University of Wisconsin - MadisonDepartment of EconomicsEco 302: Intermediate MacroeconomicsMidterm Two Practice: Key(You have 1:15 to complete this exam. The highest score is 100 points. Good Luck!)121. Short Answer, 10 Points Each, 50 Total1.1. Suppose that in 2016 the real interest rate is r = 1% and people expectinflation to be ⇡e= 2%. In 2017 th e real interest rate is still r = 1% butexpected inflation rises to ⇡e= 3%. What happens to real balance demand in2017 relative to 2016? What role of money explain s this change? .Real balance demand falls in response to the increase in expected inflation (could drawthis in the diagram). The store of value role of money is what explains this, since higherinflation makes money a worse store of value.1.2. Suppose that consumption demand is given by Cd=45⇥Y +11+rYf⇤,wherer is in decimals, Y is current inc ome, and Yfis future income. Investmentdemand is given by Id=1001+r. Solve for the IS Curve (i.e., solve for the marketclearing interest rate as a function of Y keeping Yffixed). Draw the e↵ect ofan increase in Yfon the IS Curve. .First step is to put Spvt= Y  Cd=15Y 4511+rYf. Th en set this equal to investmentdemand:15Y 4511+rYf=1001+rThis gives rIS(Y ) as:rIS(Y )=500 + 4YfY 1This looks like a convex curve plotting r again st Y and increasing Yfshifts the curveupward.31.3. Suppose that inflation is 2%, depreciation is 10%, and the nominal interestrate is 5% (all per year). An entrepreneur currently has $10, 000 worth of capitaland revenues of $100, 000 and is considering buying an additional $1000 worthof computers. If she buys these machines then her revenue next year will be$100, 000 + X (and she will sell o↵ the undepreciated computers). What is thesmallest value of X for which she buys these machines? .The user cost of the machine is (0.05  0.02 + 0.10)$1000 = $130. The marginal productof the machines is $100, 000 + X  $100, 000 = X. The firm wil l buy the machines if themarginal product is larger than the user cost, that is if X  $130.1.4. Show the e↵ ect of each of the following on the IS curve: 1) an increase ininflation expectations, 2) a decrease in initial wealth, and 3) a d ec reas e in thedepreciation rate. .The first one has no e↵ect on the investment savings market. The second one reducescurrent consumption, which means that savings rises. This causes the investment-savingsmarket’s re al interest rate to fall, therefore the IS curve shifts downward. The t h ird onecauses investment demand to rise, which means that the real i nterest r at e that clears theinvestment-savings market r is es , so the IS curve shifts upwards.41.5. Suppose that the labor supply curve is described by Ns(w)=w and theproduction function of firms is given by F (N) = 16N0.5where N is the totalamount of labor used in production. Solve for the full employment level ofoutput and draw the FE curve. First find labor d eman d by settin g the marginalproduct of labor equal to the real wage. That is, set:0.5 ⇥ 16 ⇥ Nd(w)0.51= w ! Nd(w)=✓8w◆2.Now set labor supply equal to labor demand to find the equilibrium wage:w⇤=✓8w⇤◆2! w⇤=823=4.Now plug the equilibrium wage into labor supply (or demand, they are equal at w⇤) to getthat labor is N⇤= 4. The n plug this into the production funct i on to get YFE= 16⇥ 40.5=32. The FE cur ve is then just a vertical line at YFE= 32.52. Business Cycle FactsList all of the aggregate variables from chapter 8 and say whether they are pro, counter,or a-cyclical.3. Long Problem, 40 TotalThis problem has you study the e↵ects of a technology sh ock that reduces the currentmarginal product of labor but incr ease s the expec t ed future marginal product of capital. Ine↵ect, this is a technology shock that shifts income away from labor and towards capital.While we have modeled t echnology shocks as improving productivity of both labor andcapital, there is substantial concern that recent changes have in cr eas ed capital productivityby more t h an labor productivity.In order to study two e↵ects, we do each of them separately and then check what happenswhen they are combined. You will walk through these steps below.a Fi r st do t h e analysis of a technology shock that redu ces the current marginal prod-uct of labor. Show the e↵ ec t in the labor market, the direct e↵ect in the IS-LM-FEdiagram (i.e. show which curve shifts). Supposing that the pr i ce level ad j us t s sothat the LM curve intersects the IS and FE, show in the money market how theprice level must change.b Se con d do the analysis of a technology shock that increases the future marginalproduct of capital. Show the e↵ect in the investment-savings market and the directe↵ect in the IS-LM-FE diagram. Suppose that the economy moves to the newintersection of IS and LM (the price level does not adjust). Show what musthappen in the money market in order to move along the LM curve.c Now redo the analysis of an increase i n future marginal product of capital, butassume that p ri ce s adjust so that the LM curve moves to the intersection of IS andFE. Show in the money market how the price level must adjust for this to happen.d Looking at the results from [a] and [c], what is the overall e↵ect on output and theprice level from this combination of