Department of Economics Columbia University Homework 8 Economics W3213 Intermediate Macroeconomics Consider a 2-period closed economy. Households have preferences over consumption in periods 1 and 2, denoted by c1 and c2 respectively, described by the following utility function: U(c1, c2) = ln c1 + ln c2. In period 1, households are endowed with Q1 = 8.4 units of the consumption good. In period 2, households receive profit income, 2 from their ownership of firms. Households must pay lump- sum taxes in the amount of T1 and T2, in periods 1 and 2 respectively. Initial bond holdings of households, B0, is nil and households are subject to a no-Ponzi game constraint that prevents them having negative bond holdings at the end of period 2. This constraint can be expressed as B2 0. The interest rate on bonds held from period 1 to period 2 is denoted r. 1. State the household’s budget constraints in period 1 and period 2 and derive the present value budget constraint of the household. 2. Find the slope of the household’s present value budget constraint. 3. Find the slope of the household’s indifference curve, that is, the change in C2 triggered by a unit change in C1 holding constant the level of utility. Assume that the government tries to stimulate the economy by means of 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 I > 0. That is, firms’ marginal costs, including the subsidy, are (1 – I )(1 + r), where r denotes the real rate of interest. The government finances the investment subsidy through lump-sum taxation in period 2. Government consumption is assumed to be nil in both periods and initial asset holdings of the government are zero, Bg0 = 0. 4. State the government’s budget constraint in period 2. Firms borrow I in period 1, which becomes productive in period 2. Specifically, the production function of firms is given by f(I) = 2pI. Assume that the…