Exercise 4. (25 points) Let u : R++R be the utility function of a given decision maker given by u(x) =1-e- and X the random outcome of a lottery L having cdf P(X = x) = (1 - p)*p, r = 0, ... 1. (8 points) Compute the expected utility of this lottery if the initial wealth of this decicon maker is w. 2. (8 points) Give the definition of a risk premium of a lottery and compute the risk premium of the above lottery for a decision maker with initial wealth w. 3. (5 points) Compute the derivative of the risk premium with respect to the initial wealth of the decision maker and explain why for this case the risk premium does not depend on the wealth. 4. (4 points) Is it realistic that a decision maker has the above utility function. Explain your answer! Solution. Exercise 4. (25 points) Let u : R++R be the utility function of a given decision maker given by u(x) =1-e- and X the random outcome of a lottery L having cdf P(X = x) = (1 - p)*p, r = 0, ... 1. (8 points) Compute the expected utility of this lottery if the initial wealth of this decicon maker is w. 2. (8 points) Give the definition of a risk premium of a lottery and compute the risk premium of the above lottery for a decision maker with initial wealth w. 3. (5 points) Compute the derivative of the risk premium with respect to the initial wealth of the decision maker and explain why for this case the risk premium does not depend on the wealth. 4. (4 points) Is it realistic that a decision maker has the above utility function. Explain your answer! Solution