Exercise 1 – Choice under uncertainty [18 points]

Let us assume that your utility function is given by U = √I . You have been offered two wage offers.

• In the first one you will receive a fixed salary of $54,000.

• In the second one, you will only receive $4,000 as a fixed payment, plus a bonus of $100,000 if the firm goes profitable. The probability that the firm goes profitable (and you get a total of $104,000 that year) is 0.5, while the probability that the firm does not make enough profits is 0.5.

a) Find the expected value of the lottery induced by accepting the second wage offer.

b) Find the expected utility associated with the second offer.

c) Draw an approximate figure where the following elements are clearly illustrated:

• Utility function (either concave, linear or convex)

• Utility level (in the vertical axis) from the first wage offer.

• Utility level (in the vertical axis) from each of the two possible outcomes of the second wage offer.

• Expected utility level from the second wage offer.

d) Using your answers from parts (a) and (b), find the risk premium associated with the second offer.

e) What amount of money should the first wage offer propose you in order to make you exactly indifferent between accepting the first and the second wage offers?

f) In your figure from part (c) include the risk premium of the second wage offer.

Let us assume that your utility function is given by U = √I . You have been offered two wage offers.

• In the first one you will receive a fixed salary of $54,000.

• In the second one, you will only receive $4,000 as a fixed payment, plus a bonus of $100,000 if the firm goes profitable. The probability that the firm goes profitable (and you get a total of $104,000 that year) is 0.5, while the probability that the firm does not make enough profits is 0.5.

a) Find the expected value of the lottery induced by accepting the second wage offer.

b) Find the expected utility associated with the second offer.

c) Draw an approximate figure where the following elements are clearly illustrated:

• Utility function (either concave, linear or convex)

• Utility level (in the vertical axis) from the first wage offer.

• Utility level (in the vertical axis) from each of the two possible outcomes of the second wage offer.

• Expected utility level from the second wage offer.

d) Using your answers from parts (a) and (b), find the risk premium associated with the second offer.

e) What amount of money should the first wage offer propose you in order to make you exactly indifferent between accepting the first and the second wage offers?

f) In your figure from part (c) include the risk premium of the second wage offer.

#### Top Answer

Please find... View the full answer