Homework 5 - Equilibrium Properties of the Life-Cycle ModelWe 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 ingovernment spending due to a war. In this homework we will analyze a verystylized 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 zeroto a positive level to fight the war and at time t ≥ 2 the war is over andgovernment spending is again zero.3. private agents do not value this war expenditure as a substitute for privateconsumption.4. the old and young agents who are alive at the time of the war pay equallyfor the costs of the war in that the government charges each young andold agent a lump-sum tax to pay for the war.(a) What are the effects of the war and the war financing scheme on thetime profile of the capital-labor ratio, the output-labor ratio, the wage rate andthe real interest rate?[HINT: The graph of the law of motion for the capital-labor ratio shifts. Theshift is related to the fact that young agents at t = 1 have a lower present valueof labor income after taxes than would have been the case absent the war. Tosee this, (carefully) apply the theory from Chapter 4 of the Book to the savingsdecision of the young. ](b) There is a graph attached to the homework which plots time series ofnominal interest rates on long-term bonds in the United Kingdom along with ameasure of government military spending as a fraction of GDP. To what degreeis the theoretical model’s prediction consistent with the patterns in the graph?This graph comes from Robert Barro (1987), “Government Spending, In-terest Rates, Prices and Budget Deficits in the United Kingdom, 1701- 1918”,Journal of Monetary Economics, vol. 20, 221- 47.(c) What does theory say must be true about the connection between (i) thereal 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 onthe other hand? Explain. For item (ii) how does consumption growth for youngagents relate to the marginal rate of substitution for a Cobb-Douglas