A home owner has a utility function of U (m) = √m, where m is income....

A home owner has a utility function of U (m) = √m, where m is income. The home owner is considering buying flood insurance because they live near a river that has flooded in the past. If it is a dry year, she will have an income of $60,000 to spend on other things. If it is a rainy year and there is a flood, then she has to pay for repairs to her house. Then her income will only be $20,000 to spend on non-flood costs. The probability of a flood based on historical data is 4%.

(a) (a) If the home owner can buy insurance for a premium of $0.04 per dollar of coverage, how large of an insurance policy should the homeowner buy? Set up the expected utility maximization problem and solve for K, the optimal insurance policy size.

(b) Now suppose we do not know the cost of the insurance policy. But you now know that in the event of a flood, that the insurance policy will pay you 75% of damages. What is the maximum amount the homeowner would be willing to pay for such an insurance policy?

(c) Explain in words how to generally calculate expected utility. What information do you need? What terms do you multiply versus add? Be clear in your explanation.

Expert Solution

Rahul Sunny answered 2 years ago

Suppose that an individual has a utility function of the form U = Y½ where U...

Suppose that an individual has a utility function of the form U = Y½ where U is utility and Y is income. a) Calculate the utility level for Y values of $10,000, $40,000, $90,000, $160,000, and $250,000 and then plot the individual’s total utility function. b) This individual is currently earning $90,000 but has a 50-50 chance of earning either $40,000 or $160,000 in a new job. i) Calculate the expected income and utility from the new...

(15) There are two groups of individuals, each with a utility function given by U(M)=√M, where...

(15) There are two groups of individuals, each with a utility function given by U(M)=√M, where M=8,100 is the initial wealth level for every individual. The fraction of group 1 is 3/4 . Each member of group faces a loss of 7,200 with probability 1/2. Each member of group faces a loss of 3,200 with probability 1/2. Assume that the insurance market is perfectively competitive. And the insurance company does not know who belongs to which group. (5) What is...

Suppose that Andrew has the utility function: U(C,M)= C0.5+M0.5 , where C represents cupcakes and M...

Suppose that Andrew has the utility function: U(C,M)= C0.5+M0.5 , where C represents cupcakes and M represents muffins. Andrew has income of $150. Suppose that the initial price per cupcake is $2 and the price per muffin is $1. At these prices, Andrew spends $100 on muffins. When cupcakes are on sale, each cupcake costs $1. When cupcakes are on sale, Andrew spends $75 on muffins. The price of muffins and Andrew’s income is unchanged throughout. 1. Draw a diagram...

Suppose that Anu’s utility function is given by U = √10W, where W represents annual income...

Suppose that Anu’s utility function is given by U = √10W, where W represents annual income in thousands of dollars. Suppose that Anu is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. a. Should she take the new job? b. Assume Anu takes the new...

A individual has a utility function u(c) = √ c, where c is the individual’s consumption....

A individual has a utility function u(c) = √ c, where c is the individual’s consumption. (The individual consumes his entire wealth.) The individual’s wealth is $40,000 per year. However, there is a 2% chance that he will be involved in a catastrophic accident that will cost him $30,000. PLEASE SHOW WORK a. What is the individual’s utility from consumption if there is no accident? What is his utility if there is an accident? What is his expected utility? b....

1. Suppose that an individual has the following utility function, ? = ?^0.5?.?, where U stands...

1. Suppose that an individual has the following utility function, ? = ?^0.5?.?, where U stands for utility and W for Wealth. The individual currently has a net wealth of $400,000. The individual believes there is a 5% chance they will get into a car accident this year. It is expected that a car accident would cost them $100,000 (dropping their overall wealth to $300,000). a) How much would it cost to purchase an actuarially fair insurance policy to cover...

Suppose that Elizabeth has a utility function U= (or U=W^(1/3) ) where W is her wealth...

Suppose that Elizabeth has a utility function U= (or U=W^(1/3) ) where W is her wealth and U is the utility that she gains from wealth. Her initial wealth is $1000 and she faces a 25% probability of illness. If the illness happens, it would cost her $875 to cure it. What is Elizabeth’s marginal utility when she is well? And when she is sick? Is she risk-averse or risk-loving? What is her expected wealth with no insurance? What is...

Consider a farmer with utility function U(Y) = ln(Y), where Y is the farmer's income. Supposed...

Consider a farmer with utility function U(Y) = ln(Y), where Y is the farmer's income. Supposed the farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy and he must choose which of two crops to plant: (1) wheat, which will produce an income of $28,000 in a normal year but only $10,000 in an abnormally rainy year, and (2) corn, which will produce $19,000 in a normal year but only $15,000 in an...

Every member of the population has utility function U(M) = ln(M+1). There are three groups of...

Every member of the population has utility function U(M) = ln(M+1). There are three groups of people of equal size in the population. Each group has a unique probability of getting sick, initial wealth level, and cost of treatment if sick, reported in the table below. Health insurance will cover the entire cost of health care if the individual falls sick. Probability of Illness Initial Wealth Cost of Health Care if Sick Health Nuts 0.001 $900 $50 Average Joe’s 0.01...

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40...

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? b) What is the marginal utility of good Y (MUy) for the consumer? How do I calculate these?

Question