A question about basic pricing equation for any payoff, risk-free rate changes, Sharpe ratio.

There are two equally likely states of nature that can occur at date tI 1, either there is an expansion or there is a recession. An investor has preferences over consumption at dates t and tI 1 that can be represented by the utility function c3"? c2: \"(CtrCt-l-l) = 1_1r + 5E]? m where 'y 75 1 and [3 E (0,1). The agent can trade a risk-free bond and shares of a firm in a competitive market. Let p? and p? denote the price of a bond and a share of the firm in period t, respectively. A risk-free bond issued at date t is a promise to pay 1 unit at date t+ 1. The payoff of a share at date tl 1 is pf+1 + d3\