2) (50 Points) Consider the following economy: 0 Time: Discrete, infinite horizon. - Demography: Continuum of mass 1 of (representative) consumer/worker households, a Government which has to meet a fixed per household expenditure g, and a large number of profit maximizing firms. 0 Preferences: The instantaneous household utility function over consumption, c, is u(.), which is strictly increasing and strictly concave. The discount factor is [3 lies in the interval (0, 1). 0 Technology: There is a constant returns to scale technology over capital and labor such that per capita output is f (k), where k is capital input per unit of labor. - Endowments: Households' initial capital stock is k0, each household has 1 unit of time which it can devote in any proportions to labor or leisure. Assume f (k0)+ (1 6) k0 > g. (Required to get the economy off the ground.) (i) Write down the government's budget constraing if the government imposes a proporational income tax (Tt)0n labor income of households. (ii) Write down the household's budget constraint. (iii)Write down the firm's optimization problem. (iv)Derive the Euler equation. You can assume a CRRA utility function for the households. (v) Write down the 4 conditions that will summarize equilibirum in a competitive economy. (vi)How does your answer compare to the lumpsum taxes we did in class? Does the answer surprise you? Why/Why not. Explain