Exercise 1 (Lump-Sum Taxes). Consider a two-period economy. Households preferences are described by the utility function In C, + In C2. where C, denotes consumption in period 1 and G, denotes consumption in period 2. In period 1, households receive an endowment Y, = 10. In period 2, households receive profits from firms that they own, denoted II,. Households pay lump-sum taxes 7, and 72 in periods 1 and 2, respectively, and can save or borrow at the interest rate r. Firms borrow funds in period 1 to invest I, units of goods in physical capital. In period 2, firma produce output using the technology radicalbig output in period 2 = 10 and pay back their loans. Firms maximize profits and distribute them to households. The government levics lump-sum taxes to households in the amounts 7, and 72 in periods 1 and 2, respectively, and consumes G, = 2 units of goods in period 1. Government consumption in period 2 is zero. Taxes in period 1 equal 1 (7, = 1). 1. Find the equilibrium interest rate, investment, and consumption in period 1. 2. Suppose the government spending in period 1 increases by 10 percent. Find the new equilibrium levels of the interest rate, investment, and consumption in period 1. Provide intuition. Exercise 2 (Investment Subsidy). Consider a 2-period production economy. Households have preferences over consumption in periods 1 and 2, denoted by C, and C, respectively, described by the utility function: In C + In C2- In period 1, households are endowed with Y, units of the consumption good. In period 2, they receive profit income, denoted II,, from the ownership of firma. Households pay lump-sum taxes in the amount of 7%, 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 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. 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