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

Consider the utility function U(W) = W^0.5 where W = wealth a) Perform the necessary calculations...

Consider the utility function U(W) = W^0.5 where W = wealth a) Perform the necessary calculations to demonstrate the order of preference of an investor with this utility function. Order them from most preferred to least preferred. -Prospect 1: 50% chance of $1000, 50% chance of $2000 -Prospect 2: 25% chance of $500, 25% chance of $2000, 50% chance of $1000 -Prospect 3: $1000 for certain. b) Explain the meaning of the expression certainty equivalent. (That is, Provide the definition)...

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

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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...

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

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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?

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...

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