Consider a variant of the dynamic GE model with production. In this problem you will extend the model to allow for three periods instead of two. Specifically, suppose the representative household has preferences given by U(Co, C1, C2, lo, l1, 12)] = u(Co, lo) + Bu(C1, hi) + Bau( C2, 12), (1) where 3 = 1/(1 + p), p 2 0, and u(.) satisfies the usual assumptions. The household's endowments are h units of time in each period, and So units of capital in period 0. The firm produces output according the following production technology: Yt = > F(Kt, NF), for t = 0, 1, 2, (2) where F() satisfies the usual assumptions including constant returns to scale. The firm supplies output to and demands capital and labour from the household each period in competitive spot markets