Suppose that you are the only income earner, and you have a good job guaranteed to...

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Suppose that you are the only income earner, and you have a good job guaranteed to give you your current (family) income every year for life. You are given the opportunity to take a new and equally good job, with 50% chance it will double your income and 50% chance that it will cut your income and it falls to the fraction (0 < < 1) of your current income. (1) What is your value at which you would take a new job? (If you are willing to take the job when the new job cut your income a third or less than a third, your is 1(1/3)= 2/3.) (2) Assume you have the power utility function with RRA= y, which was assumed in Question 1. Derive the relation between and y. (hint) An expected utility maximizer will choose the 50-50 gamble of doubling lifetime income as opposed to having it fall by the fraction of 1- if 1 U(2c) + U(2) U(c), UC 2 2 where U is utility function and c is permanent consumption guaranteed by current income. (3) In (y,)-plane, draw the graph that represents the equation obtained in the previous question. (4) From the graph drawn, estimate your y value. Suppose that you are the only income earner, and you have a good job guaranteed to give you your current (family) income every year for life. You are given the opportunity to take a new and equally good job, with 50% chance it will double your income and 50% chance that it will cut your income and it falls to the fraction (0 < < 1) of your current income. (1) What is your value at which you would take a new job? (If you are willing to take the job when the new job cut your income a third or less than a third, your is 1(1/3)= 2/3.) (2) Assume you have the power utility function with RRA= y, which was assumed in Question 1. Derive the relation between and y. (hint) An expected utility maximizer will choose the 50-50 gamble of doubling lifetime income as opposed to having it fall by the fraction of 1- if 1 U(2c) + U(2) U(c), UC 2 2 where U is utility function and c is permanent consumption guaranteed by current income. (3) In (y,)-plane, draw the graph that represents the equation obtained in the previous question. (4) From the graph drawn, estimate your y value.

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1 To determine the value at which you would take the new job we need to find the income level at whi... View the full answer