Question 1: Consider the following representative agent economy. Households solve the following problem: (29-0-1 c8 ) max EO 1-0 t=0 subject to: Ct + kt+1 = wint +r+kt+ (1 - 8) kt Tt It + nt 1 where ko > 0, 0 > 0, 0 (0,1). Notation should be obvious. Tt denotes lump-sum taxes. (a) Derive the first-order necessary conditions of the household. What is the Frisch labor supply elasticity for these preferences? Is there a wealth effect on labor supply? (b) Suppose that output is produced by competitive firms with the production func- tions: Yt = kt-onio where a (0,1). Find the firms' first-order conditions. (c) The government uses the tax revenue to finance a stream of government spending. Assume that government spending is exogenous and equal to , a constant. The government budget constraint is: = Tt Define a competitive equilibrium and derive the conditions that must be satisfied in the competitive equilibrium. (d) Derive the deterministic steady-state and examine how steady-state hours worked, output and investment depend on the steady-state level of government spending. (e) Repeat question (d) when government spending is financed by either a labor income tax or by a capital income tax. Question 1: Consider the following representative agent economy. Households solve the following problem: (29-0-1 c8 ) max EO 1-0 t=0 subject to: Ct + kt+1 = wint +r+kt+ (1 - 8) kt Tt It + nt 1 where ko > 0, 0 > 0, 0 (0,1). Notation should be obvious. Tt denotes lump-sum taxes. (a) Derive the first-order necessary conditions of the household. What is the Frisch labor supply elasticity for these preferences? Is there a wealth effect on labor supply? (b) Suppose that output is produced by competitive firms with the production func- tions: Yt = kt-onio where a (0,1). Find the firms' first-order conditions. (c) The government uses the tax revenue to finance a stream of government spending. Assume that government spending is exogenous and equal to , a constant. The government budget constraint is: = Tt Define a competitive equilibrium and derive the conditions that must be satisfied in the competitive equilibrium. (d) Derive the deterministic steady-state and examine how steady-state hours worked, output and investment depend on the steady-state level of government spending. (e) Repeat question (d) when government spending is financed by either a labor income tax or by a capital income tax