We can use the Life-Cycle model to analyze the effect of one-time shocks. A potentially interesting case of a one-time shock is a temporary increase in government spending due to a war. In this homework we will analyze a very stylized increase in government spending. We make the following assumptions: 1. the economy is in steady state initially at time t = 0. 2. at time t 2 1 government spending increases from it previous level of zero to a positive level to ght the war and at time t 2 2 the war is over and government spending is again zero. 3. private agents do not value this war expenditure as a substitute for private consumption. 4. the old and young agents who are alive at the time of the war pay equally for the costs of the war in that the government charges each young and old agent a lump-sum tax to pay for the war. (a) What are the effects of the war and the war nancing scheme on the time prole of the capital-labor ratio, the output-labor ratio, the wage rate and the real interest rate? [HINT: The graph of the law of motion for the capital-labor ratio shifts. The shift is related to the fact that young agents at t = 1 have a lower present value of labor income after taxes than would have been the case absent the war. To see this, (carefully) apply the theory from Chapter 4 of the Book to the savings decision of the young. ]