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HW6_sol - Chapter 11 3 a Aggregate Demand II 103 tion and...

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Chapter 11 Aggregate Demand II 103 tion and because income falls. Investment rises because of the lower interest rates and partially offsets the effect on output of the fall in consumption. If the Federal Reserve wants to keep output constant, then they must increase the money supply in order to reduce the interest rate and increase output back to its original level. The increase in the money supply will shift the LM curve down and to the right. Output will remain at its original level, consumption will be lower, investment will be higher, and interest rates will be lower. 3. a. The IS curve is given by: Y = C ( Y T ) + I ( r ) + G . We can plug in the consumption and investment functions and values for G and T as given in the question and then rearrange to solve for the IS curve for this econ- omy: Y = 200 + 0.75( Y – 100) + 200 – 25 r + 100 Y – 0.75 Y = 425 – 25 r (1 – 0.75) Y = 425 – 25 r Y = (1/0.25) (425 – 25 r ) Y = 1,700 – 100 r. This IS equation is graphed in Figure 11–11 for r ranging from 0 to 8. b. The LM curve is determined by equating the demand for and supply of real money balances. The supply of real balances is 1,000/2 = 500. Setting this equal to money demand, we find: 500 = Y – 100 r . Y = 500 + 100 r . This LM curve is graphed in Figure 11–11 for r ranging from 0 to 8. c. If we take the price level as given, then the IS and the LM equations give us two equations in two unknowns, Y and r . We found the following equations in parts (a) and (b): IS : Y = 1,700 – 100 r . LM : Y = 500 + 100 r . LM IS Y 1,700 1,100 500 0 6 8 r Interest rate Income, output Figure 11–11
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Equating these, we can solve for r : 1,700 – 100 r = 500 + 100 r 1,200 = 200 r r = 6. Now that we know r , we can solve for Y by substituting it into either the IS or the LM equation. We find Y = 1,100. Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of output is 1,100, as depicted in Figure 11–11. d. If government purchases increase from 100 to 150, then the IS equation becomes: Y = 200 + 0.75( Y – 100) + 200 – 25 r + 150. Simplifying, we find: Y = 1,900 – 100 r . This IS curve is graphed as IS 2 in Figure 11–12. We see that the IS curve shifts to the right by 200. By equating the new IS curve with the LM curve derived in part (b), we can solve for the new equilibrium interest rate: 1,900 – 100 r = 500 + 100 r 1,400 = 200 r 7 = r . We can now substitute r into either the IS or the LM equation to find the new level of output. We find Y = 1,200. 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 1,200. This is depicted in Figure 11–12. 104 Answers to Textbook Questions and Problems 1,200 500 1,100 LM 200 Y 1,900 1,700 0 6 7 r Interest rate Income, output IS 2 IS 1 8 Figure 11–12
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e. If the money supply increases from 1,000 to 1,200, then the LM equation becomes: (1,200/2) = Y – 100 r , or Y = 600 + 100 r . This LM curve is graphed as LM 2 in Figure 11–13. We see that the LM curve shifts to the right by 100 because of the increase in real money balances.
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