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1 Numerical Problems 1. (a) S d = Y C d G = Y ( r + 0.2Y) 2000 = r + 0.8Y. (b) (1) Using the equation that goods supplied equals goods demanded gives Y = C d + I d + G = ( r + 0.2Y) + ( r) = r + 0.2Y. So 0.8Y = r, or 8000r = Y. (2) Using the equivalent equation that desired saving equals desired investment gives S d = I d r + 0.8Y = r 0.8Y = r, or 8000r = Y.

2 Chapter 9 The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis 173 So we can use either equilibrium condition to get the same result. When Y = 10,000, 8000r = 8400 (0.8 10,000) = 400, so r = When Y = 10,200, 8000r = 8400 (0.8 10,200) = 240, so r =.03. (c) When G = 2400, desired saving becomes S d = r + 0.8Y. S d is now 400 less for any given r and Y. Setting S d = I d, we get r + 0.8Y = r 8000r = Y. Similarly, using the equation that goods supplied equals goods demanded gives: Y = C d + I d + G = ( r + 0.2Y) + ( r) = r + 0.2Y. So 0.8Y = r, or 8000r = Y. At Y = 10,000, this is 8000r = 8800 (0.8 10,000) = 800, so r = The market-clearing real interest rate increases from 0.05 to Thus the IS curve shifts up and to the right from IS 1 to IS 2 in Figure Figure 9.19

3 Chapter 9 The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis (a) M d /P = Y 10,000i = Y 10,000(r + π e ) = Y 10,000(r +.02) = Y 10,000r. Setting M/P = M d /P: 6000/2 = Y 10,000r 10,000r = Y r = (Y/100,000). When Y = 8000, r = When Y = 9000, r = These points are plotted as line LM a in Figure Figure 9.20 (b) M = 6600, so M/P = Setting money supply equal to money demand: 3300 = Y 10,000r 10,000r = Y r = (Y/100,000). When Y = 8000, r = When Y = 9000, r = The LM curve is shifted down and to the right from LM a to LM b in Figure 9.20, since the same level of Y gives a lower r at equilibrium.

4 Chapter 9 The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis 175 (c) M d /P = Y 10,000(r + π e ) = Y 10,000r (10,000.03) = Y 10,000r. Setting money supply equal to money demand: 3000 = Y 10,000r 10,000r = Y r = (Y/100,000). When Y = 8000, r = When Y = 9000, r = The LM curve is shifted down and to the right from LM a to LM c in Figure 9.20, since there is a higher real interest rate for every given level of output. The LM curve shifts down and to the right by one percentage point (the increase in π e ) because for any given Y, the same nominal interest rate clears the asset market. With an unchanged nominal interest rate, the increase in π e is matched by an equal decrease in r. 3. (a) First, we ll find the IS curve. S d = Y C d G = Y [ (Y T) 500r] G = Y [200 + (0.6Y 16) 500r] G = Y + 500r G Setting S d = I d gives Y + 500r G = r. Solving this for Y in terms of r gives Y = ( G) 2500r. When G = 196, this is Y = r. Next, we ll find the LM curve. Setting money demand equal to money supply gives 9890/P = 0.5Y 250r 25, which can be solved for Y = 19,780/P r. With full-employment output of 1000, using this in the IS curve and solving for r gives r = Using Y = 1000 and r = 0.18 in the LM curve and solving for P gives P = 23. Plugging these results into the consumption and investment equations gives C = 694 and I = 110. (b) With G = 216, the IS curve becomes Y = r. With Y = 1000, the IS curve gives r =.20, the LM curve gives P = 23.27, the consumption equation gives C = 684, and the investment equation gives I = (a) First, look at labor market equilibrium. Labor supply is NS = (1 t)w. Labor demand (ND) comes from the equation w = 5A (0.005A ND). Substituting the latter equation into the former, and equating labor supply and labor demand gives N = 100. Using this in either the labor supply or labor demand equation then gives w = 9. Using N in the production function gives Y = 950.

5 Chapter 9 The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis 176 (b) 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 r = ( G)/ /3Y. When G = 50, this is r = /3 Y. With full-employment output of 950, using this in the IS curve and solving for r gives r = Plugging these results into the consumption and investment equations gives C = 654 and I = 246. (c) Next, look at asset market equilibrium and the LM curve. Setting money demand equal to money supply gives 9150/P = 0.5Y 250(r ), which can be solved for r = [0.5Y ( /P)]/250. With Y = 950 and r = 0.05, solving for P gives P = 20. (d) With G = 72.5, the IS curve becomes r = /3 Y. With Y = 950, the IS curve gives r =.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. 5. The IS curve is found by setting desired saving equal to desired investment. Desired saving is S d = Y C d G = Y [ (Y T) 200r] G. Setting S d = I d gives Y [ (Y T) 200r] G = r, or Y = r + 2G T. The LM curve is M/P = L = 0.5Y 200i = 0.5Y 200(r + π) = 0.5Y 200r. (a) T = G = 450, M = The IS curve gives Y = r + 2G T = r + (2 450) 450 = r. The LM curve gives 9000/P = 0.5Y 200r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve. LM: 9000/P = 0.5Y 200r. Multiplying by 4 gives 36,000/P = 2Y 800r. Rearranging gives 800r = 2Y 36,000/P. IS: Y = r. Rearranging gives 800r = 4800 Y. Setting the righthand sides of these two equations to each other (since both equal 800r) gives: 2Y (36,000/P) = 4800 Y, or 3Y = (36,000/P), or Y = (12,000/P); this is the AD curve. With Y = 4600 at full employment, the AD curve gives 4600 = (12,000/P), or P = 4. From the IS curve Y = r, so 4600 = r, or 800r = 200, so r = Consumption is C = (Y T) 200r = ( ) ( ) = Investment is I = r = 900 ( ) = 850. (b) Following the same steps as above, with M = 4500 instead of 9000, gives the aggregate demand curve AD: Y = (6000/P). With Y = 4600, this gives P = 2. Nothing has changed in the IS equation, so it still gives r = And nothing has changed in either the consumption or investment equations, so we still get C = 3300 and I = 850. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply.

6 Chapter 9 The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis 177 (c) T = G = 330, M = The IS curve is Y = r + 2G T = r + (2 330) 330 = r. LM: 36,000/P = 2Y 800r, or 800r = 2Y 36,000/P. IS: Y = r, or 800r = 4680 Y. AD: 2Y (36,000/P) = 4680 Y, or (36,000/P) = 3Y, or Y = (12,000/P). With Y = 4600 at full employment, the AD curve gives 4600 = (12,000/P), or P = From the IS curve, Y = r, so 4600 = r, or 800r = 80, so r = Consumption is C = (Y T) 200r = ( ) ( ) = Investment is I = r = 900 ( ) = (a) A = 2, f 1 = 5, f 2 = 0.005, n 0 = 55, n w = 10, c 0 = 300, c Y = 0.8, c r = 200, t 0 = 20, t = 0.5, i 0 = 258.5, i r = 250, l 0 = 0, l Y = 0.5, l r = 250. (b) These values are all calculated directly, using the equations in the Appendix. They should match the results in Numerical Problem 4, above. (c) See the answer to part b.

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