Problem 1. Certainty Equivalents and Risk Premia Consider utility function of the form U (x1, x2)...

 

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Problem 1. Certainty Equivalents and Risk Premia Consider utility function of the form U (x1, x2) = 7₁x³ +2x²³, where X1 and x₂ are (monetary) consumption levels in states 1 and 2, respec- tively, which occur with probabilities T₁ = 32 and ₂ = = 392. 39 33 (a) Calculate the expected utility of a lottery that pays nothing in state 1 and 216 in state 2. Calculate the expected value of this lottery, and the util- ity of receiving this expected value with certainty, i.e., of receiving this expected value in both states of nature. Which is larger - the expected utility of the lottery, or the utility of the expected value of the lottery? What does this tell you about this person's attitude toward risk? (b) The certainty equivalent of the lottery is a payoff which, if received with certainty, would make this person indifferent between the lottery and receiving the certainty equivalent in each state. Calculate the certainty equivalent in part (a). How does it compare to the expected value? (c) Use the definition of concavity to show in general that if one is risk averse, then the certainty equivalent of a lottery falls short of its ex- pected value. The difference between these two is often called the risk premium for the lottery. Problem 1. Certainty Equivalents and Risk Premia Consider utility function of the form U (x1, x2) = 7₁x³ +2x²³, where X1 and x₂ are (monetary) consumption levels in states 1 and 2, respec- tively, which occur with probabilities T₁ = 32 and ₂ = = 392. 39 33 (a) Calculate the expected utility of a lottery that pays nothing in state 1 and 216 in state 2. Calculate the expected value of this lottery, and the util- ity of receiving this expected value with certainty, i.e., of receiving this expected value in both states of nature. Which is larger - the expected utility of the lottery, or the utility of the expected value of the lottery? What does this tell you about this person's attitude toward risk? (b) The certainty equivalent of the lottery is a payoff which, if received with certainty, would make this person indifferent between the lottery and receiving the certainty equivalent in each state. Calculate the certainty equivalent in part (a). How does it compare to the expected value? (c) Use the definition of concavity to show in general that if one is risk averse, then the certainty equivalent of a lottery falls short of its ex- pected value. The difference between these two is often called the risk premium for the lottery.

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Sel 213 U 71 241 Pstete 3972 12x 8 in state I empected utility of lottery 0 x x ... View the full answer