Advanced Macroeconomic Hw questions 1-7 need to be answered.

. Assume a young agents utility function is given by: U ( CY, C(+ 1 ) = = In CY + = In Ci+1. (1) The budget constraints when young and when old are given by; ( 1 + 20) Ci + P. Mi = WV Mt Cut1 = Wo+ Piti Where y is a consumption tax on young agents. 1. What is the consumer's intertemporal budget constraint? 2. Write down the resource constraint for this economy, assuming that at each point in time there are N young agents and N old agents along with a government sector that consumes G units of the consumption good at each point in time. 3. In words compare and contrast the resource constraint for the economy and the con- sumer's lifetime budget constraint. 4. Derive the government budget constraint. In this model, how is government spending financed? 5. From the consumer's maximization problem, solve for each of the endogenous variables in terms of the exogenous variables. Explain the intuition behind the solutions, also, explain what the first order necessary conditions imply. 6. Assume Wy = 2, 000, Wo = 400, # = 100. (a) Suppose government spending is financed solely by a consumption tax on old agents, (i.e., * = 1CY) solve for the steady state values for Rt, Ct, Ci+1, and Up. (b) Suppose government spending is financed solely by an inflation tax, (i.e., * = S(Rt) - S(Rt-1) Rt-1) solve for the steady state values for Rt, Ct, Cf+1, and Ur. 7. Draw a picture of the above 2 results on a single diagram and explain intuitively why the utility is higher under one particular taxing scheme compared to the other (your intuition must be in terms of the burden of taxation and how " distortionary" the tax is