5. Consider a representative firm with the following real profit function over their two-period planning horizon: Profit

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5 Consider A Representative Firm With The Following Real Profit Function Over Their Two Period Planning Horizon Profit 1 (45.28 KiB) Viewed 13 times

5. Consider a representative firm with the following real profit function over their two-period planning horizon: Profit = (1 − 7) (ƒ(k₁, n₁) — wins) - invet + (1-7) (5 (127 f(k₂, n2) W272 1+r 1+r invnet 1+r 1-a where 7 is a tax on the firm's revenues less wage expense, f(ke, ne) = kena is the Cobb- Douglas production function, w, is the real wage rate paid to labor input ne, r is the real interest rate, and inuet is the real flow of net investment defined as: invet = kt+1-(1-6) ke where ke is the current-period real stock of capital which depreciates at rate 6 > 0. Assume that ki is predetermined. 1-0 (a) Using the real profit function, derive the optimality conditions for n1, n2, and k₂. (b) Let qe kon denote the amount of output produced by the firm. Express the firm's demand for labor in periods 1 and 2, and the firm's demand for capital in period 2, as derived demand functions. (c) Use your answers from part (b) to derive an expression for the firm's desired capital to labor ratio in period 2, k₂*/n2*. (d) Perform comparative static analysis to show how an increase in the tax rate on the firm's revenue would affect the amount of capital relative to labor that the firm desires to use in production during period 2.