose a quarter of its value; otherwise, the...
(Mathematical Question) Suppose you have a utility function where W is the level of wealth you end up with. You are currently in possession of 81 dollars. There is a 1/3 chance that a miserable event will happen and cost you all 81 dollars. Assume your preference over uncertainty is characterized by the expected utility. a. (5pts) Define the gamble b. (5pts) What is the expected value of this gamble? c. (10pts) Find the certainty equivalent of the gamble. Then find the insurance premium...
6. You have u = x1/2 risk averse utility. Your initial wealth consists of $225 cash and a $175 Apple Pencil III. This means that your initial wealth is Xo = 225 +175 = 400. There is a n = 10% chance the pencil will die and be worth $0. Apple offers insurance. They will replace the pencil if it dies. a. What is the maximum fee F, you would pay for this insurance? b. Provide a Utility of Wealth...
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? ( Answer: MUx = 10) b) What is the marginal utility of good Y (MUy) for the consumer? ( Answer: MUy = 1) c)...