Summer 2014 Week 13 Tutorial Questions Solutions (Ch9)

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1 Chapter 9: Q1: Macroeconomics P.324 Numerical Problems #1 Q2: Macroeconomics P.325 Numerical Problems #4 Chapter 10: Q3: Macroeconomics P.391 Review Questions #1 Q4: Macroeconomics P.391 Review Questions #3 Q5: Macroeconomics P.392 Numerical Problems #3 part (a) and (b) Q1: Desired consumption and investment are C d = r Y; I d = r As usual, Y is output and r is the real interest rate. Government purchases G are 120. a. Find an equation relating desired national saving S d to r and Y. S d = Y C d G= Y ( r+ 0.1 Y) 120 = r+ 0.9Y. b. What value of the real interest rate clears the goods market when Y = 600? Use both forms of the goods market equilibrium condition. What value of the real interest rate clears the goods market when Y = 640? Graph the IS curve. (1) Using the equation that goods supplied equals goods demanded gives Y = C d + I d + G= ( r + 0.1Y) + ( r) + 120= r + 0.1Y. So 0.9Y= r. At full employment, Y = 600. Solving = r, we get r = When Y = 640, we get r = (2)Using the equivalent equation that desired saving equals desired investment gives S d = I d, thus r + 0.9Y= r 0.9Y = r When Y= 600, r = 0.10.So we can use either equation to get the same result. When Y= 640, we get r = Week 13 Page 1

2 r c. Government purchases rise to 132. How does this increase change the equation for national saving in part (a)? What value of the real interest rate clears the goods market when Y = 600? Use both forms of the goods market equilibrium condition. How is the IS curve affected by the increase in G? IS Y When G= 132, desired saving becomes S d = r+ 0.9Y. S d is now 12 less for any given rand Y; this shows up as a shift in the S d line from S 1 to S 2 in the figure below. Setting S d = I d, we get r + 0.9Y= r thus 600r+ 0.9Y= 612.At Y= 600, this is 600r= 612 (0.9 x 600) = 72, so r= The market-clearing real interest rate increases from 0.10 to r S 2 S S d, I d I Week 13 Page 2

3 Q2: The production function in an economy is Y = A(5N N 2 ), where A is productivity. With this production function, the marginal product of labour is MPN = 5A 0.005AN. Suppose that A = 2. The labour supply curve is NS = (1-t)w, where NS is the amount of labour supplied, w is the real wage, and t is the tax rate, which is 0.5. Desired consumption and investment are C d = (Y T) 200r; I d = r. Taxes and government purchases are T = Y; G = 50. Money demand is M d /P = 0.5Y 250(r + π e ). The expected rate of inflation π e is 0.02, and the nominal money supply M is a. What are the general equilibrium levels of the real wage, employment, and output? First, look at labour market equilibrium. Labour supply is NS = (1 t)w NS = w. Labour demand comes from the equation w = MPN = 5A 0.005A ND ND = w. Equating labour supply and labour demand gives N= 100. Using this in either the labour supply or labour demand equation then gives w= 9. Using N in the production function gives Y= 950. b. For any level of output Y, find an equation that gives the real interest rate r that clears the goods market; this equation descries the IS curve. (Hint: write the goods market equilibrium condition and solve for r in terms of Y and other variables.) What are the general equilibrium values of the real interest rate, consumption, and investment? Next, look at goods market equilibrium and the IS curve. S d =Y C d G = Y [ (Y T) 200r] G =Y [300 (0.4Y 16) 200r] G= Y+200r G. Setting S d = I d gives Y + 200r G = r. Solving this for r in terms of Y gives 450r= ( G 0.6 Y. When G= 50, and with full-employment output of 950, using this in the IS curve and solving for r gives r= 0.05.Plugging these results into the consumption and investment equation gives C= 654 and I= 246. c. For any level of output Y, find an equation that gives the real interest rate that clears the asset market; this equation describes the LM curve. (Hint: As in part (b), write the appropriate equilibrium condition and solve for r in terms of Y and other variables.) What is the general equilibrium value of the price level? Next, look at asset market equilibrium and the LM curve. Setting money demand equal to money supply gives 9150/P = 0.5Y 250(r +0.02), which can be solved for r = 0.002Y /P. With Y= 950 and r = Solving for P gives P = 20. Week 13 Page 3

4 d. Suppose that government purchases increase to G = Now what are the general equilibrium values of the real wage, employment, output, the real interest rate, consumption, investment, and the price level? With G= 72.5, the IS curve becomes 450r = Y r = Y. With Y = 950. The IS curve gives r =0.10, the LM curve gives P= 20.56, the consumption equation gives C= 644. And the investment equation gives I= The real wage, employment, and output are unaffected by the change. Q3: Define nominal exchange rate and real exchange rate. How are changes in the real exchange rate and the nominal exchange rate related? The nominal exchange rate is the rate at which two currencies can be exchanged for each other in the market. The real exchange rate is the price of domestic goods relative to foreign goods. Changes in the real exchange rate are related to changes in the nominal exchange rate depending on changes in the price levels of the two countries: Δe/e = ΔE/E+ ΔP/ P - ΔP*/ P* Q4. Define purchasing power parity or PPP. Does PPP work well empirically? Explain. Purchasing power parity, PPP, is the idea that similar foreign and domestic goods, or baskets of goods, should have the same price when priced in terms of the same currency. Purchasing power parity does seem to explain exchange rates in the long run, but over shorter periods it doesn't work well because countries produce very different sets of goods, because some goods aren't traded internationally, and because there are transportation costs and legal barriers. Q5. Consider the following classical economy: Desired consumption Desired investment C d = Y 200r I d = r Government purchases G = 100 Net exports NX = Y 0.5e Real exchange rate e = r Full-employment output Y* = 900 Week 13 Page 4

5 In this economy, the real interest rate does not deviate from the foreign interest rate. a. What are the equilibrium values of the real interest rate, the real exchange rate, consumption, investment, and net exports? Begin by writing the equation for the IS curve, which is S d I d = NX. S d =Y C d G = Y ( Y 200r) G. NX = Y 0.5e= Y 0.5( r) = Y- 300r. Using these in the IS curve equation gives :( 0.5Y r G) ( r) = Y 300r.Rearranging terms and simplifying gives the IS curve: 800r = Y+G. With G= 100 and Y*= 900, the IS curve gives 800r= = 200, so r = Then e= r = 170, NX = = 25, C = = 700, and I= = 125 b. Now, suppose that full-employment output increases to 940. What are the equilibrium values of the real interest rate, the real exchange rate, consumption, investment, and net exports? With Y*= 940, the IS curve gives 800r= = 176, so r=0.22. Then e= r= 152, NX = = 20, C= = 726, and I = = 134. The rise in domestic output reduces the real interest rate and real exchange rate, and increases net exports, consumption, and investment. Week 13 Page 5

Solutions to Spring 2015 Week 13 Tutorial Questions (Ch9)

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