4 solution

Knowing r we solve we can substituting it

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Unformatted text preview: quations give us two equations i quating these, we and r. We found En two unknowns, Ycan solve for r: the following equations in parts (a) and (b): 1,700 – 100r = 500 + 100r IS: Y = 1,700 – 100r. LM: Y = 500 + 100r. d. 1,200 = 200r r – 100 Equating these, we can solve for r: 1,700 = 6. r = 500 + 100r so 1,200 = 200r and r = 6. Now that we know r, for Y by solve for Y by into either theitSintothe LM equation to get Y = 1,100. Knowing r, we solve we can substituting it substituting I or either the IS or the LM equation. We find Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of Y = 1,100. output is 1,100. Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of d. If governmentas depictedincrease from 100 to 150, then the IS equation becomes: output is 1,100, purchases in Figure 11–11. If government purchases increase from 100 to 150, then the IS equation becomes: Y = 200 + 0.75(Y – 100)=+200 +–0.75(+ 150. Simplifying, we find: 200 25r Y – 100) + 200 – 25r + 150. Y Simplifying, we find: Y = 1,900 – 100r. Y = 1,900 – 100r. This IISccurve is graphed as 2S2 in Figure –12. WeWe see that IS curve shifts to theto This S urve is graphed as IS I in Figure 11 11–12. see that the the IS curve shifts right by 200. the right by 200. r IS1 IS2 Figure 11–12 LM 8 7 Interest rate 04 6 200 0 500 1,100 1,200 1,700 1,900 Income, output Y By equating the new IS curve with the LM curve derived in part (b), we can solve for the new eBy equating the new IS curve with the LM curve derived in part (b), we can quilibrium interest rate: solve for the new equilibrium interest rate: 1,900 – 100r = 500 + 100r 1,400 100r = 500 + 100r e can now substitute r into either the IS or the 1,900 – = 200r so r = 7. W LM equation to find the new level of output. We find Y = 1,200. 1,400 = 200r 7 = r. We can now substitute r into either the IS or the LM equation to find the new levelTherefore, the increase in government purchases causes the equilibrium interest rate to rise from of output. We find 6 percent to 7 percent, while output= 1,200. from 1,100 to 1,200. This is depicted in Figure 11– Y increases 12. Therefore, the increase in government purchases causes the equilibrium interest rate to rise from 6 percent to 7 percent, while output increases from 1,100 to e. If the money supply increases from 1,000 to 1,200, the LM equation is: (1,200/2) = Y – 100r, or 1,200. This is depicted in Figure 11–12. Chapter 11 e. Aggregate Demand II 105 If the money supply increases from 1,000 to 1,200, then the LM equation becomes: (1,200/2) = Y – 100r, Y or 600 + 100r.This LM curve is graphed as LM2 in Figure 11–13. We see that the LM curve = shifts to the right by 100 because of the=increase in r. money balances. Y 600 + 100 real This LM curve is graphed as LM2 in Figure 11–13. We see that the LM curve shifts to the right by 100 because of the increase in real money balances. r Interest rate IS Figure 11–13 LM1 LM2 6.0 5.5 100 0 500 600 1,100 1,150 Income, output 1,700 Y To determine the new equilibrium interest rate and level of output, equate the IS curve from part To determine the derived above: (a) with the new LM curvenew equilibrium interest rate and level of output, equate the IS curve from part (a) with the new LM curve derived above: 1,700 – 100r = 600 + 100r 1,100 = 200r100r = .600 + 100r  1,700 – 5.5 = r 1,100 = 200r 5.5 = r. Substituting this into either the I supply causes the interest find Therefore, the increase in the money S or the LM equation, werate to fall from 6 percent to 5.5 Substituting this into either the IS or the LM equation, we find Y = 1,150. percent, while output increases from 1,100 to 1,150. This is depicted in Figure 11–13. Y = 1,150. Therefore, the increase in the money supply causes the interest rate to fall from 6 f. If the price level rises from 2 to 4, then real money balances fall from 500 to 1,000/4 = 250. percent to 5.5 percent, while output increases from 1,100 to 1,150. This is depicted The Figure 11–13. in LM equation becomes: f. If the price level rises from 2 to 4, then real money balances fall from 500 to Y 1,000/4 = 250. The LM equation becomes: = 250 + 100r. Y = shifts to the As shown in Figure 11–14, the LM curve250 + 100r. left by 250 because the increase in the price level reduces real money balances. Answers to Textbook Questions and Problems As shown in Figure 11–14, the LM curve shifts to the left by 250 because the in...
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