CHAPTER 11 Aggregate Demand II

Transcription

1 CHPTER 11 ggegate Demand II Questions fo Review 1. The aggegate demand cuve epesents the negative elationship between the pice level and the level of national income. In Chapte 9, we looked at a simplified theoy of aggegate demand based on the quantity theoy. In this chapte, we exploe how the model povides a moe complete theoy of aggegate demand. We can see why the aggegate demand cuve slopes downwad by consideing what happens in the model when the pice level changes. s Figue 11 1() illustates, fo a given money supply, an incease in the pice level fom P 1 to P 2 shifts the cuve upwad because eal balances decline; this educes income fom 1 to 2. The aggegate demand cuve in Figue 11 1() summaizes this elationship between the pice level and income that esults fom the model.. The Model (P = P 2 ) Figue 11 1 (P = P 1 ) P 2 1. The ggegate Demand Cuve Pice level P 2 P 1 D

2 92 nswes to Textbook Questions and Poblems 2. The tax multiplie in the Keynesian-coss model tells us that, fo any given inteest ate, the tax incease causes income to fall by T [ MPC/(1 MPC)]. This cuve shifts to the left by this amount, as in Figue The equilibium of the economy moves fom point to point. The tax incease educes the inteest ate fom 1 to 2 and educes national income fom 1 to 2. Consumption falls because disposable income falls; investment ises because the inteest ate falls. Figue T MPC 1 MPC Note that the decease in income in the model is smalle than in the Keynesian coss, because the model takes into account the fact that investment ises when the inteest ate falls. 3. Given a fixed pice level, a decease in the nominal money supply deceases eal money balances. The theoy of liquidity pefeence shows that, fo any given level of income, a decease in eal money balances leads to a highe inteest ate. Thus, the cuve shifts upwad, as in Figue The equilibium moves fom point to point. The decease in the money supply educes income and aises the inteest ate. Consumption falls because disposable income falls, wheeas investment falls because the inteest ate ises. 2 1 Figue

3 Chapte 11 ggegate Demand II Falling pices can eithe incease o decease equilibium income. Thee ae two ways in which falling pices can incease income. Fist, an incease in eal money balances shifts the cuve downwad, theeby inceasing income. Second, the cuve shifts to the ight because of the Pigou effect: eal money balances ae pat of household wealth, so an incease in eal money balances makes consumes feel wealthie and buy moe. This shifts the cuve to the ight, also inceasing income. Thee ae two ways in which falling pices can educe income. The fist is the debt-deflation theoy. n unexpected decease in the pice level edistibutes wealth fom debtos to ceditos. If debtos have a highe popensity to consume than ceditos, then this edistibution causes debtos to decease thei spending by moe than ceditos incease theis. s a esult, aggegate consumption falls, shifting the cuve to the left and educing income. The second way in which falling pices can educe income is though the effects of expected deflation. Recall that the eal inteest ate equals the nominal inteest ate i minus the expected inflation ate π e : = i π e. If eveyone expects the pice level to fall in the futue (i.e., π e is negative), then fo any given nominal inteest ate, the eal inteest ate is highe. highe eal inteest ate depesses investment and shifts the cuve to the left, educing income. Poblems and pplications 1. a. If the cental bank inceases the money supply, then the cuve shifts downwad, as shown in Figue Income inceases and the inteest ate falls. The incease in disposable income causes consumption to ise; the fall in the inteest ate causes investment to ise as well. 1 Figue

4 94 nswes to Textbook Questions and Poblems b. If govenment puchases incease, then the govenment-puchases multiplie tells us that the cuve shifts to the ight by an amount equal to [1/(1 MPC)] G. This is shown in Figue Income and the inteest ate both incease. The incease in disposable income causes consumption to ise, while the incease in the inteest ate causes investment to fall. Figue 11 5 G 1 MPC c. If the govenment inceases taxes, then the tax multiplie tells us that the cuve shifts to the left by an amount equal to [ MPC/(1 MPC)] T. This is shown in Figue Income and the inteest ate both fall. Disposable income falls because income is lowe and taxes ae highe; this causes consumption to fall. The fall in the inteest ate causes investment to ise. 1 MPC Figue 11 6 MPC T

5 Chapte 11 ggegate Demand II 95 d. We can figue out how much the cuve shifts in esponse to an equal incease in govenment puchases and taxes by adding togethe the two multiplie effects that we used in pats (b) and (c): = [(1/(1 MPC))] G] [(MPC/(1 MPC)) T] ecause 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 how output changes, holding the inteest ate constant. It says that an equal incease in govenment puchases and taxes shifts the cuve to the ight by the amount that G inceases. This shift is shown in Figue Output inceases, but by less than the amount that G and T incease; this means that disposable income T falls. s a esult, consumption also falls. The inteest ate ises, causing investment to fall. Figue 11 7 G

6 96 nswes to Textbook Questions and Poblems 2. a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease in the demand fo investment goods shifts the cuve out, aising income and employment. Figue 11 8 shows the effect gaphically. Figue The incease in income fom the highe investment demand also aises inteest ates. This happens because the highe income aises demand fo money; since the supply of money does not change, the inteest ate must ise in ode to estoe equilibium in the money maket. The ise in inteest ates patially offsets the incease in investment demand, so that output does not ise by the full amount of the ightwad shift in the cuve. Oveall, income, inteest ates, consumption, and investment all ise. b. The inceased demand fo cash shifts the cuve up. This happens because at any given level of income and money supply, the inteest ate necessay to equilibate the money maket is highe. Figue 11 9 shows the effect of this shift gaphically. 2 Figue

7 Chapte 11 ggegate Demand II 97 The upwad shift in the cuve lowes income and aises the inteest ate. Consumption falls because income falls, and investment falls because the inteest ate ises. c. t any given level of income, consumes now wish to save moe and consume less. ecause of this downwad shift in the consumption function, the cuve shifts inwad. Figue shows the effect of this shift gaphically. Figue Income, inteest ates, and consumption all fall, while investment ises. Income falls because at evey level of the inteest ate, planned expenditue falls. The inteest ate falls because the fall in income educes demand fo money; since the supply of money is unchanged, the inteest ate must fall to estoe money-maket equilibium. Consumption falls both because of the shift in the consumption function and because income falls. Investment ises because of the lowe inteest ates and patially offsets the effect on output of the fall in consumption.

8 98 nswes to Textbook Questions and Poblems 3. a. The cuve is given by: = C( T) + I() +G. We can plug in the consumption and investment functions and values fo G and T as given in the question and then eaange to solve fo the cuve fo this economy: = ( 100) = (1 0.75) = = (1/0.25) (425 25) = 1, This equation is gaphed in Figue fo anging fom 0 to 8. Figue ,100 1,700 b. The cuve is detemined by equating the demand fo and supply of eal money balances. The supply of eal balances is 1,000/2 = 500. Setting this equal to money demand, we find: 500 = 100. = This cuve is gaphed in Figue fo anging fom 0 to 8. c. If we take the pice level as given, then the and the equations give us two equations in two unknowns, and. We found the following equations in pats (a) and (b): : = 1, : = Equating these, we can solve fo : 1, = ,200 = 200 = 6. Now that we know, we can solve fo by substituting it into eithe the o the equation. We find = 1,100. Theefoe, the equilibium inteest ate is 6 pecent and the equilibium level of output is 1,100, as depicted in Figue

9 Chapte 11 ggegate Demand II 99 d. If govenment puchases incease fom 100 to 150, then the equation becomes: = ( 100) Simplifying, we find: = 1, This cuve is gaphed as 2 in Figue We see that the cuve shifts to the ight by Figue ,100 1,200 1,700 1,900 y equating the new cuve with the cuve deived in pat (b), we can solve fo the new equilibium inteest ate: 1, = ,400 = =. We can now substitute into eithe the o the equation to find the new level of output. We find = 1,200. Theefoe, the incease in govenment puchases causes the equilibium inteest ate to ise fom 6 pecent to 7 pecent, while output inceases fom 1,100 to 1,200. This is depicted in Figue

10 100 nswes to Textbook Questions and Poblems e. If the money supply inceases fom 1,000 to 1,200, then the equation becomes: (1,200/2) = 100, o = This cuve is gaphed as 2 in Figue We see that the cuve shifts to the ight by 100 because of the incease in eal money balances. 1 2 Figue ,100 1,150 1,700 To detemine the new equilibium inteest ate and level of output, equate the cuve fom pat (a) with the new cuve deived above: 1, = ,100 = =. Substituting this into eithe the o the equation, we find = 1,150. Theefoe, the incease in the money supply causes the inteest ate to fall fom 6 pecent to 5.5 pecent, while output inceases fom 1,100 to 1,150. This is depicted in Figue f. If the pice level ises fom 2 to 4, then eal money balances fall fom 500 to 1,000/4 = 250. The equation becomes: =

11 Chapte 11 ggegate Demand II 101 s shown in Figue 11 14, the cuve shifts to the left by 250 because the incease in the pice level educes eal money balances. 2 1 Figue ,200 1,100 1,700 To detemine the new equilibium inteest ate, equate the cuve fom pat (a) with the new cuve fom above: 1, = ,450 = =. Substituting this inteest ate into eithe the o the equation, we find = 975. Theefoe, the new equilibium inteest ate is 7.25, and the new equilibium level of output is 975, as depicted in Figue g. The aggegate demand cuve is a elationship between the pice level and the level of income. To deive the aggegate demand cuve, we want to solve the and the equations fo as a function of P. That is, we want to substitute out fo the inteest ate. We can do this by solving the and the equations fo the inteest ate: : = 1, = 1,700. : (M/P) = = (M/P). Combining these two equations, we find 1,700 = (M/P) 2 = 1,700 + M/P = M/2P. Since the nominal money supply M equals 1,000, this becomes = /P.

12 102 nswes to Textbook Questions and Poblems This aggegate demand equation is gaphed in Figue P Figue Pice level ,100 1,350 1,850 How does the incease in fiscal policy of pat (d) affect the aggegate demand cuve? We can see this by deiving the aggegate demand cuve using the equation fom pat (d) and the cuve fom pat (b): : = 1, = 1,900. : (1,000/P) = = (1,000/P). Combining and solving fo : 1,900 = (1,000/P), o = /P. y compaing this new aggegate demand equation to the one peviously deived, we can see that the incease in govenment puchases by 50 shifts the aggegate demand cuve to the ight by 100. How does the incease in the money supply of pat (e) affect the aggegate demand cuve? ecause the D cuve is = M/2P, the incease in the money supply fom 1,000 to 1,200 causes it to become = /P. y compaing this new aggegate demand cuve to the one oiginally deived, we see that the incease in the money supply shifts the aggegate demand cuve to the ight. 4. a. The cuve epesents the elationship between the inteest ate and the level of income that aises fom equilibium in the maket fo goods and sevices. That is, it descibes the combinations of income and the inteest ate that satisfy the equation = C( T) + I() +G.

13 Chapte 11 ggegate Demand II 103 If investment does not depend on the inteest ate, then nothing in the equation depends on the inteest ate; income must adjust to ensue that the quantity of goods poduced,, equals the quantity of goods demanded, C + I + G. Thus, the cuve is vetical at this level, as shown in Figue Figue Monetay policy has no effect on output, because the cuve detemines. Monetay policy can affect only the inteest ate. In contast, fiscal policy is effective: output inceases by the full amount that the cuve shifts. b. The cuve epesents the combinations of income and the inteest ate at which the money maket is in equilibium. If money demand does not depend on the inteest ate, then we can wite the equation as M/P = L(). Fo any given level of eal balances M/P, thee is only one level of income at which the money maket is in equilibium. Thus, the cuve is vetical, as shown in Figue Fiscal policy now has no effect on output; it can affect only the inteest ate. Monetay policy is effective: a shift in the cuve inceases output by the full amount of the shift. c. If money demand does not depend on income, then we can wite the equation as M/P = L().

14 104 nswes to Textbook Questions and Poblems Fo any given level of eal balances M/P, thee is only one level of the inteest ate at which the money maket is in equilibium. Hence, the cuve is hoizontal, as shown in Figue Figue Fiscal policy is vey effective: output inceases by the full amount that the cuve shifts. Monetay policy is also effective: an incease in the money supply causes the inteest ate to fall, so the cuve shifts down, as shown in Figue d. The cuve gives the combinations of income and the inteest ate at which the supply and demand fo eal balances ae equal, so that the money maket is in equilibium. The geneal fom of the equation is M/P = L(, ). Suppose income inceases by $1. How much must the inteest ate change to keep the money maket in equilibium? The incease in inceases money demand. If money demand is extemely sensitive to the inteest ate, then it takes a vey small incease in the inteest ate to educe money demand and estoe equilibium in the money maket. Hence, the cuve is (nealy) hoizontal, as shown in Figue Figue 11 19

15 Chapte 11 ggegate Demand II 105 n example may make this cleae. Conside a linea vesion of the equation: M/P = e f. Note that as f gets lage, money demand becomes inceasingly sensitive to the inteest ate. Reaanging this equation to solve fo, we find = (e/f) (1/f)(M/P). We want to focus on how changes in each of the vaiables ae elated to changes in the othe vaiables. Hence, it is convenient to wite this equation in tems of changes: = (e/f) (1/f) (M/P). The slope of the equation tells us how much changes when changes, holding M fixed. If (M/P) = 0, then the slope is / = (e/f). s f gets vey lage, this slope gets close and close to zeo. If money demand is vey sensitive to the inteest ate, then fiscal policy is vey effective: with a hoizontal cuve, output inceases by the full amount that the cuve shifts. Monetay policy is now completely ineffective: an incease in the money supply does not shift the cuve at all. We see this in ou example by consideing what happens if M inceases. Fo any given (so that we set = 0), / (M/P) = ( 1/f); this tells us how much the cuve shifts down. s f gets lage, this shift gets smalle and appoaches zeo. (This is in contast to the hoizontal cuve in pat (c), which does shift down.) 5. To aise investment while keeping output constant, the govenment should adopt a loose monetay policy and a tight fiscal policy, as shown in Figue In the new equilibium at point, the inteest ate is lowe, so that investment is highe. The tight fiscal policy educing govenment puchases, fo example offsets the effect of this incease in investment on output. Figue

16 106 nswes to Textbook Questions and Poblems The policy mix in the ealy 1980s did exactly the opposite. Fiscal policy was expansionay, while monetay policy was contactionay. Such a policy mix shifts the cuve to the ight and the cuve to the left, as in Figue The eal inteest ate ises and investment falls. Figue a. n incease in the money supply shifts the cuve to the ight in the shot un. This moves the economy fom point to point in Figue 11 22: the inteest ate falls fom 1 to 2, and output ises fom to 2. The incease in output occus because the lowe inteest ate stimulates investment, which inceases output. = Figue Since the level of output is now above its long-un level, pices begin to ise. ising pice level lowes eal balances, which aises the inteest ate. s indicated in Figue 11 22, the cuve shifts back to the left. Pices continue to ise until the economy etuns to its oiginal position at point. The inteest ate etuns to 1, and investment etuns to its oiginal level. Thus, in the long un, thee is no impact on eal vaiables fom an incease in the money supply. (This is what we called monetay neutality in Chapte 4.)

17 Chapte 11 ggegate Demand II 107 b. n incease in govenment puchases shifts the cuve to the ight, and the economy moves fom point to point, as shown in Figue In the shot un, output inceases fom to 2, and the inteest ate inceases fom 1 to 2. = Figue C The incease in the inteest ate educes investment and cowds out pat of the expansionay effect of the incease in govenment puchases. Initially, the cuve is not affected because govenment spending does not ente the equation. fte the incease, output is above its long-un equilibium level, so pices begin to ise. The ise in pices educes eal balances, which shifts the cuve to the left. The inteest ate ises even moe than in the shot un. This pocess continues until the long-un level of output is again eached. t the new equilibium, point C, inteest ates have isen to 3, and the pice level is pemanently highe. Note that, like monetay policy, fiscal policy cannot change the long-un level of output. Unlike monetay policy, howeve, it can change the composition of output. Fo example, the level of investment at point C is lowe than it is at point. c. n incease in taxes educes disposable income fo consumes, shifting the cuve to the left, as shown in Figue In the shot un, output and the inteest ate decline to 2 to 2 as the economy moves fom point to point. = 1 Figue C 1 2 2

18 108 nswes to Textbook Questions and Poblems Initially, the cuve is not affected. In the longe un, pices begin to decline because output is below its long-un equilibium level, and the cuve then shifts to the ight because of the incease in eal money balances. s fall even futhe to 3 and, thus, futhe stimulate investment and incease income. In the long un, the economy moves to point C. Output etuns to, the pice level and the inteest ate ae lowe, and the decease in consumption has been offset by an equal inceases in investment. 7. Figue 11 25() shows what the model looks like fo the case in which the Fed holds the money supply constant. Figue 11 25() shows what the model looks like if the Fed adjusts the money supply to hold the inteest ate constant; this policy makes the effective cuve hoizontal. Figue Holding the Money Supply Constant. Holding the Inteest Rate Constant a. If all shocks to the economy aise fom exogenous changes in the demand fo goods and sevices, this means that all shocks ae to the cuve. Suppose a shock causes the cuve to shift fom 1 to 2. Figues 11 26() and () show what effect this has on output unde the two policies. It is clea that output fluctuates less if the Fed follows a policy of keeping the money supply constant. Thus, if all shocks ae to the cuve, then the Fed should follow a policy of keeping the money supply constant. Figue Holding the the Money Supply Constant.. Holding the Inteest Rate Rate Constant

19 Chapte 11 ggegate Demand II 109 b. If all shocks in the economy aise fom exogenous changes in the demand fo money, this means that all shocks ae to the cuve. If the Fed follows a policy of adjusting the money supply to keep the inteest ate constant, then the cuve does not shift in esponse to these shocks the Fed immediately adjusts the money supply to keep the money maket in equilibium. Figues 11 27() and () show the effects of the two policies. It is clea that output fluctuates less if the Fed holds the inteest ate constant, as in Figue 11 27(). If the Fed holds the inteest ate constant and offsets shocks to money demand by changing the money supply, then all vaiability in output is eliminated. Thus, if all shocks ae to the cuve, then the Fed should adjust the money supply to hold the inteest ate constant, theeby stabilizing output. Figue Holding the Money Supply Constant. Holding the Inteest Rate Constant a. The analysis of changes in govenment puchases is unaffected by making money demand dependent on disposable income instead of total expenditue. n incease in govenment puchases shifts the cuve to the ight, as in the standad case. The cuve is unaffected by this incease. Thus, the analysis is the same as it was befoe; this is shown in Figue

20 110 nswes to Textbook Questions and Poblems Figue b. tax cut causes disposable income T to incease at evey level of income. This inceases consumption fo any given level of income as well, so the cuve shifts to the ight, as in the standad case. This is shown in Figue If money demand depends on disposable income, howeve, then the tax cut inceases money demand, so the cuve shifts upwad, as shown in the figue. Thus, the analysis of a change in taxes is alteed dastically by making money demand dependent on disposable income. s shown in the figue, it is possible fo a tax cut to be contactionay. Figue