The certainty equivalent of a lottery is the amount of money you would have to be given with certainty to be just as well-off with that lottery. Suppose that your von Neumann-Morgenstern utility function over lotteries that give you an amount x if Event 1 happens and y if Event 1 does not happen is U(x, y, π) = π √ x+(1−π) √ y, where π is the probability that Event 1 happens and 1−π is the probability that Event 1 does not happen.
(a) If π = .5, calculate the utility of a lottery that gives you $10,000 if Event 1 happens and $100 if Event 1 does not happen.
(b) If you were sure to receive $4,900, what would your utility be?
(c) Given this utility function and π = .5, write a general formula for the certainty equivalent of a lottery that gives you $x if Event 1 happens and $y if Event 1 does not happen.
(d) Calculate the certainty equivalent of receiving $10,000 if Event 1 happens and $100 if Event 1 does not happen.