12. normal density Ralph must select between two lotteries. Either one will net him some cash in the amount w, where w is a normally distributed random variable. The first lottery has a mean of μ1 = 200 and a variance of

σ21

= 50 while the second has a a mean of μ2 = 210 and a variance of

σ21

= 150. Ralph displays constant absolute risk aversion, and thus uses a utility function of the form U(w) = −exp(−ρw). Determine

ρ such that Ralph is indifferent between the two lotteries.