The two periods are indexed by t = 0 and 1. There is no uncertainty in period 0 and let c(0) be the household's consumption in period 0. There is uncertainty in the second period and the household's consumption plan is denoted by c(1) = (c1, c2, ..., cN ), where N is the number of states. The household's preferences for consumption in two periods are summarized by the following utility function: ((0), (1)) = ((0)) ( ) where =1,2,3,,,,N where () = 1/(1) ((^(1)) 1) and is the time discount factor, 0 < < 1. The objective probability for state i is . The household is endowed with a certain income y0 in period 0, which the household can use for consumption in period 0, and invest in a risk-free bond that pays $1 in period 1, or invest in a stock that yields a risky payoff of = (1, 2, ... , ) in period 1. The household's budget constraint in period 0 is: c(0) b s = y0 where is the price of the risk-free bond, b is the amount invested in the risk-free bond and is the price of the stock