equilibrium in the money market

Transcription

1 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I I A Review of Closed Economy Macoeconomics We begin by eviewing some of the basics of closed economy macoeconomics that ae indispensable in undestanding the est of the couse Specifically, we would like to emind ouselves of; (i) endogenous vs exogenous vaiables and movements of a cuve vs movements along a cuve, (ii) how to conduct Compaative Statics in an IS-M model and (iii) the elation between IS-M and aggegate supply/demand functions Endogenous and exogenous vaiables An endogenous vaiable is a vaiable whose value is detemined inside the model, by solving the model (ie by finding an equilibium) An exogenous vaiable is a vaiable whose value is set/changed outside the model, by the economist conducting the analysis Unless changed delibeately, the value emains constant Fo instance, in this simple IS-M model: C T + I + equilibium in the goods maket IS: ( ( )) ( ) G M M: (, ) equilibium in the money maket the endogenous vaiables ae,, and the exogenous vaiables ae G, M, ( is often teated as a constant in basic Keynesian settings) Compaative Statics The pupose of macoeconomic analyses is to detemine what happens to the endogenous vaiables when the exogenous vaiables change The pocess of detemining this is called Compaative Statics Thee ae two methods: Find the equilibium point by dawing the IS and M cuves in the(, ) plane, and study how the equilibium point moves in esponse to changes in the exogenous vaiables Solve the equations mathematically fo the endogenous vaiables, and study how the equilibium values change in esponse to changes in the exogenous vaiables Eithe method can be used, both lead to the same conclusion The IS-M cuves The IS and M equations show the combinations of (, ) that maintain equilibium in, espectively, the goods and money makets The cuves coesponding to these equations tace combinations (, ) that maintain equilibium in, espectively, the goods and money I-

2 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I makets Both of these cuves ae dawn fo given levels of exogenous vaiables The cuves shift when the exogenous vaiables change (change in exogenous vaiables shift of the cuve itself) The cuves do NOT shift when the endogenous vaiables change (change in endogenous vaiables movement along the cuve) In ode to daw these cuves in the (, )plane, we need to find thei slopes This is done by totally diffeentiating the two equations IS d C d CT d + Id dg dc whee C is the maginal popensity to consume out of D d + Fom this we have [ C ( T )] d I d dg + disposable income D ( T( )) so d d IS C ( T ) given G I I < 0 C ( ) > 0 d and theefoe, < 0 d IS M dm M d d + d so d d M given M, > 0 < 0 d and theefoe, > 0 d M The IS cuve is downwad sloping and the M cuve is upwad sloping in the (, ) plane Again, the IS and M cuves ae dawn fo given values of G, M, When one of the exogenous vaiables G, M, changes, the cuves shift Exogenous vaiables ae usually changed one at a time The shifts of the cuves detemine how the exogenous changes influence the endogenous vaiables (, ) In this model, G appeas only in the IS and M only appeas in the M So when only I-

3 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I G changes ( dg 0 ), only the IS cuve shifts and when only M changes ( dm 0 ), only the M cuve shifts ehaps it would be helpful to see this in tems of a moe familia equation Think of an equation such as y ax + b, whee a is the slope and b is the intecept The line coesponding to this equation in (y, x) space shifts when the intecept b changes This line will not shift when a diffeent intecept, such as d in y cx + d changes In the same way, when only G in the IS changes and G does not appea in the M, then only the IS will shift and the M will not shift Note that both and change even when only one of G o M changes (only one of the cuves shifts) This is because and ae simultaneously detemined, at the equilibium whee the two cuves intesect Compaative Statics using the IS-M cuves Now we ae eady to examine how (, ) espond to changes in G and M By totally diffeentiating the IS and M, we have: IS [ C ( T )] d I d dg M M d d + d dm Recall that the IS and M tace the combinations (, ) that maintain equilibium in the goods and money makets Theefoe, the total diffeentiations of these equations show the mutual elationship which the small changes in each vaiable must maintain, if the espective makets ae to emain in equilibium In othe wods, the vaiables in these equations can change in esponse to the exogenous changes, but if the makets ae to stay in equilibium, the changes must stay within the confines of the mutual elationship shown by these diffeentiated foms Using this featue, we can find out which way the cuves shift, and theefoe whee the new equilibium point goes afte a change in G o M Imagine what would happen if one of the endogenous vaiables did not eact at all The othe vaiable will have to bae the entie buden of adjustment, and the change in this othe vaiable will show us the diection in which the cuves must shift It does not matte which endogenous vaiable is assumed to emain constant, the esult will be the same Nomally, it suffices to hypothetically stop one of the endogenous vaiables But fo confimation, we will ty both and hee I-3

4 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I dg > 0 d Suppose hypothetically that d 0, then > 0 dg C ( T ) IS, d 0 This means that fo a given level of, must be at a highe level afte a ise in G ( dg > 0 ), if the IS equilibium is to be maintained Theefoe, the IS cuve will shift above and to the ight The esult;, Suppose hypothetically that d 0, then d dg I IS, d 0 > 0 This means that fo a given level of, must be at a highe level afte a ise in G ( dg > 0 ), if the IS equilibium is to be maintained Theefoe, the IS cuve will shift above and to the ight The esult;, dm > 0 d Suppose hypothetically that d 0, then > 0 dm M, d 0 This means that fo a given level of, must be at a highe level afte a ise in M ( dm > 0 ), if the M equilibium is to be maintained Theefoe, the M cuve will shift down and to the ight The esult;, d Suppose hypothetically that d 0, then < 0 dm M, d 0 This means that fo a given level of, must be at a lowe level afte a ise in M ( dm > 0 ), if the M equilibium is to be maintained Theefoe, the M cuve will shift down and to the ight The esult;, Once we have the esults of ou Compaative Statics execises, we need to explain the esults using economic logic An expansion in govenment spending inceases effective demand and leads to, but to a smalle degee than if emained constant, because suppesses spending Highe levels of and ae also consistent with maintaining M equilibium, afte an incease in G An incease in the money supply leads to excess supply of money leading to, which stimulates investment and poduces A lowe level of and a highe level of ae also consistent with maintaining IS I-4

5 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I equilibium, afte an incease in M Compaative Statics using Came s Rule Came s Rule is a fomula we can use in solving o a a M a n a a a M n a a a n n nn x x M x n b b M b The ule tells us that when solving fo n x ( i,, n) i fo x i, we can make a new matix i by eplacing the i-th ow of the coefficient matix with the matix (vecto), deive the deteminant of i and divide it by the deteminant of the oiginal coefficient matix In othe wods, i x povided 0 i Details on Came s Rule can be found in lectue #0 (unde `Came's Rule, Invese Matix, and Volume ) of ofesso Stang s lectues at Going back to ou IS-M analysis, the total diffeentials we deived above [ C ( T )] d Id dg M d + d dm d can be ewitten as C ( T ) I dg d M d dm d We now apply Came s Rule to deive d d d d dg dg dm dm dg > 0 et dm 0 Then, [ C ( T )] d Id dg d + d 0 I-5

6 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I Divide both sides by dg and we have C ( T ) I d dg d 0 dg The deteminant of the coefficient matix is D [ C ( T )] + I < 0 So we can use Came s Rule and d dg D 0 I D > 0 G ) ) (, to ecove M equilibium (, to maintain M equilibium, not zeo Aggegate Supply < Aggegate Demand to ecove IS equilibium d C ( T ) dg D > 0 0 D to maintain M equilibium I( to ecove IS G (, ) (, ) Aggegate Supply < Aggegate Demand ) equilibium dm > 0 etting dg 0 and dividing both sides by dm, C ( T ) I d dm d dm 0 d dm / (, ) 0 I I > 0 D D M I M > ) to maintain IS equilibium (C is smalle than ) (, to ecove M equilibium I-6

7 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I d dm D / (, ) C ( T ) M I via M > ) 0 C ( T D ) < 0 to maintain IS equilibium (, to ecove M equilibium We can confim that the two methods (IS-M cuves and Came s Rule) lead us to the same Compaative Statics esult The impotance of patial deivatives In Compaative Statics, the impotance of patial deivatives cannot be oveemphasised An example of a patial deivative is the maginal popensity to consume out of disposable income T C It shows how C eacts when disposable income ( ( )) changes, and is deived by diffeentiating the consumption function C C( T ( )) with espect to ( T ( )) Moe geneally, patial deivatives show how economic vaiables such as consumption, investment, tax evenue and money demand eact to changes in the vaiables they depend on Many of the vaiables they depend on ae endogenous vaiables Hee in this model, the endogenous vaiables ae income and the ate of inteest and change in esponse to changes in exogenous vaiables such as M and G In othe wods, patial deivatives show the eaction of an economic agent (economic vaiable) to exogenous changes (including but not only policy changes) We can confim the impotance of patial deivatives by going back to ou Compaative Statics esults In the analysis using IS-M cuves, the patial deivatives detemine the slope of the cuves as well as the diection and amount of shifts (in esponse to changes in exogenous vaiables) of the cuves When we use Came s Rule, the esults of ou calculations ae functions of patial deivatives Clealy, the effects of monetay and fiscal policy ae detemined by patial deivatives, o how economic agents espond One might think that it is only natual that policy effectiveness depends on how economic agents eact Macoeconomic models coectly eflect this atial deivatives also guide us in giving economic intepetations to the esults This is moe visible when we use Came s Rule The patial deivatives appea in the esults of ou calculation, showing us the path though which the exogenous changes come to affect the endogenous vaiables I-7

8 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I All of this means that we must be caeful Because the esult of Compaative Statics depends on patial deivatives, the analysis could tun out ielevant o even hamful if the actual patial deivatives took values that wee vey diffeent fom those assumed Take as an example the effect of a tax cut on the economy A tax cut inceases disposable income The expansionay effect on the economy is highe, the highe the maginal popensity to consume (esponse of consumption to changes in disposable income) Suppose the economy was in a ecession and the govenment budget was in deficit Assuming that the maginal popensity to consume was high enough, we could conclude that a tax cut was desiable Even if it tempoaily inceased the budget deficit, the esulting economic expansion would eventually impove tax evenue This scenaio beaks down if the maginal popensity to consume wee too low We may even end up with a lage budget deficit and an economy that has not expanded at all In fact, changes in patial deivatives in esponse to policy wee at the coe of the citicism against taditional Keynesian economic policies put foth in the 970s and 80s In applying esults of economic analyses to policy ecommendations, we need to pay close attention to the values of patial deivatives, along with the stuctue of the model itself IS-M and aggegate demand/supply We tun now to the elationship of the IS-M and aggegate demand/supply functions Technically, this involves moving fom a system that detemines two endogenous vaiables (, ),, The vaiable to one that detemines thee endogenous vaiables ( ) which used to be exogenous in the IS-M analysis now becomes endogenous This means that we need to add anothe independent equation to the model To be solvable, a model must have at least as many independent equations as endogenous vaiables In the pesent case, we add the poduction function of the epesentative fim This equation, togethe with the fist-ode-condition fo the fim s optimisation, gives us the aggegate supply function The aggegate demand function is obtained by substituting out fom the IS and M equations The aggegate supply function The poduction function of a epesentative fim, in its most geneal fom, would be: f ( N, K) whee d dn > 0 f > 0 If this epesentative fim maximises pofit o d dn < 0 f < 0 I-8

9 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I the fist-ode-condition (foc) is max ( WN ) given, N d dn W d and the eal wage dn W 0 maginal poductivity of labou ( Classical Axiom No ) Since the maginal poductivity of labou is a function of N, we can wite Theefoe W Substituting this into Fom which ( N K ) g( N ) f, W W N g h, h < 0 d d f And since the invese has the same sign, h ( N K ) f, - W > 0, we have W W f g, K f h, K In othe wods, in the (, ) plane, the aggegate supply cuve slopes upwad d d > 0 Moe specifically, if we use the Cobb-Douglas poduction function N K 0 < <, d W theefoe dn N p N The fim s demand fo labou is and substituting this into N N K, W W K K W W K I-9

10 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I W K Theefoe, d d S W K > 0 whee we have used + d And since the invese has the same sign, > 0 d o the slope of the aggegate supply cuve is upwad in the (, ) plane The aggegate demand function In the IS-M analysis ealie, we set d 0 and allowed only dm, dg to be non-zeo Now, d is also non-zeo and what we would like to do is to deive a elationship p, fom the patial deivatives between ( ) [ C ( T )] d d I d 0 M + d d In ode to do that, we substitute out d of IS fo d, I d [ C ( T )] d d d We do this by fist solving the total diffeential C ( T ) I then substituting it into the d in the total diffeential of M to have: M d + [ C ( T )] d d I d d + M D I Theefoe, [ C ( T )] < 0 And the aggegate demand cuve is downwad sloping in the (, ) plane Note that this slope accoding as I 0 I-0

11 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I The equilibium values of (, ) ae found whee the aggegate supply and aggegate demand cuves intesect Both cuves shift in eaction to changes in exogenous vaiables,, As with and the esulting change in the intesection will show us the changes in ( ) the IS and M cuves, the aggegate supply and aggegate demand cuves shift only in esponse to changes in exogenous vaiables they ae functions of Fo the aggegate supply cuve, these ae all vaiables taken as exogenous in the poduction function and the fim s optimization pocess (such as K, W o technology) Fo the aggegate demand cuve, these ae exogenous vaiables that shift IS and M It is extemely impotant to keep in mind that emains endogenous thoughout the aggegate supply and demand analysis When an endogenous vaiable is substituted out, it does not become exogenous Rathe, it keeps changing in the backgound, along with the endogenous vaiables that emain visible We can find the change in the hidden endogenous vaiable by using the elationship between endogenous vaiables In the d d C T to find d pesent case, we can substitute d into ( ) I A note about Economic Models Some people citicise economic models fo not depicting the actual economy in which we live They think that economic models ae fa too simplified and ationalised compaed to the eal wold, and that policy ecommendations deived fom such models ae dangeous o even downight hamful To be sue, the economies descibed by economic models neve coespond exactly to eality, and in that sense, do not eally exist But that is no eason to deny the usefulness of economic models To undestand the aison d ête of economic models, it is useful to think of them as compising two types One type of model tells us how an economy should be An example is a model with pefect competition It has been said that most economists endose the theoem that a pefectly competitive maket bings about a aeto Optimal esouce allocation This theoem is often misundestood as a eflection of blind faith in the maket mechanism But even economists know that the eal wold is not exactly the same as a pefectly competitive maket The model is useful because it shows how the economy will wok unde pefect competition Knowing the wokings of such a model is like knowing the wokings of a completely healthy human body In the eal wold, thee is no such thing as a pefectly healthy body Some people have bad teeth o bad backs, yet othes moe seious conditions that equie hospitalisation In any event, nobody has a body that fits a textbook desciption of pefect I-

12 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I health et, the idea of how a body should be if it has no illnesses (which we might call a model body), is indispensable if we wanted to stay healthy It is because we have this model that doctos can examine us, compae us to this model and make a diagnosis Nobody says that this idea of a pefectly healthy body is useless o hamful, just because no such thing eally exists In fact we should be gateful fo its existence, because that is pecisely why doctos can tell us how we ae diffeent fom how we should be, and help us In the same way, an economic model which depicts an economy without inefficiencies and idigities offes a benchmak It was because economists knew the outcome when esouce allocation was left to a pefectly competitive maket that they could poceed to investigate the implications of maket failues such as extenalities and impefect infomation The othe type of economic model steps somewhat close to the economy as it is Such a model incopoates those aspects of the eal economy most elevant to the question the economist is asking If an economist ties to incopoate eveything, the model becomes too complicated to be wokable, so the economist must choose Fo instance, if the issue in question is how to educe unemployment, then it may be wise to put wage stickiness into the model Obviously, economists need to emain awae of the limits of the models they ae using Thei diagnosis is useful in as much as thei model eflected the featues of the economy most elevant to the investigation undeway If some impotant featues wee missing, the model needs to be evised Even if the topic of investigation emained the same, the appopiate model might change with the times This is because economic stuctues and people s eactions change with the times We will come back to this latte point, when we discuss the implications of esponse of economic agents (change in patial deivatives) to policy effectiveness Summay In this section we went ove some of the basics in closed macoeconomics that ae needed in following the est of the couse The main points can be summaized as follows The model s equilibium detemines the value of endogenous vaiables, while the economist (o someone outside the model) detemines the value of exogenous vaiables Compaative Statics is an execise in which we analyse the effects of changes in exogenous vaiables on endogenous vaiables, using the IS-M cuves o Came s Rule I-

13 Sahoko KAJI --- Open Economy Macoeconomics ectue Notes I atial deivatives decide and explain the esults of Compaative Statics This eflects the simple fact that effects of policy depend on the eaction of economic agents 3 The aggegate supply and demand system simultaneously detemines the thee endogenous vaiables (, ), In moving to this system fom to the IS-M system, does not become exogenous o emain at levels inconsistent with equilibium In ode to tun fom an exogenous vaiable into an endogenous vaiable, we need anothe equation, the poduction function Behind the aggegate supply function, thee is the poduction function and the optimizing behaviou of the epesentative fim Behind the aggegate demand function is the IS-M equilibium I-3