what are the equilibrium conditions for Isoelastic utility crra?

Consider a household with preferences represented by constant relative risk aversion (CRRA), given by: leo' . u(c) =4 1- ?fg 71, log(c) ifc=1, where denotes the coefficient of relative risk aversion, and the household exhibits impatience through the discount factor p. The output in each period is generated by a production function with linear technology, Y7 = A;K; for the first period and Y, = A;K; for the second period. The agent begins with an endowment of capital K; in period 1. This capital then fully depreciates by period 2, making the investment decision in period 1 crucial as I; = Kj. The consumption in period 1 is determined by C; = Y7 I;. In period 2, the agent consumes the entire output, with C; = Y>