Consider the two period model of tax smoothing discussed in the handout on Fiscal Policy. Suppose the real interest rate r is constant, the level of government debt outstanding at time O is zero and that the fiscal authority's discount rate r is equal to p. It was shown there that the optimal levels of the tax rates ( t1 and t2) are equal to the ratio of the present discounted value of government spending to the present discounted value of output over the two periods. (a) Assume that there is peace (i.e., no war) during period 1 while there is a war in period 2 so that government expenditure G is expected to be low in period 1 and high in period 2. The level of output Y, on the other hand, is expected to be constant during the two periods. What would be the optimal path of tax revenues and government deficit? Explain your answer. [8 marks] (b) Now assume that the path of government spending is constant in the two periods but there is a boom in period 1 followed by a recession in period 2. What would be the optimal path of tax revenues and government deficit? Explain your answer. [8 marks] (c) Assume now that the path of government spending is permanently lower (that is, lower in both periods 1 and 2). What would be the impact of this change on the optimal tax rates? Explain your answer. [9 marks]