This problem takes you through the formal definition of risk aversion / risk loving. Given a...

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This problem takes you through the formal definition of risk aversion / risk loving. Given a lottery P, let E (P) be the expected value of the lottery P. For example, if P = ($10,0.5; $0,0.5), then E(P) = 0.5 x 10 + 0.5 x 0 = 5 We say a person is • Risk averse if he chooses E (P) dollars for sure over the lottery P • Risk neutral if he is indifferent between E (P) dollars and the lottery P • Risk loving if he chooses the lottery P over E (P) dollars for sure. One way to measure "how" risk averse someone is is to use something called the Arrow- Pratt coefficient of risk aversion. Given a vNM utility u, the Arrow-Pratt coefficient is -u" (x) r(r) u' (r) (1) Ann has vNM utility u (r) = r, Bob has utility u2 (r) = log (2r + 1) and Carl has utility uz (r) = r'. Who is risk neutral, risk averse and risk loving? (2) Consider the lottery P again. Find the dollar amount r such that each person is indifferent between the lottery P and Sr (r is the certainty equivalent of P) (3) Calculate the Arrow-Pratt coefficients for everyone. How do they compare? Does this agree with your answers before? (4) Calculate the Arrow-Pratt coefficient for utility u (r) = -e-p where p> 0. This type of utility is called Constant Absolute Risk Aversion (CARA). Why do you think it's called CARA? (5) Calculate the Arrow-Pratt coefficient for utility u (x) = where p> 0. This type of utility is called Constant Relative Risk Aversion (CRRA). Why do you think it's called CRRA? This problem takes you through the formal definition of risk aversion / risk loving. Given a lottery P, let E (P) be the expected value of the lottery P. For example, if P = ($10,0.5; $0,0.5), then E(P) = 0.5 x 10 + 0.5 x 0 = 5 We say a person is • Risk averse if he chooses E (P) dollars for sure over the lottery P • Risk neutral if he is indifferent between E (P) dollars and the lottery P • Risk loving if he chooses the lottery P over E (P) dollars for sure. One way to measure "how" risk averse someone is is to use something called the Arrow- Pratt coefficient of risk aversion. Given a vNM utility u, the Arrow-Pratt coefficient is -u" (x) r(r) u' (r) (1) Ann has vNM utility u (r) = r, Bob has utility u2 (r) = log (2r + 1) and Carl has utility uz (r) = r'. Who is risk neutral, risk averse and risk loving? (2) Consider the lottery P again. Find the dollar amount r such that each person is indifferent between the lottery P and Sr (r is the certainty equivalent of P) (3) Calculate the Arrow-Pratt coefficients for everyone. How do they compare? Does this agree with your answers before? (4) Calculate the Arrow-Pratt coefficient for utility u (r) = -e-p where p> 0. This type of utility is called Constant Absolute Risk Aversion (CARA). Why do you think it's called CARA? (5) Calculate the Arrow-Pratt coefficient for utility u (x) = where p> 0. This type of utility is called Constant Relative Risk Aversion (CRRA). Why do you think it's called CRRA?

Answer rating: 100% (QA)

Ann has vNM utility u1x x VP 05 u110 05 u10 05 10 05 0 5 Here EPVP is Ann is risk neutral Bob has ut... View the full answer