UT ECO 320L - midterm2-practice-key (7 pages)

University of Wisconsin Madison Department of Economics Eco 302 Intermediate Macroeconomics Midterm Two Practice Key You have 1 15 to complete this exam The highest score is 100 points Good Luck 1 2 1 Short Answer 10 Points Each 50 Total 1 1 Suppose that in 2016 the real interest rate is r 1 and people expect inflation to be e 2 In 2017 the real interest rate is still r 1 but expected inflation rises to e 3 What happens to real balance demand in 2017 relative to 2016 What role of money explains this change Real balance demand falls in response to the increase in expected inflation could draw this in the diagram The store of value role of money is what explains this since higher inflation makes money a worse store of value 1 1 2 Suppose that consumption demand is given by C d 45 Y 1 r Y f where r is in decimals Y is current income and Y f is future income Investment 100 demand is given by I d 1 r Solve for the IS Curve i e solve for the market clearing interest rate as a function of Y keeping Y f fixed Draw the e ect of an increase in Y f on the IS Curve First step is to put S pvt Y demand C d 15 Y 1 Y 5 4 1 f 5 1 r Y Then set this equal to investment 4 1 100 Yf 51 r 1 r This gives rIS Y as 500 4Y f 1 Y This looks like a convex curve plotting r against Y and increasing Y f shifts the curve upward rIS Y 3 1 3 Suppose that inflation is 2 depreciation is 10 and the nominal interest rate is 5 all per year An entrepreneur currently has 10 000 worth of capital and revenues of 100 000 and is considering buying an additional 1000 worth of 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 the smallest 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 product of the machines is 100 000 X 100 000 X The firm will buy the machines if the marginal 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 in inflation expectations 2 a decrease in initial wealth and 3 a decrease in the depreciation rate The first one has no e ect on the investment savings market The second one reduces current consumption which means that savings rises This causes the investment savings market s real interest rate to fall therefore the IS curve shifts downward The third one causes investment demand to rise which means that the real interest rate that clears the investment savings market rises so the IS curve shifts upwards 4 1 5 Suppose that the labor supply curve is described by N s w w and the production function of firms is given by F N 16N 0 5 where N is the total amount of labor used in production Solve for the full employment level of output and draw the FE curve First find labor demand by setting the marginal product of labor equal to the real wage That is set 2 8 d 0 5 1 d 0 5 16 N w w N w w Now set labor supply equal to labor demand to find the equilibrium wage 2 2 8 w w 8 3 4 w Now plug the equilibrium wage into labor supply or demand they are equal at w to get that labor is N 4 Then plug this into the production function to get Y F E 16 40 5 32 The FE curve is then just a vertical line at Y F E 32 5 2 Business Cycle Facts List all of the aggregate variables from chapter 8 and say whether they are pro counter or a cyclical 3 Long Problem 40 Total This problem has you study the e ects of a technology shock that reduces the current marginal product of labor but increases the expected future marginal product of capital In e ect this is a technology shock that shifts income away from labor and towards capital While we have modeled technology shocks as improving productivity of both labor and capital there is substantial concern that recent changes have increased capital productivity by more than labor productivity In order to study two e ects we do each of them separately and then check what happens when they are combined You will walk through these steps below a First do the analysis of a technology shock that reduces the current marginal product of labor Show the e ect in the labor market the direct e ect in the IS LM FE diagram i e show which curve shifts Supposing that the price level adjusts so that the LM curve intersects the IS and FE show in the money market how the price level must change b Second do the analysis of a technology shock that increases the future marginal product of capital Show the e ect in the investment savings market and the direct e ect in the IS LM FE diagram Suppose that the economy moves to the new intersection of IS and LM the price level does not adjust Show what must happen in the money market in order to move along the LM curve c Now redo the analysis of an increase in future marginal product of capital but assume that prices adjust so that the LM curve moves to the intersection of IS and FE 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 the price level from this combination of shocks