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1. (45 points) An infinitely lived representative household enjoys consumption and leisure stream {ct, li} o which is evaluated by: Vt = En. BU(ct, It). BE (0, 1) is the discount in both arguments. factor and U(., .) is increasing, strictly concave, and two times continuously differentiable This file ha Do not copy culataled for gen compile The household is endowed with one unit of time that can be used for leisure It and labor nt: It + nt = 1. Let the period utility function be given by: U(ct, 1 - n) = een ? log(ct) + plog(1 - nt) where p > 0 is a parameter that measures disutility from work. MID One unit of labor time earns the average wage rate in the economy wt. The household preciation rate o equal to zero, i.e. 8 = 0. can invest / save in capital assets kt which earn the interest rate rt. Let the capital de- comp mate. The household pays taxes on both income from labor and income from capital assets. A This file has been o not copy or circul stock. cir representative firm produces a single output good using labor nt and capital kt. Output compiled lul This file has beer Do not copy or can be consumed by households, used by the government, or used to augment the capital compiled for ulate ID The production function F(nt, kt) is a standard concave production function which has constant returns to scale, given by F(kt, nt) = kant , where 0