Autonoous Planned Aggregate Expendture rses at any level of the nterest rate. The level of output that satsfes goods-arket equlbru rses. As output rses, oney deand rses as well, leadng to hgher nterest rates n the cobned equlbru. Hgher output pressures nvestent up; hgher nterest rates put downward pressure on nvestent. Expansonary onetary Polcy ncreases the oney supply at any level of output. The level of nterest rates that satsfes oneyarket equlbru falls. Lower nterest rates rase nvestent and (by the ultpler process), expendture and output. Hgher output rases oney deand and puts upward pressure nterest rates, partally offsettng the effect of the onetary expanson. Consuer confdence ncreases, followng favorable poltcal developents. Consuer spendng rses at any level of ncoe. Does ths change expendture before changng nterest rates (goods arket) or does t change nterest rates frst (oney arket)? What s the effect on the other arket? What s the feedback effect on the frst arket?
An unfavorable busness envronent brngs planned nvestent spendng down. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? A recesson n foregn countres reduces exports (and reduces net exports). Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? Governent expendture on natonal defense rses Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? To keep Socal Securty fnanced wthout changng the retreent age, Congress rases taxes on households. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket?
The falure of a ajor nvestent bank causes a draatc ncrease n the deand for lqud balances. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? In a preeptve strke aganst nflaton, the Central Bank tghtens onetary polcy. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? Hgher prces reduce the real oney supply. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? (trck queston) Ol prces shoot up, rasng producton costs. Is the frst effect of ths event a change n expendture or a change n nterest rates? 3
Cultural changes lead to an ncrease n the argnal propensty to consue. For a gven change n nterest rates, s the effect on output larger or saller when the pc s larger? Is the relevant curve, then, flatter or steeper? If nterest rates change by, nvestent changes by I = b ( ). Output changes by = b ( c b ) ( ). Ths eans that the slope of the curve s = ( c b ) ( ) b At a gven rate of growth of oney supply, nflaton falls, allowng real oney supply to grow faster. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? Expectatons of lower nterest rates (n the near future) encourage long-ter busness nvestent, even though current onetary polcy s unchanged. Is ths a goods-arket or a oney-arket event? What s the effect on the other arket? What s the feedback effect on the frst arket? The new governent s expected to rase taxes and lower spendng n order to close the defct. Trcky! What s the effect of a fscal consoldaton (lower G and hgher T) on nterest rates? What wll ths change n nterest rates do to nvestent? 4
. Suppose consuer confdence rses, rasng consuer expendture. a. Is ths a goods-arket or a oney-arket event? It s a goods arket event, so the Z curve shfts n the goods-arket graph. Because ths change n expendture that leads to a change n output s not due to a change n nterest rates, t s a shft of the curve. b. What happens n the other arket? Because output rses, oney deand wll rse n the other arket, rasng nterest rates. Ths s shown n the oney-arket graph. Because ths s a change n nterest rates that s due to a change n output, t s a oveent along the curve. c. Show the feedback effect. Hgher nterest rates put downward pressure on nvestent, and partally counteract the expansonary effect of rsng consuer confdence. d. Show the effect n the approprate graph; show also what happens n the other graph, and show what happens n the - dagra. Goods arket - oney arket e. Suppose that the Central Bank wants to keep output constant. Show what the Central Bank has to do. If output has to return to ts orgnal level, then the Z curve wll have to shft back all the way (fro Z back to Z). If output wll end up n the sae place, but C s now hgher, then soe coponent of expendture (I, G, or NX) has to fall. The Central Bank can affect Investent by rasng nterest rates. Snce ths fall n expendture s due to a rse n nterest rates, t s a oveent along the curve (the new curve). The Central Bank can rase nterest rates by reducng the oney supply (to S ). Snce ths change n nterest rates s exogenous (the Central Bank decded to do ths on ts own), and not due to output, t s an upward shft of to. 5
Goods arket - oney arket f. Suppose that the Central Bank wants to keep nterest rates constant. Show what the onetary polcy has to do. g. Suppose, nstead, that t s the Governent that wants to keep output constant. Show what fscal polcy has to do. If output has to return to ts orgnal level, then the Z curve wll have to shft back all the way (fro Z back to Z). If output wll end up n the sae place, but C s now hgher, then soe coponent of expendture (I, G, or NX) has to fall. Fscal polcy can affect G drectly (and also C ndrectly, by rasng taxes). Snce ths fall n expendture s not due to a rse n nterest rates, t s a shft of the curve (fro the curve to the old curve). Because output falls back, oney deand falls back and nterest rates return to ther orgnal level. Because ths change n nterest rates s due to a change n output, t s a oveent along the curve. h. Suppose that the Governent wants to keep nterest rates constant. Show the approprate fscal polcy.. Suppose net exports fall. a. Is ths a goods-arket or a oney-arket event? b. What happens n the other arket? c. Show the feedback effect. d. Show the effect n the approprate graph; show also what happens n the other graph, and show what happens n the - dagra. Goods arket - oney arket 6
e. Suppose that the Central Bank wants to keep output constant. Show what the Central Bank has to do. Goods arket - oney arket f. Suppose that the Central Bank wants to keep nterest rates constant. Show what the onetary polcy has to do. g. Suppose, nstead, that t s the Governent that wants to keep output constant. Show what fscal polcy has to do. h. Suppose that the Governent wants to keep nterest rates constant. Show the approprate fscal polcy. 3. Suppose oney deand falls. a. Is ths a goods-arket or a oney-arket event? b. What happens n the other arket? c. Show the feedback effect. d. Show the effect n the approprate graph; show also what happens n the other graph, and show what happens n the - dagra. e. Suppose that the Central Bank wants to keep output constant. Show what the Central Bank has to do. f. Suppose that the Central Bank wants to keep nterest rates constant. Show what the onetary polcy has to do. g. Suppose, nstead, that t s the Governent that wants to keep output constant. Show what fscal polcy has to do. h. Suppose that the Governent wants to keep nterest rates constant. Show the approprate fscal polcy. 7
Nuercal Exercse for the curve Here s a general forula for equlbru output as a functon of (exogenous) nterest rates n the Goods arket: = ( c b ) [c 0 c T + b 0 + G + NX ] b ( c b ) Horzontal ntercept Here t s, rewrtten as the -functon (however, reeber that t s that causes n the Goods arket, not the other way around): = [c 0 c T + b 0 + G + NX ] b ( c b ) b Vertcal ntercept slope Suppose that the Goods arket s characterzed by the followng equatons C = 00 + 0.5 D I = 00 + 0.4 000 G = 00 T = 00 NX = 0 Fnd a nuercal forula for equlbru output at any gven level of (exogenous) nterest rates. 5% Draw the functon here: Fnd a nuercal forula for the functon. 5000 Draw what happens: Suppose that autonoous Consupton Expendtures rse fro 00 to 300. Go back to the orgnal, and assue Governent Expendtures rse to 300 Now (back to the orgnal nubers) suppose a trade surplus opens, so that NX = 50. By how uch does G have to fall to brng the curve back to where t started? 8
Nuercal Exercse for the curve Here s a general forula for equlbru nterest rates n the oney arket. Because equlbru nterest rates are expressed as a functon of (exogenous) output, ths s the functon = 0 /P Vertcal ntercept + slope Suppose that the oney arket s characterzed by the followng equatons P D = 0,000 + 3.5 70,000 = 8,50 Fnd a nuercal forula for equlbru nterest rates at any gven level of (exogenous) output. 5% Draw the functon here: 5000 Draw what happens: Suppose that autonoous oney Deand rse fro 0,000 to 3,500. Go back to the orgnal, and assue oney Supply falls to 4750 Now ake exogenous oney Deand,750. What does oney Supply have to be to brng the curve back to where t started? 9
Nuercal Exercses for the - odel Suppose that the oney arket s characterzed by the followng equatons P D = 0,000 + 3.5 70,000 = 8,50 and that the Goods arket s characterzed by the followng equatons C = 00 + 0.5 D I = 00 + 0.4 000 G = 00 T = 00 NX = 0 a. Fnd a nuercal forula for equlbru output at any gven level of (exogenous) nterest rates. Draw t on the graph. b. Fnd a nuercal forula for equlbru nterest rates at any gven level of (exogenous) output. Draw t on the graph. c. Plug the result fro (b) nto the result fro (a) to fnd equlbru output. ark t on the graph. d. Then plug the result fro (c) nto the result fro (b) to fnd equlbru nterest rates. ark the result on the graph. 5% 5000 0
e. Draw what happens n each case on the graph, and calculate the effect of each change on both output and nterest rates (usng the forulas).. Suppose that autonoous Consupton Expendtures rse fro 00 to 300. 5% The new * s = The new * s =. Go back to the orgnal, and assue Governent Expendtures rse to 300 5000. Now (back to the orgnal nubers) suppose a trade surplus opens, so that NX = 50. By how uch does G have to fall to brng output and nterest rates back to where they started? v. Suppose, nstead, that the Central Bank takes t upon tself to respond to the trade surplus wth onetary polcy. It ay choose to stablze output or nterest rates, but not both (that s, when the curve shfts, onetary polcy can brng output back to the orgnal level, or nterest rates back to ther orgnal level, but not both). Why not? Suppose that t chooses to stablze output. Does t have to ncrease or reduce oney supply? By how uch? Suppose that t chooses to stablze nterest rates. Does t have to ncrease or reduce oney supply? By how uch?
f. Draw what happens n each case on the graph, and calculate the effect of each change on both output and nterest rates (usng the forulas).. Startng fro the begnnng, suppose that autonoous oney Deand rse fro 0,000 to 3,500. 5% The new * s = The new * s =. Go back to the orgnal, and assue oney Supply falls to 4750. Now ake exogenous oney Deand,750. What does oney Supply have to be to brng output and nterest rates back to where they started? 5000 v. Suppose, nstead, that the Governent decdes that ts job ncludes respondng to changes n oney deand wth fscal polcy. Agan, t ay choose to stablze output or nterest rates, but not both (that s, when the curve shfts, fscal polcy can brng output back to the orgnal level, or nterest rates back to ther orgnal level, but not both). Why not? Suppose that t chooses to stablze output. Does t have to ncrease or reduce the budget surplus (T G)? By how uch? Suppose that t chooses to stablze nterest rates. Does t have to ncrease or reduce the budget surplus (T G)? By how uch?
Algebrac Exercse for the - odel Here are the forulas for equlbru output n the Goods arket = ( c b ) [c b 0 c T + b 0 b + G + NX ] ( c b ) and equlbru nterest rates n the oney arket. = + 0 /P Ths s the proper way to wrte the (although t akes dervng equlbru a lttle ore coplcated) because t akes t clear that Output s deterned n the goods arket (nterest rates are exogenous). Interest rates are deterned n the oney arket (output s exogenous). Let s derve equlbru output and nterest rates n a way that akes the algebra spler.. Consder a closed econoy characterzed by the followng equatons for consupton, nvestent, governent spendng, ncoe taxes, oney supply, and oney deand. C = c 0 + c ( T) I = b 0 + b b G = G T = T d P = 0 + S = a. Frst, set the quantty of oney suppled equal to the quantty of oney deanded, and solve the result for the nterest rate: that s the curve. b. Then, plug that equaton for the nterest rate nto the nvestent functon. c. Then, plug consupton, nvestent, governent spendng, and taxes nto the deand functon for the closed econoy, Z C + I + G. 3
d. Solve for equlbru output. The answer should be that, n equlbru = c b + b [c P 0 0 c T + b 0 + G + NX ] + b. Consder a closed econoy characterzed by the followng equatons for consupton, nvestent, governent spendng, ncoe taxes, oney supply, and oney deand. C = c 0 + c ( T) I = b 0 + b b G = G T = t 0 + t d P = 0 + S = e. Frst, set the quantty of oney suppled equal to the quantty of oney deanded, and solve the result for the nterest rate: that s the curve. f. Then, plug that equaton for the nterest rate nto the nvestent functon. g. Then, plug consupton, nvestent, governent spendng, and taxes nto the deand functon for the closed econoy, Z C + I + G. h. Solve for equlbru output. Show that the ultpler s now saller. The ultpler should be c ( t ) b + b For ths reason, we say that ncoe taxes work as an autoatc stablzer. Why? 4
3. Consder a closed econoy characterzed by the followng equatons for consupton, nvestent, governent spendng, ncoe taxes, and oney deand. C = c 0 + c ( T) c I = I G = g 0 + g T = t d P = 0 + S = a. Frst, set the quantty of oney suppled equal to the quantty of oney deanded, and solve the result for the nterest rate: that s the curve. b. Then, plug that equaton for the nterest rate nto the consupton functon (because, the way that I ve wrtten t, nvestent doesn t depend out nterest rates but consupton does). c. Then, plug consupton, nvestent, governent spendng, and taxes nto the deand functon for the closed econoy, Z C + I + G. d. Solve for equlbru output. 5
4. What happens to output and nterest rates when G rses (a stulus package)? Hgher governent expendture G ncreases expendture drectly. = c b + b [c P 0 0 c T + b 0 + G + NX ] + b a. Show that an ncrease n governent expendture of ΔG ncreases total expendture and output (after the ultpler process) by G = b + ( c b ) Is ths a postve or a negatve nuber? b. Use the functon, = + 0 /P, to show what happens to equlbru nterest rates when output changes by. = c. Cobne (a) and (b) to show what happens to nterest rates when governent spendng changes. Δ ΔG = Δ Δ Δ ΔG Δ ΔG = Is ths a postve or a negatve nuber? d. Investent s gven by I = b 0 + b b b + ( c b ) Ths eans that nvestent changes (ΔI) when output or nterest rates change I = b b Now that we know ths, we can say what happens to nvestent when G rses: the effect of a change n governent spendng on nvestent s. I ΔG = b ΔG b ΔG 6
Show that ths can be rewrtten as I ΔG = b b + ( c b ) b And now show that ths can be rewrtten as b + ( c b ) I ΔG = b b b + ( c b ) Is ths a postve or a negatve nuber? What does the sgn of the effect of governent spendng on nvestent depend upon? An ncrease n governent expendture G > 0 wll crowd out (reduce) nvestent G < 0 f b < b If the output effect s relatvely sall (sall b ), nvestent won t be pushed up uch. If nterest rates have a bg effect on nvestent (large b ), nvestent wll be pushed down a lot. If nterest rates change by a lot when output changes (large ), nvestent wll fall uch. A large (large D senstvty to output) or sall (low D senstvty to the nterest rate) produce a large change n the nterest rate. o For exaple, let s say that output changes by $00 bllon. What wll happen to D and nterest rates? D wll react ore (to a gven change n output) and nterest rates wll rse by ore f s larger. S S D D large sall 7
o Or let s say that people deand $50 llon extra cash, at every level of nterest rates. Ths eans that D shfts rght, creatng a dsequlbru n the oney arket: nterest rates need to rse to brng the quantty of oney deanded back down. If oney deand s not senstve to nterest rates (sall ), t wll take a huge ncrease n nterest rates to push people away fro holdng oney. Interest rates wll rse by less f oney deanded s ore senstve (f s larger). S S D D large sall 5. What happens to output and nterest rates when T falls? Hgher taxes (ΔT > 0) reduce consupton by C = c T, so they only affect expendture ndrectly. A tax cut (ΔT < 0) ncreases expendture a. Show that a tax cut of ΔT ncreases total expendture and output (after the ultpler process) by T = c b + ( c b ) Why s ths a negatve nuber? b. We know that equlbru nterest rates change by = when output changes by. Then show what happens to nterest rates when taxes are cut. Δ ΔT = Δ Δ Δ ΔT Δ ΔT = Is ths a postve or a negatve nuber? A negatve Δ ΔT would ean that nterest rates would rse after a tax cut. c. Snce the effect of a tax cut on nvestent can be wrtten as I = b ΔT b ΔT derve the condton that deternes the effect of a tax change on nvestent. When wll ths effect be postve? negatve? When s a tax cut good for nvestent? ΔT 8