A farmer has a utility function of u(w) = w^0.5. If there is good weather, the...

A farmer has a utility function of u(w) = w^0.5. If there is good weather, the farmer will earn 100,000. If there is bad weather, she will earn 50,000. The probability of bad weather in any given year is 0.3. An insurance company offers the farmer a contract where the farmer would receive a 50,000 payout when there is bad weather. The insurance premium is denoted as p. What is the maximum premium that the farmer would be willing to pay for the insurance contract? Show your calculations and draw your answer on a graph.

Expert Solution

Rahul Sunny answered 1 year ago

A person has an expected utility function of the form U(W) = W . He owns...

A person has an expected utility function of the form U(W) = W . He owns a house worth $ 500,000. There is a 50% chance that the house will be burned down. Then, he will become literally penniless . Luckily, however, there are insurance companies which make up for losses from house fire. Currently, they charge $q for $1 compensation (in cases of fire). In other words, the home owner should pay $qK for K units of fire insurance...

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...

An individual's utility function is U= (X+1)0.5 (Y+2)0.5

An individual's utility function isU= (X+1)0.5 (Y+2)0.5(a) By implicit differentiation, find the slope of any indifference curve and show that it is given by the ratio of marginal utilities of the two goods.(b) Find the indifference curve for U= 6 and show that it is negatively sloped and convex. Does the indifference curve cut the axes? What does this imply about this individual's tastes?

Utility function is U = 0.5 ln q1 + 0.5 ln q2 a) What is the...

Utility function is U = 0.5 ln q1 + 0.5 ln q2 a) What is the compensated demand function for q1? b) What is the uncompensated demand function for q1? c) What is the difference between uncompensated demand functions and compensated demand functions?

Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W)...

Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W) indicates the natural logarithm of wealth. What is the maximum amount this individual would pay for full insurance to cover a loss of $5,000 with probability 0.10?

A person with initial wealth w0 > 0 and utility function U(W) = ln(W) has two...

A person with initial wealth w0 > 0 and utility function U(W) = ln(W) has two investment alternatives: A risk-free asset, which pays no interest (e.g. money), and a risky asset yielding a net return equal to r1 < 0 with probability p and equal to r2 > 0 with probability 1 (>,<,=) p in the next period. Denote the fraction of initial wealth to be invested in the risky asset by x. Find the fraction x which maximizes the...

Tim has a concave utility function u(w) = w ‐ w²/2, where w∈[0,1] His only major...

Tim has a concave utility function u(w) = w ‐ w²/2, where w∈[0,1] His only major asset is shares in an Internet start‐up company. Tomorrow he will learn his stock's value. He believes that it is worth $w0 with probability 4/5 and $w1 with probability 1/5, with w1 > w0. 1) Calculate the expected value of the lottery, the expected utility, and the utility of the expected value. 2) If w0 = 1/3 and w1 = 2/3. Compute the risk...

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 a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices...

Suppose that a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices are p1 =1and p2 =1,andincomeism=100. Now, the price of good1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compensating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (c) What is amount of the equivalent variation? How to interpret it?

.Suppose that an individual has the following utility function: ?(?, ?) = ? 0.5? 0.5 in...

.Suppose that an individual has the following utility function: ?(?, ?) = ? 0.5? 0.5 in which L is leisure time in hours per day and C is the time for a one-way commuting to work in hours per day. It is also known that leisure time for this individual has opportunity cost of $5 per hour while commuting costs $4 per hour. If you assume that this individual is a rational person who spends 7 hours for sleep and...

Question