University of Wisconsin - MadisonDepartment of EconomicsEco 302: Intermediate MacroeconomicsFinal Exam(You have 2:00 to complete this exam. The highest score is 115 points but the grade will be out of100. Good Luck!)121. Short Answer, 10 Points Each1.1. Consider the Solow Growth model with the assumption that people requiresome minimum consumption, so that the per-worker investment is given byit= sAf (kt) − m. Plot “required” investment per worker for the economy tobe in a steady state as well as “actual” investment per worker and show thatthere can be two steady-states. .1.2. Suppose that Starbucks sells $1 Billion dollars worth of coffee and pays$500 million for the beans (they are imported). At the same time, householdsbuy $500 million worth of beans to brew at home, half of which is importedand half of which is grown domestically. Calculate the change in consumption,net-exports, investment, and GDP from this coffee drinking activity. .31.3. Your statistician friend estimates that consumption demand is given byCd=45Y +11+rYf , where r is in decimals, Y is current income, and Yfis futureincome. She also estimates that investment demand is given by Id=Af1+r,where Afis future capital productivity. Solve for the IS Curve (i.e., solve forthe market clearing interest rate as a function of Y keeping Yfand Affixed).Draw how the IS curve shifts if there is a simultaneous rise in Afand Yf? .1.4. You find data on the country of Stankonia. In this country, nominal GDPgrows at 10% per year, total labor grows at 0% per year, the nominal valueof capital grows at 5% per year, and the annual inflation rate is 5%. If theproduction function is given by Yt= AtN0.7tK0.3t, where Ytand Ktrepresentreal GDP and value of capital, what is the growth rate of At? Show yourcalculations. .41.5. Suppose that the federal reserve attempts to keep the price level constantover time. Show in the money-market diagram how they would need to changethe nominal money-supply in the long-run if labor productivity was to increase..1.6. Consider the endogenous growth model and suppose that human capitalis proportional to GDP per capita. That is, htis human capital per workerand ht= sαyt, with yt= kαth1−αt. Recall that the law of motion for capital iskt+1= (1 − δ)kt+ sytand show that GDP per capita grows at the rate s − δ.52. Business Cycle Facts (15 Pts)For each of the following variables, indicate whether it is pro, counter, or a- cyclical andwhether it is leading, lagging, or coincident with GDP.(1) Inventories(2) Average labor productivity(3) Stock Prices(4) Consumption(5) Inflation63. Long Problems, 20 each3.1. Housing Wealth. In 2008 the housing market crashed, which lead to a large fall inhousehold wealth as home prices fell but mortgage debt remained constant. In our models,this would be like reducing the wealth parameter of households (a is the variable we haveused). This question has you think through the effects of such a decline in wealth.(1) Consider the labor market effects of this change in wealth in the labor market inthe short run when prices are fixed (i.e. the Keynesian short-run model). Assumethat, due to efficiency wages, the labor market does not clear fully. What happensto GDP in the short-run? What about unemployment (i.e. the amount of laborsupply in excess of demand)?(2) We also learned how a change in wealth affects the household’s consumption andsavings decision. For the next part, show how this decrease in wealth affects theequilibrium of the investment and savings market and the IS curve. First assumethat the price can adjust immediately as in the classical model, show how to shiftthe LM curve using the money market diagram. What happens to GDP? Prices?(3) Reconsider part (2) above but in the Keynesian short-run when prices cannot ad-just. Again, fully explain how you move along the LM curve using the moneymarket diagram. What happens to GDP?(4) Now combine the two effects in the short-run. What happens to GDP and the realinterest rate?7Scrap8Scrap9Scrap103.2. Ricardian Equivalence. We studied Ricardian Equivalence in class, which taughtus that a tax cut in the present would lead households to increase their savings in orderto offset future taxes and therefore had no effect on GDP or the real interest rate. Oneof the assumptions needed was that the government paid the same real interest rate ashouseholds. Suppose instead that the government can borrow at a lower real rate. Forsimplicity, assume the government borrowers at a real interest rate of 0%, while householdsborrow and save at rate r > 0. We will explore the effects of deficit financed tax cuts inthis situation.(1) Draw the household’s budget line when net-taxes equal to nt1and future net-taxesare ntf1, then show what happens if the government reduces nt1by $1, borrows tokeep government spending constant, and increases taxes in the future to keep theirpresent-value budget balanced.(2) Suppose that households increase savings just enough to pay the extra taxes in thefuture. Do they save more or less or exactly $1? What happens to national savingsin response to this deficit financed tax cut?(3) Show the effect of this deficit-financed tax cut in the short-run in the IS-LM-FEmodel when prices are fixed. What happens to GDP? Fully explain how you movealong