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 = 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. (c) What does theory say must be true about the connection between (i) the real interest rate and the marginal product of capital on the one hand and (ii) the real interest rate and the marginal rate of substitution of young agents on the other hand? Explain. For item (ii) how does consumption growth for young agents relate to the marginal rate of substitution for a Cobb-Douglas consumer