DE homework10_2023.pdf * + X C 2 | C:/Users/ibsyd/Downloads/homework 10_2023.pdf ... b N Netflix 1 7989246... 0 use qy! Di Index-Torrents Saginaw Valley Stat... [ 898 179 0 028 20401.. DJ 4K Hologram Leade... A TAXI 81 # 13... (D) iKIET-652_815+4. V 12171 2 12 1 401 9171 - + 2 | 1 92 | 2 1 0 Department of Economics Columbia University Spring 202 Instructor: Martin Uribe Homework 10 O Economics UN3213 Intermediate Macroeconomics Due April 19, before class on Gradescope Exercise 1 (Lump-Sum Taxes). Consider a two-period economy. Households preferences are described by the utility function + In C1 + In C2, where Ci denotes consumption in period 1 and C2 denotes consumption in period 2. In period 1, households receive an endowment Y1 = 50. In period 2, households receive profits from firms that they own, denoted II2. Households pay lump-sum taxes Ti and T2 in periods 1 and 2, respectively, and can save or borrow at the interest rate ri. Firms borrow funds in period 1 to invest /1 units of goods in physical capital. In period 2, firms produce output using the technology output in period 2 = 10 V/1 and pay back their loans. Firms maximize profits and distribute them to households. The government levies lump-sum taxes to households in the amounts Ti and T2 in periods 1 and 2, respectively, and consumes G1 = 2 units of goods in period 1. Government consumption in period 2 is zero. Taxes in period 1 equal 1 (71 = 1). 1. Derive the investment schedule, I1 = I(r1). 2. Find the equilibrium interest rate, 71, investment, 1 and consumption in period 1, C1. Your answer should be three numbers. 3. Suppose now the government embarks on a massive spending program in period 1. As a result we now have G1 = 23. Find the new equilibrium levels of the interest rate, investment, and consumption in period 1. Provide intuition. 4. Assume now that households have a Leontief utility function: min { C1, C2}. Solve part 2 for this case. Q #' ALOOCHO 28 10:16 2023-04-18 19*Homework Help - Q&A from Or x homework10_2023.pdf X + X C @ file:///C:/Users/ibsyd/Downloads/homework10_2023.pdf TAIS ... col DU| X) do Transfer Credit Info... do Making Your Onlin... S | |x yEU|... do The Core CU Directory of Cl... to Contemporary Civil... do Quantitative Reaso... do Writing 0. That is, firms' marginal cost of funds, including the subsidy, are (1 - 7 ) (1+ 51). The government finances the investment subsidy through lump-sum taxation in period 2, T2. Government consumption is assumed to be nil in both periods. State the government's budget constraint in period 1 and in period 2. 3. Firms borrow I1 in period 1, which becomes productive in period 2. The production function of firms is given by output in period 2 = 2V /1. State the firm's profit maximization problem taking into account the investment subsidy. 4. Find the firm's investment demand as a function of the interest rate, 71, and the investment subsidy rate, T', and provide an intuitive interpretation of your findings. 5. Assume that Y1 = 1. Assume further that the investment subsidy is 0. Find the equilibrium level of investment, /1, consumption in periods 1 and 2, C1 and C2, output in period 2, and 28 10:16 2023-04-18 19DE homework10_2023.pdf * + 0 X C 1 2 | C:/Users/ibsyd/Downloads/homework10_2023.pdf ... b N Netflix # 4719832419... 0 use a! Di Index-Torrents Saginaw Valley Stat... [ 8|98 79 0 08 2001... DJ 4K Hologram Leade... A TAXI 81 # 13... (D.) iKIET-652_915+4. +| 2 912 2 1 ED In period 1, households are endowed with Y1 units of the consumption good. In period 2, they receive profit income, denoted II2, from the ownership of firms. Households pay lump-sum taxes in the amount of T2, in periods 2. Lump-sum taxes in period 1 are zero. The interest rate on assets held from period 1 to period 2 is denoted r1. 1. State the household's budget constraints in period 1 and period 2 and derive the present value budget constraint of the house O 2. Assume that the government in an effort to stimulate the economy implements an investment subsidy. Specifically, the policy takes the form of a proportional subsidy to the firm's marginal costs of investment. Denote the subsidy rate by 7 > 0. That is, firms' marginal cost of funds, including the subsidy, are (1 - 7 ) (1 +71). The government finances the investment subsidy through lump-sum taxation in period 2, + T2. Government consumption is assumed to be nil in both periods. State the government's budget constraint in period 1 and in period 2. 3. Firms borrow I1 in period 1, which becomes productive in period 2. The production function of firms is given by output in period 2 = 2V /1- State the firm's profit maximization problem taking into account the investment subsidy. 4. Find the firm's investment demand as a function of the interest rate, 71, and the investment subsidy rate, T', and provide an intuitive interpretation of your findings. 5. Assume that Y1 = 1. Assume further that the investment subsidy is 0. Find the equilibrium level of investment, /1, consumption in periods 1 and 2, C1 and C2, output in period 2, and the real interest rate, 71. 6. Now assume that that the investment subsidy is 50 percent, 7 = 0.5. Find the equilibrium levels of investment, consumption in periods 1 and 2, output in period 2, and the real interest rate. 7. Is the 50-percent investment subsidy successful in stimulating investment? Does it improve welfare, In C1 + In C2? Explain why or why not. 8. Find the welfare maximizing value of 7, that is, the value of r that maximizes In C1 + In C2. Provide an intuitive explanation of your findings. Q #4 28 10:16 2023-04-18 19