Exercise 1. Distortionary taxes [46 points] Consider a small open economy with 2 periods. There is a single non-storable good. Pref- erences of the representative household are described by the following utility function: U(C1, C2) = In C1 + In C2. In period 1 and 2 households receive an endowment of Q1 = Q2 = 10. In period 1, households also pay a proportional tax on consumption To, and a proportional tax on their endowment To. In period 2, households don't pay taxes. Households are born with zero initial financial assets, Bo = 0. They have unrestricted access to international credit markets a the international interest rate r* = 0. In both periods the government consumes a constant level of expenditure G1 = G2 = 1. The government has unrestricted access to the world financial markets. The initial financial position of the government is zero, Bi = 0. (a) [8 points] Set up the budget constraint of households for periods 1 and 2. Derive the inter-temporal household budget constraint. (b) [8 points] Set up the budget constraint of the government for periods 1 and 2. Derive the inter-temporal government budget constraint. (c) [12 points] Suppose To = 0. Find the equilibrium levels of consumption C1, C2, tax on endowments To, the current account in period 1 and the level of utility attained by households. (d) [12 points] Now suppose To = 0. Find the equilibrium levels of consumption C1, C2, tax on consumption To, the current account in period 1 and the level of utility attained by households. (e) [6 points] Compare the levels of utility obtained by the household in the last two parts. Provide intuition for your results