CHAPTER 10 Aggregate Demand I


 Maximillian Grant
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1 CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income causes highe consumption. Fo example, an incease in govenment puchases of G aises expenditue and, theefoe, income by G. This incease in income causes consumption to ise by MPC G, whee MPC is the maginal popensity to consume. This incease in consumption aises expenditue and income even futhe. This feedback fom consumption to income continues indefinitely. Theefoe, in the Keynesiancoss model, inceasing govenment spending by one dolla causes an incease in income that is geate than one dolla: it inceases by G/(1 MPC). 2. The theoy of liquidity pefeence explains how the supply and demand fo eal money balances detemine the inteest ate. A simple vesion of this theoy assumes that thee is a fixed supply of money, which the Fed chooses. The pice level P is also fixed in this model, so that the supply of eal balances is fixed. The demand fo eal money balances depends on the inteest ate, which is the oppotunity cost of holding money. At a high inteest ate, people hold less money because the oppotunity cost is high. By holding money, they fogo the inteest on inteestbeaing deposits. In contast, at a low inteest ate, people hold moe money because the oppotunity cost is low. Figue 10 1 gaphs the supply and demand fo eal money balances. Based on this theoy of liquidity pefeence, the inteest ate adjusts to equilibate the supply and demand fo eal money balances. Supply of eal money balances Figue 10 1 Inteest ate L () = Demand fo eal money balances M/P Real money balances M/P 82
2 Chapte 10 Aggegate Demand I 83 Why does an incease in the money supply lowe the inteest ate? Conside what happens when the Fed inceases the money supply fom M 1 to M 2. Because the pice level P is fixed, this incease in the money supply shifts the supply of eal money balances M/P to the ight, as in Figue Figue 10 2 Inteest ate 1 2 L () M 1 /P M 2 /P Real money balances M/P The inteest ate must adjust to equilibate supply and demand. At the old inteest ate 1, supply exceeds demand. People holding the excess supply of money ty to convet some of it into inteestbeaing bank deposits o bonds. Banks and bond issues, who pefe to pay lowe inteest ates, espond to this excess supply of money by loweing the inteest ate. The inteest ate falls until a new equilibium is eached at The IS cuve summaizes the elationship between the inteest ate and the level of income that aises fom equilibium in the maket fo goods and sevices. Investment is negatively elated to the inteest ate. As illustated in Figue 10 3, if the inteest ate ises fom 1 to 2, the level of planned investment falls fom I 1 to I 2. Figue Inteest ate 1 I() I () I 2 I 1 Investment I
3 84 Answes to Textbook Questions and Poblems The Keynesian coss tells us that a eduction in planned investment shifts the expenditue function downwad and educes national income, as in Figue 10 4(A). Planned expenditue = 1 = C ( T ) + I ( 1 ) + G I 2 = C ( T ) + I ( 2 ) + G Figue (A) Inteest ate 2 1 IS 2 1 (B) Thus, as shown in Figue 10 4(B), a highe inteest ate esults in a lowe level of national income: the IS cuve slopes downwad.
4 Chapte 10 Aggegate Demand I The LM cuve summaizes the elationship between the level of income and the inteest ate that aises fom equilibium in the maket fo eal money balances. It tells us the inteest ate that equilibates the money maket fo any given level of income. The theoy of liquidity pefeence explains why the LM cuve slopes upwad. This theoy assumes that the demand fo eal money balances L(, ) depends negatively on the inteest ate (because the inteest ate is the oppotunity cost of holding money) and positively on the level of income. The pice level is fixed in the shot un, so the Fed detemines the fixed supply of eal money balances M/P. As illustated in Figue 10 5(A), the inteest ate equilibates the supply and demand fo eal money balances fo a given level of income. Figue 10 5 M / P LM Inteest ate 2 1 L (, 2 ) Inteest ate 2 1 L (, 1 ) M / P Real money balances 1 2 (A) (B) Now conside what happens to the inteest ate when the level of income inceases fom 1 to 2. The incease in income shifts the money demand cuve upwad. At the old inteest ate 1, the demand fo eal money balances now exceeds the supply. The inteest ate must ise to equilibate supply and demand. Theefoe, as shown in Figue 10 5(B), a highe level of income leads to a highe inteest ate: The LM cuve slopes upwad.
5 86 Answes to Textbook Questions and Poblems Poblems and Applications 1. a. The Keynesian coss gaphs an economy s planned expenditue function, = C( T) + I + G, and the equilibium condition that actual expenditue equals planned expenditue, =, as shown in Figue = Figue 10 6 Planned expenditue expeditue G A B 2 = C( T) + I + G 2 1 = C( T) + I + G An incease in govenment puchases fom G 1 to G 2 shifts the planned expenditue function upwad. The new equilibium is at point B. The change in equals the poduct of the govenmentpuchases multiplie and the change in govenment spending: = [1/(1 MPC)] G. Because we know that the maginal popensity to consume MPC is less than one, this expession tells us that a onedolla incease in G leads to an incease in that is geate than one dolla. b. An incease in taxes T educes disposable income T by T and, theefoe, educes consumption by MPC T. Fo any given level of income, planned expenditue falls. In the Keynesian coss, the tax incease shifts the plannedexpenditue function down by MPC T, as in Figue = Figue 10 7 Planned expenditue A MPC T = C( T ) + I + G B MPC 1 MPC T
6 Chapte 10 Aggegate Demand I 87 The amount by which falls is given by the poduct of the tax multiplie and the incease in taxes: = [ MPC/(1 MPC)] T. c. We can calculate the effect of an equal incease in govenment expenditue and taxes by adding the two multiplie effects that we used in pats (a) and (b): = [(1/(1 MPC)) G] [(MPC/(1 MPC)) T]. Govenment Tax Spending Multiplie Multiplie Because govenment puchases and taxes incease by the same amount, we know that G = T. Theefoe, we can ewite the above equation as: = [(1/(1 MPC)) (MPC/(1 MPC))] G = G. This expession tells us that an equal incease in govenment puchases and taxes inceases by the amount that G inceases. That is, the balancedbudget multiplie is exactly a. Total planned expenditue is = C( T) +I + G. Plugging in the consumption function and the values fo investment I, govenment puchases G, and taxes T given in the question, total planned expenditue is = ( 100) = This equation is gaphed in Figue = Figue 10 8 Planned expenditue 325 = * = 1,300 b. To find the equilibium level of income, combine the plannedexpenditue equation deived in pat (a) with the equilibium condition = : = = 1,300. The equilibium level of income is 1,300, as indicated in Figue c. If govenment puchases incease to 125, then planned expenditue changes to = quilibium income inceases to = 1,400. Theefoe, an
7 88 Answes to Textbook Questions and Poblems incease in govenment puchases of 25 (i.e., = 25) inceases income by 100. This is what we expect to find, because the govenmentpuchases multiplie is 1/(1 MPC): because the MPC is 0.75, the govenmentpuchases multiplie is 4. d. A level of income of 1,600 epesents an incease of 300 ove the oiginal level of income. The govenmentpuchases multiplie is 1/(1 MPC): the MPC in this example equals 0.75, so the govenmentpuchases multiplie is 4. This means that govenment puchases must incease by 75 (to a level of 175) fo income to incease by a. When taxes do not depend on income, a onedolla incease in income means that disposable income inceases by one dolla. Consumption inceases by the maginal popensity to consume MPC. When taxes do depend on income, a onedolla incease in income means that disposable income inceases by only (1 t) dollas. Consumption inceases by the poduct of the MPC and the change in disposable income, o (1 t)mpc. This is less than the MPC. The key point is that disposable income changes by less than total income, so the effect on consumption is smalle. b. When taxes ae fixed, we know that / G = 1/(1 MPC). We found this by consideing an incease in govenment puchases of G; the initial effect of this change is to incease income by G. This in tun inceases consumption by an amount equal to the maginal popensity to consume times the change in income, MPC G. This incease in consumption aises expenditue and income even futhe. The pocess continues indefinitely, and we deive the multiplie above. When taxes depend on income, we know that the incease of G inceases total income by G; disposable income, howeve, inceases by only (1 t) G less than dolla fo dolla. Consumption then inceases by an amount (1 t) MPC G. xpenditue and income incease by this amount, which in tun causes consumption to incease even moe. The pocess continues, and the total change in output is = G {1 + (1 t)mpc + [(1 t)mpc] 2 + [(1 t)mpc] } = G [1/(1 (1 t)mpc)]. Thus, the govenmentpuchases multiplie becomes 1/(1 (1 t)mpc) athe than 1/(1 MPC). This means a much smalle multiplie. Fo example, if the maginal popensity to consume MPC is 3/4 and the tax ate t is 1/3, then the multiplie falls fom 1/(1 3/4), o 4, to 1/(1 (1 1/3)(3/4)), o 2. c. In this chapte, we deived the IS cuve algebaically and used it to gain insight into the elationship between the inteest ate and output. To detemine how this tax system altes the slope of the IS cuve, we can deive the IS cuve fo the case in which taxes depend on income. Begin with the national income accounts identity: = C + I + G. The consumption function is C = a + b( T t). Note that in this consumption function taxes ae a function of income. The investment function is the same as in the chapte: I = c d. Substitute the consumption and investment functions into the national income accounts identity to obtain: = [a + b( T t)] + c d + G. Solving fo : = a + c + 1 G + b T + d. 1 b(1 t) 1 b(1 t) 1 b(1 t) 1 b(1 t)
8 Chapte 10 Aggegate Demand I 89 This IS equation is analogous to the one deived in the text except that each tem is divided by 1 b(1 t) athe than by (1 b). We know that t is a tax ate, which is less than 1. Theefoe, we conclude that this IS cuve is steepe than the one in which taxes ae a fixed amount. 4. a. If society becomes moe thifty meaning that fo any given level of income people save moe and consume less then the plannedexpenditue function shifts downwad, as in Figue 10 9 (note that C 2 < C 1 ). quilibium income falls fom 1 to 2. = Figue 10 9 Planned expenditue B A 1 = C 1 + c ( T ) + I + G 2 = C 2 + c ( T ) + I + G 2 1 b. quilibium saving emains unchanged. The national accounts identity tells us that saving equals investment, o S = I. In the Keynesiancoss model, we assumed that desied investment is fixed. This assumption implies that investment is the same in the new equilibium as it was in the old. We can conclude that saving is exactly the same in both equilibia. c. The paadox of thift is that even though thiftiness inceases, saving is unaffected. Inceased thiftiness leads only to a fall in income. Fo an individual, we usually conside thiftiness a vitue. Fom the pespective of the Keynesian coss, howeve, thiftiness is a vice. d. In the classical model of Chapte 3, the paadox of thift does not aise. In that model, output is fixed by the factos of poduction and the poduction technology, and the inteest ate adjusts to equilibate saving and investment, whee investment depends on the inteest ate. An incease in thiftiness deceases consumption and inceases saving fo any level of output; since output is fixed, the saving schedule shifts to the ight, as in Figue At the new equilibium, the inteest ate is lowe, and investment and saving ae highe. S 1 S 2 Figue Real inteest ate 1 A 2 B I() Investment, Saving I, S Thus, in the classical model, the paadox of thift does not exist.
9 90 Answes to Textbook Questions and Poblems 5. a. The downwad sloping line in Figue epesents the money demand function (M/P) d = 1, With M = 1,000 and P = 2, the eal money supply (M/P) s = 500. The eal money supply is independent of the inteest ate and is, theefoe, epesented by the vetical line in Figue (M/P) s Figue Inteest ate 5 (M/P) d 500 1,000 Real money balances M/P b. We can solve fo the equilibium inteest ate by setting the supply and demand fo eal balances equal to each othe: 500= 1, = 5. Theefoe, the equilibium eal inteest ate equals 5 pecent. c. If the pice level emains fixed at 2 and the supply of money is aised fom 1,000 to 1,200, then the new supply of eal balances (M/P) s equals 600. We can solve fo the new equilibium inteest ate by setting the new (M/P) s equal to (M/P) d : 600 = 1, = 400 = 4. Thus, inceasing the money supply fom 1,000 to 1,200 causes the equilibium inteest ate to fall fom 5 pecent to 4 pecent. d. To detemine at what level the Fed should set the money supply to aise the inteest ate to 7 pecent, set (M/P) s equal to (M/P) d : M/P = 1, Setting the pice level at 2 and substituting = 7, we find: M/2 = 1, M = 600. Fo the Fed to aise the inteest ate fom 5 pecent to 7 pecent, it must educe the nominal money supply fom 1,000 to 600.
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