1. Consider a two-period economy, if : 1,2. There is a single representative household with preferences 2 \" (10g(0t) + 910g(1 - 1a)) , i=1 with 5 6 (0,1) and 6 > 0, where at is consumption and nt is labor effort. The consumer has free access to the credit market at the equilibrium interest rate r, and suppose that the initial stock of assets at the start of the rst period is zero. There is a representative rm producing every period 25 according to yt : 2m, with z > 0. Finally, there is also a government who every period 15 needs to fund an exogenous level of lump-sum transfers to the consumer Tt (no other public spending), by either taxing total (labor plus (net) interest) income at the proportional rate 'rt 6 (0,1), or by issuing public debt bt+1. Assume the level of public debt at the start of the rst period is zero. (a) Write down the consumer's ow budget constraints. (b) Derive the consumer's lifetime budget constraint. (c) Derive the intratemporal optimality condition and the Euler equation, and interpret them. (d) Are taxes distortionary? Explain how they affect individual behavior. (e) For the remainder of the question, assume 6 = 0. Suppose, differently from above, that the government is able to tax labor and interest income at different rates, call them 7;\" and 'rtf, respectively. What's the socially optimal composition of labor and interest income tax rates? Explain. (f) Suppose the government decides not to tax interest income, and to tax only labor earn- ings. Suppose also, similar to the policy reaction of many governments during the pandemic, that the government wishes to increase current transfers T1, without chang- ing current taxes Ti\". How can the government accomplish such policy? Please state explicitly how the policy variables must change. (g) Describe how consumers react in equilibrium to the policy described in the previous point: how does labor effort, consumption, and saving change? Please solve the model explicitly, and explain you reasoning