(b) Suppose the government spending in period 1 increases by 10 percentFind the new equilibrium levels of the interest rate, investment, and consumption in period 1. Provide intuition. 3. Investment Subsidy Consider a 2-period production economy. Households have preferences over consumption in periods 1 and 2, denoted by, and Cy respectively, described by the following utility function: U(C, G) = Ing, + InC2- In period 1, households are endowed with , units of the consumption good. In period 2, households receive profit income, I, from the ownership of firms. Households pay lump-sum taxes in the amount off2, 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 (a) State the household's budget constraints in period 1 and period 2 and derive the present value budget constraint of the household. 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 2 0. That is, firms' marginal costs, including the subsidy, are (1 - T') (1 +7 ). The government finances the investment subsidy through lump-sum taxation in period 2, Ty Government consumption is assumed to be nil in both periods. (b) State the government's budget constraint in period 1 and in period 2. And file. Firms borrow I, in period 1, which becomes productive in period 2Specifically, the production function of firms is given by radicalbig (c) State the firm's profit maximization problem taking into account the investment subsidy. (d) Find the firm's investment demand as a function of the interest rate, and the investment subsidy rate, T, and provide an intuitive interpretation of your findings. (e) State the market clearing condition in the goods market in period 1. (f) State the market clearing condition in the goods market in period 2. Assume that the investment subsidy was initially zero and then is raised to 50 percent, that is, T/ changes from 0 to (6. Assume that Y, = 1