Chapter 7: Equilibrium in the Flexible Price Model


 Marjorie Small
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1 Copyight MHHE 2005 Chapte 7: Equilibium in the Flexible Pice Model knowing what has happened to consumption spending. But consumption spending depends on income, which in tun depends on the levels o net expots and investment spending. QUESTIONS In the lexiblepice model, what keeps aggegate demand and the level o poduction equal to potential output? We need a way o analyzing the macoeconomy as an intedependent system, athe than as a collection o pats we stack next to each othe. What ae the oces in the economy that make aggegate demand equal output? Thee ae two answes to the question. One answe is coect when we assume pices ae ully lexible. In the lexiblepice model, what makes the supply o unds saving equal to the demand o unds investment in inancial makets? A second dieent answe is coect when we assume pices ae sticky. Stating in Chapte 9, we will look at the stickypice model o the macoeconomy. In this chapte, we assume pices ae ully lexible. When thee is a change in saving o investment demand, what happens in this lexiblepice model to the eal inteest ate, and why,? When pices ae ully lexible, the amount o output the economy poduces Y is always equal to its potential output Y. So what guaantees that in a lexiblepice economy, this ullemployment level o As govenment policies, the intenational economic envionment, o othe eatues o policy o the economic envionment change, what happens in this lexiblepice model to consumption, investment, govenment, and net expot spending? 7.1 FullEmployment Equilibium Chapte 6 set out the deteminants o the components o total spending. But knowing what detemines consumption spending C, investment spending I, and net expots NX is not enough o undestanding the macoeconomy. The macoeconomy is a system. The deteminants o net expots ae aected indiectly by the level o investment spending. Investment spending cannot be analyzed without output will also be an equilibium level o output, whee output equals aggegate demand? It is the eal inteest ate that assues equilibium in a lexiblepice macoeconomy. We saw in Chapte 6 that the eal inteest ate detemines investment spending. Also, the eal inteest ate detemines the eal exchange ate g, and this eal exchange ate detemines net expots. What you will lean in this chapte is that changes in the eal inteest ate ae what make the demand o output AD equal to the available output which in this lexiblepice economy is the potential output Y. We will call this the lowooutput appoach to undestanding macoeconomic equilibium in a lexiblepice economy. Page 71 Page 72
2 Copyight MHHE Assumption o Pice Flexibility The FlowoFunds Appoach What you will also lean is that an equivalent appoach is to stat with the supply o unds saving and the demand o unds investment. We will call this the lowounds appoach to undestanding macoeconomic equilibium in a lexiblepice economy. The lowounds though inancial makets is key to undestanding why the eal inteest ate bings the macoeconomy to equilibium. The key assumption that sepaates how we analyze equilibium in this chapte om ou analysis that begins in Chapte 9 is the assumption o pice lexibility. In this chapte, we assume pices ae ully lexible. (See Box 7.1 o an example o what it means o pices to be ully lexible.) We must coness: this assumption is not a ealistic desciption o the shot un. We use it because assuming pices ae lexible is vey helpul o analyzing the economy in the long un. What is the eal inteest ate that it plays this ole? The eal inteest ate is simultaneously the pice the lende chages and the pice o boowing money. Money lows though inancial makets. Saves ty to ind a poductive, poitable, and inteesteaning place to put thei savings. Businesses ty to ind cheap inancing o the investment pojects they hope will be poitable. Why do people lend money? Because they have no immediate spending use o it, and eceiving some inteest is bette than having it sit undeneath the mattess. Why do businesses boow money? They boow money because they hope to make a poit by using the unds they boow to invest in new plant and equipment in ode to expand thei opeations. Thus the saving o households and othes low into inancial makets, and the boowing o businesses seeking to inance investment low out o inancial makets. This lowounds though inancial makets is a key set o economic tansactions. The eal inteest ate is the pice chaged and eceived in this maket o loanable unds. When the inteest ate is at its longun equilibium level, the supply o loanable unds equals the demand o loanable unds. Financial makets ae in balance. Box 7.1 I Pices Wee Tuly Flexible... What does it mean o pices to be lexible? The authos wok in Bekeley, whee sometimes it seems evey student in a moning class aives with a pape coee cup in hand. The lines at one o the most popula caés, Caé Stada, typically go out the doo just beoe the 10:00 a.m. classes begin. Eveyone in line needs to have thei cappuccino, latte, o espesso i they e going to make it though class. This is especially the case on ou oggy, chilly monings in late sping. I pices wee ullylexible, the pice o the coee dinks would ise between the time the last student got in line and the time she eached the counte. The chill in the ai inceased demand. The time (moning) inceased demand. In a wold o ully lexible pices, the pice o the poduct would espond by ising immediately. As you stood thee, waiting to each the counte, you d see the pice o you coee dink ise. But 45 minutes late, when the sun had buned o the og so the chill in the ai was gone, and when eveyone was aleady in class, the subsequent all in demand would lead to alling pices. That swing in pices in immediate esponse to changes in demand would be an example o ully lexible pices. Page 73 Page 74
3 Copyight MHHE 2005 This is, o couse, an example on a mico scale. When the same stoy applies in industy ate industy, But beoe we get too a ahead o ouselves, let s build the model. then you have a maco stoy. RECAP: FullEmployment Equilibium In a lexiblepice economy, eal output Y always equals potential output Y. At equilibium in output makets, this potential output Y will equal aggegate demand AD; this is the lowooutput appoach. The long un model we aleady studied was Chapte 4's model o economic gowth. Remembe o We can also look at equilibium with the lowounds appoach; saving equals investment in equilibium. Changes in the eal inteest ate will take the economy to equilibium. eview that when the saving ate inceases in the long un, the capitaltolabo atio and the capitaltooutput atio both incease. Moe saving poduces a highe standad o living. But in Chapte 4, we had no stoy about how an incease in saving poduces a highe capitaltolabo atio. What is the mechanism? Chapte 7 povides the answe to that question: the eal inteest ate. You will lean in this chapte that when saving inceases, eal inteest ates decline, and so investment spending inceases. And moe investment in plant and equipment poduces a lage capital stock, which in the vey long un inceases the capitaltolabo atio, the capitaltooutput atio, and output pe woke. 7.2 Two Appoaches: One Model The goal o this chapte is to show how the eal inteest ate assues ullemployment equilibium in an economy with lexible pices. At equilibium, two statements will be tue: the supply o unds will equal the demand o unds, and aggegate demand o output will equal potential output. Both statements ae tue because thee ae two appoaches to this one lexiblepice model. In this section, we Note that thee will be a cetain tension in this chapte. Pices ae lexible: the time scale o the analysis must be long enough o pices to adjust so that thee is not excess demand o excess supply in any o the economy s makets. So this analysis o Chapte 7 applies to changes in the economy only i they take signiicantly longe than a month, o a quate. On the othe hand, we ae going to assume that potential output Y does not change, which means that the analysis o Chapte 7 applies to changes in the economy only i they take signiicantly less than a decade. The useulness o the lexiblepice model thus tends to get squeezed between the stickypice luctuations model coveed in late chaptes and the longun gowth model coveed ealie. will show that these two appoaches the lowounds appoach and the lowooutput appoach ae mathematically equivalent. Why, i the two appoaches to this one model ae equivalent mathematically, do we bothe with two appoaches? The answe is woth emembeing, because this will not be the last time in you studies o economics that a second, mathematically equivalent, appoach is suddenly substituted o an appoach you have aleady igued out. Thee ae times in economics and this is one o them when a Page 75 Page 76
4 Copyight MHHE 2005 mathematically equivalent appoach has much bette economic intuition than the oiginal appoach you have aleady masteed. And the best economics is always the most intuitive stoy. Figue 7.1 The Cicula Flow Diagam Thee ae two ways to show that the lowounds appoach and the lowooutput appoach ae equivalent ways o modeling the lexiblepice economy. We can show the equivalence with algeba. And we can show the equivalence using the dawing intoduced in Chapte 2 o the economy s cicula low. Let s stat with the cicula low, depicted in Figue 7.1. Page 77 Page 78
5 Copyight MHHE Using The Cicula Flow Diagam Goods and sevices output ae poduced in businesses, geneating income (the blue low) o esponse to this aggegate demand. So though the output makets, aggegate demand equals output. This is the lowooutput appoach to equilibium. households. Household income includes not just wage and salay income, but inteest income, ent income, etained business eanings, and moe. Households can do thee things with this income (the geen lows): consume goods and sevices that ae poduced by businesses, pay net taxes to govenment, And the output poduced by businesses geneates income o households. O we go on anothe ound though the cicula low. o save household saving in inancial makets. With the net tax evenues, govenment can buy goods and sevices om businesses (the pink low) o accumulate a suplus (geen low) which it saves in inancial makets. Some goods and sevices ae impoted om othe counties, so not all o the spending o goods and sevices lows back to domestic businesses; some o it lows to the est o the The cicula low diagam is one way to undestand that the lowounds and lowooutput appoaches to the macoeconomy ae equivalent. We can also demonstate that equivalence a second way: Algeba. wold. Impots ae at least patially oset by ou expots o goods and sevices to othe counties. The dieence impots less expots epesents unds om ou economy that accumulate in the est o the wold. This net inlow o inancial capital om the est o the wold (ed low) is saved in inancial makets Using Some Algeba We stat om the amilia lowooutput equilibium condition, and deive the lowounds equilibium condition. Begin with the deinition o aggegate demand AD: AD = C + I + G + NX The inancial makets lend the unds saved by households, govenment, and the est o the wold to businesses, which use the unds to invest in plant and equipment (pink low). Total saving S is the sum o household saving S H, govenment saving S G, and oeign saving by the est o the wold S F. So though the inancial makets, total saving S equals investment I. This is the lowounds appoach to equilibium. Unde the lowooutput appoach, aggegate demand AD and output Y ae equal in macoeconomic equilibium. When wages and pices ae lexible, then output Y equals the economy s potential poductive output Y. So in lowooutput equilibium, potential output Y will equal aggegate demand AD. We have Y = C + I + G + NX The sum o consumption spending (pink low om households), govenment spending (pink low om govenment), investment spending (pink low om inancial makets), less the net impots (ed low to est o the wold) lows into businesses. This is aggegate demand. Businesses poduce output in Page 79 Page 710
6 Copyight MHHE 2005 Now a ew steps will take us to the equivalent lowounds equilibium statement. Subtact consumption C, govenment puchases G, and net expots NX om both sides in ode to move Figue 7.2: The Flow o Funds Though Financial Makets eveything except o investment spending I to the lethand side: Y C G NX = I And then a little math tick will give us economically meaningul concepts: subtact and add net taxes T on the lethand side by subtacting it om income Y and adding it to G. Add some paentheses so we can goup tems by economic concepts: (Y T C) + (T G) + ( NX ) = I Now let s step back and look at what this equation means Unpacking the FlowoFunds Equation The ighthand side o this equation is simply investment spending I. Unde the lowooutput appoach, investment spending is simply spending by ims to build actoies and stuctues and boost thei poductive capacity. But unde the lowounds appoach, we think o investment I not as the output that businesses buy, but as the unds that businesses allocate to buying these investment goods. Investment spending I is the low o unds out o inancial makets to businesses which then use the unds to undetake investment. It is the demand o loanable unds. The lethand side o the equation measues the total saving lowing into inancial makets om thee dieent goups households (which, emembe, include not only the wokes but also the ownes o businesses), the govenment, and the est o the wold (see Figue 7.2). The ist tem Y T  C is equal to household saving S H. In this lexiblepice model, potential output Y is equal to eal output. Output and household income ae always equal. So Y is just household income. Subtact net taxes T and consumption spending C om household income Y and what is let? What is let is household saving the low o unds om households into inancial makets because saving is the only thing that households do with income othe than pay it to the govenment as taxes and spend it on consumption goods. The second tem T G is equal to govenment saving S G. T is simply the taxes the govenment collects minus the tanse payments it makes to individuals. G is govenment puchases. So T G is the Page 711 Page 712
7 Copyight MHHE 2005 dieence between the taxes that the govenment collects and the tanse payments and puchases the govenment makes. When T G is positive, the govenment is unning a budget suplus. The suplus is Figue 7.3 Impots Minus Expots Equals Foeign Saving govenment saving S G. When T G is negative, the govenment is unning a deicit (as it is today). Then S G will be less than zeo. The last tem the opposite o net expots, NX is oeign saving S F. It is the capital inlow, the net low o unds that the est o the wold channels into domestic inancial makets. As Figue 7.3 illustates, net expots ae the dieence between the dollas oeignes spend buying ou expots and the dollas eaned by oeignes selling us impots. I net expots ae less than zeo which they typically ae o Ameica oeignes have dollas let ove ate they buy all ou expots they want. These intenationallyowned dollas low into inancial makets. They aen t spent buying ou expots, and the only othe useul thing the est o the wold can do with them is save them. (When net expots ae positive, this tem has a dieent intepetation. It is the net amount o domestic saving that is diveted into intenational inancial makets the amount o saving that does not show up as loanable unds available to inance investment at home, but instead inance investment aboad.) We have deived the lowounds equilibium equation. The thee lethand side tems o (Y T  C) + (T G) + ( NX) = I ae the thee lows o puchasing powe into the inancial makets: household saving S H, govenment saving S G, and oeign saving S F. Added togethe they make up total saving S, which is the supply o loanable unds. The demand o loanable unds is simply investment spending I the ight hand side o the equation above. So the lowounds equilibium equation can also be witten S H + S G + S F = I Page 713 Page 714
8 Copyight MHHE 2005 What we have shown is that the lowooutput equilibium condition output equals aggegate demand is equivalent to the lowounds equilibium condition saving equals investment. When one statement is tue, the othe must also be tue. When one is alse, the othe must also be alse. I supply equals demand in the maket o loanable unds: S H + S G + S F = I then aggegate demand in the lexiblepice economy is equal to ullemployment output. And i output equals aggegate demand in the makets o goods and sevices: Y = C + I + G + NX then the supply and demand in the low o unds though inancial makets balances as well. (Although, as Box 7.2 points out, the elationship between the supply and demand o unds is not diect.) Box 7.2: Financial Tansactions and the Flow o Funds: Some Details The elationship between the unds that low into and the unds that low out o inancial makets is indiect. When the govenment uns a suplus, it does not diectly lend money to a business that wants to build a new actoy. Instead, the govenment uses the suplus to buy back some o the bonds that it peviously issued. The bank that owned those bonds then takes the cash it eceived om the govenment and uses it to buy some othe inancial asset pehaps bonds issued by a copoation. Similaly households o oeignes using inancial makets to save aely buy newly issued copoate bonds. No do they oten buy shaes o stock that ae pat o an initial public oeing. On the ae occasion when they do, they ae diectly tanseing puchasing powe to a company undetaking investment. Instead, households and oeignes usually save by puchasing aleadyexisting secuities o RECAP: Two Appoaches: One Model We can appoach equilibium in two ways. One is the lowooutput appoach: in equilibium, output equals aggegate demand. The othe is the lowounds appoach: in equilibium, saving equals investment. We can show that these two appoaches ae equivalent using the cicula low diagam. We can also show they ae equivalent algebaically, by stating with one equilibium condition, Y = AD, and simply depositing thei wealth in a bank. The elationship between the lows o unds into and out o inancial makets is indiect, but it is vey eal. deiving om it the othe, S = I. 7.3 The Real Inteest Rate Adjusts to Assue Equilibium In a lexiblepice economy, equilibium exists when aggegate demand equals potential output. But what economic oces will make aggegate demand equal potential output? The deteminants o C, I, G, and NX ae things like consumes optimism, inteest ates, the sensitivity o expots to exchange ates, and so on. These deteminants seem to have nothing at all to do with the deteminants o Y. It is the Page 715 Page 716
9 Copyight MHHE 2005 om o the poduction unction and the available esouces on the supply side that detemine the level o potential output Y. So what will make the sum o C, I, G, and NX equal potential output? As the eal inteest ate alls, two things happen. The numbe and value o investment pojects that ims and entepeneus ind it poitable to undetake ises. Investment spending ises, closing the gap The answe is: the eal inteest ate plays the key ole. I govenment policy, the intenational economic envionment, o domestic conditions change, then the eal inteest ate changes in esponse. In tun, the change in the eal inteest ate causes changes in investment spending, the exchange ate, and net expots. The eal inteest ate will continue to change until the economy is again at equilibium. It is these changes in the eal inteest ate that assue that in the long un a lexiblepice macoeconomy eaches and stays at equilibium whee aggegate demand equals potential output. between saving and investment. (And, not coincidentally, closing the gap between aggegate demand and potential output.) And net expots ise, deceasing oeign saving and uthe closing the gap between saving and investment. (And, again not coincidentally, uthe closing the gap between aggegate demand and potential output.) The pocess will stop when the inteest ate has allen just enough to make the low o saving into the inancial makets equal to investment. So that s the big bottom line: the eal inteest ate assues equilibium in the lexiblepice model because both investment and saving espond to changes in the eal inteest ate. But how could a disequilibium between aggegate demand and output lead to a change in the eal inteest ate? Hee is whee the lowounds appoach comes in. Equilibium with aggegate demand equal to potential output is equivalent to equilibium with the supply o unds saving equal to the demand o unds investment. When aggegate demand is less than potential output, saving is geate than investment. And when aggegate demand is geate than potential output, investment is geate Gaphing the SavingInvestment Relationship We can depict these elationships gaphically. Investment spending is the demand o loanable unds. As the eal inteest ate alls, investment spending I ises. The gaph in Figue 7.4 should emind you o Figue 6.10, though we have switched the hoizontal and vetical axes. than saving. When the supply o unds saving is geate than the demand o unds investment what will happen? The pice o unds the eal inteest ate will all. Some inancial institutions banks, mutual unds, ventue capitalists, insuance companies, whateve will ind puchasing powe piling up as moe money lows into thei accounts than they can ind good pojects to commit to. They will ty to undebid thei competitos. How do they undebid? They undebid by saying that they will accept a lowe inteest ate than the cuent eal inteest ate. Page 717 Page 718
10 Copyight MHHE Figue 7.4 The Demand o Loanable Funds The elationship is depicted in Figue 7.5. It is impotant to emembe that oeign saving can be eithe negative o positive. When a county uns a tade suplus, oeign saving is negative. When it uns a tade deicit, as the United States has been doing o many yeas, oeign saving is positive. To emind ouselves that oeign saving can be negative o positive, we daw the oeign saving cuve cossing the vetical axis, as in Figue Figue 7.5 The Foeign Supply o Loanable Funds Total saving is the supply o loanable unds. It has thee components: household saving S H, govenment saving S G, and oeign saving S F. Let s stat with oeign saving. As the eal inteest ate alls, oeign saving S F alls. The intuition is a bit oundabout. As the eal domestic inteest ate alls, the nominal and eal exchange ates ise. (I you want to eview why this is so, see Section 6.3.) When the eal exchange ate g ises, goss expots GX ise. When goss expots ise, net expots NX ise, which is the same thing as saying net impots ( NX) all. When net impots all, net oeign inlow o inancial capital alls. And net oeign inlow o inancial capital is just a long phase o oeign saving, S F. Household saving is anothe component o total saving. Household saving S H is what s let ove ate net taxes T and consumption C have been subtacted om household income Y. Consumption Page 719 Page 720
11 Copyight MHHE 2005 spending depends on income, as do net taxes. But as we noted in Appendix 6.A eal inteest ates do not aect consumption. And because we ae assuming that household income is always equal to potential 3Figue 7.6 Household and Govenment Supply o Loanable Funds output Y, which depends upon the supplies o inputs and the poduction unction, then income is not dependent upon the eal inteest ate. And since neithe the tax ate no income depend upon the eal inteest ate, net taxes don t change when the eal inteest ate changes. So household saving S H does not change when the eal inteest ate changes. We show the elationship between household saving and the eal inteest ate as a vetical line, as in panel (a) o Figue 7.6. Govenment saving S G is the inal component o total saving. But its value also does not depend upon the value o the eal inteest ate. So hee again, we would show the elationship between govenment saving and the eal inteest ate as a vetical line. I govenment saving was negative i the govenment was unning a deicit then the govenment saving line would be to the let o the vetical axis, as shown in panel (b) o Figue 7.6. Total saving is the sum o oeign, household, and govenment saving. Gaphically, we take the oeign saving line, shit it ove by the amount o household saving, and shit it ove again o in the case o a govenment budget deicit shit it back  by the amount o govenment saving. This gives us the elationship between total saving S and the eal inteest ate. We do this in Figue 7.7. Page 721 Page 722
12 Copyight MHHE 2005 Figue 7.7 Total Saving: The Supply o Loanable Funds 4Figue 7.8 Equilibium in the Flow o Loanable Funds We now have the two sides o the loanable unds maket. The demand o loanable unds is investment spending, depicted in Figue 7.4. The supply o loanable unds is total saving, depicted in Figue 7.7. Bing them togethe to see the maket o loanable unds, as we have done in Figue 7.8. When total saving S equal investment demand I, the maket o loanable unds will be in equilibium The Adjustment to FlowoFunds Equilibium Suppose that the eal inteest ate is initially geate than the equilibium eal inteest ate, as shown in Figue 7.9. Saving will exceed investment by the amount labeled excess saving. Some lendes will oe to accept a lowe inteest ate. As inteest ates all, investment spending will incease, moving along the investment demand cuve. And as inteest ates all, oeign saving will all, moving along the total saving cuve. The macoeconomy will move to the equilibium inteest ate, whee saving equals Page 723 Page 724
13 Copyight MHHE 2005 investment. And, as we showed above, when saving equals investment, aggegate demand equals potential output. When pices ae ully lexible, the eal inteest ate adjusts to assue ull employment. saving into the inancial makets exceeds the demand by copoations and othes o puchasing powe to inance investment? Then the pice o loans the eal inteest ate will all, until the supply o unds saving equals the demand o unds investment. Convesely, i investment demand exceeds saving, the eal inteest ate will ise. When the eal inteest ate is at its equilibium value, saving equals investment, S = I, and aggegate demand equals ullemployment eal GDP, AD = Y. 7.4 Using the Model: What Makes the Real Inteest Rate Change? We can use this gaphical way o looking at the lowounds to igue out what happens to the equilibium eal inteest ate when thee is some change in the economic envionment o in economic policy. Some changes make eithe the saving o the investment cuve shit. Othe changes also aect the slope o the saving o investment cuve. When one o both o the cuves shit o change slope, thee will be a new equilibium eal inteest ate. Let s take a look The Eect o a Change in Saving Total saving S is the sum o household, govenment, and oeign saving. So a decease in any o those components o S will decease total saving. It could be a decease in household saving, deceasing S H. It could be an incease in govenment spending which deceases govenment saving S G. It could be a RECAP: The Real Inteest Rate Adjusts to Assue Equilibium In the lexiblepice model, the eal inteest ate is the pice that equilibates the maket o loanable unds the place whee saving lows into and investment inancing lows out o inancial makets. What happens i the low o unds does not balance i at the cuent eal inteest ate, the low o decease in ou impots, which deceases oeign saving S F. Any o these changes would be shown by a shit to the let o the total saving S cuve, as shown in Figue As an example, let s suppose the economy is in equilibium when policy makes decide to incease Page 725 Page 726
14 Copyight MHHE 2005 annual govenment puchases by the amount G. Moe govenment puchases mean less govenment saving. Less govenment saving means that the supplyosaving in the loanable unds maket is shited to the let: at each possible inteest ate, thee is less in the way o total saving lowing into the loanable unds maket. At the oiginal eal inteest ate, investment demand will now exceed total saving. This shotall in saving will cause the eal inteest ate to ise; some boowes bid up inteest ates in an attempt to obtain unding o thei investment pojects. But the ising inteest ate squeezes othe boowes out o the maket; the total quantity o unds demanded o investment alls, moving us up and to the let along the investment demand cuve. The ising eal inteest ate also lowes the eal exchange ate g, which inceases oeign saving lowing into domestic inancial makets, moving us along the second total saving cuve. The eal inteest ate will ise until saving again equals investment. In the end, the lowounds maket settles down to equilibium at a new, highe equilibium inteest ate with a new, lowe level o investment. When the supply o unds S deceases, the eal inteest ate ises, investment spending alls, and (not supisingly) the amount o saving alls. But notice what has happened. The inal change in investment and saving, shown along the hoizontal axis, is smalle than the change in saving that thew the lowounds makets out o equilibium. How could that be? The inal change in saving is smalle than the initial change in saving because oeign saving ose when the eal inteest ate ose. But this ise in oeign saving is elatively small so, oveall, saving still alls. Page 727 Page 728
15 Copyight MHHE 2005 A dop in household saving S H would be analyzed the same way, as would a dop in oeign saving S F that occued at evey inteest ate. In both o these cases, the total saving cuve shits to the let, aising the eal inteest ate, inceasing oeign saving slightly to oset pat but not all o the initial dop in saving, and deceasing investment demand The Eect o a Change in Investment Demand We can also use the lowounds gaph to see the eect o an incease in investment I. Suppose that businesses suddenly become moe optimistic about the utue and incease the amount they wish to spend on new plant and equipment (as they did in the late 1990s). What would be the eect o such a domestic investment boom? A tax cut has a slightly dieent eect. It is vey like the eect o a govenment puchases incease. But because a tax cut inceases disposable income and the maginal popensity to consume is less than 1, so thee is one dieence. The dieence is that a potion o the addition to household income om the tax cut shows up as household saving. So the initial shit to the let o the Total Saving cuve is smalle than the dop in govenment saving by the amount o this change in household saving. Othewise the eects ae vey simila: like a govenment puchases incease, a tax cut leads to an incease in the inteest ate, a ise in oeign saving, and a all in investment spending. Investment the demandoloanableunds cuve shits to the ight, as Figue 7.11 shows. At the initial inteest ate, investment demand now exceeds saving. Fims that wish to incease thei investment spending will bid up inteest ates as they compete o scace loans. As inteest ates ise, two things happen. One, othe ims will decease thei investment spending because thei planned investment pojects ae no longe poitable at these nowhighe inteest ates a movement along the new investment demand cuve. Also, the highe eal inteest ate leads to a all in the eal exchange ate, to a all in net expots, and thus to an incease in oeign saving lowing into domestic inancial makets Why do economists make such a big deal out o a decease in govenment saving whethe it s due to a decease in taxes o an incease in govenment puchases? Because as Figue 7.10 illustates, in the long a movement along the saving cuve. In the end, the lowounds maket settles down to a highe inteest ate with an inceased level o saving and investment. un, a decease in govenment saving an incease in the budget deicit makes inteest ates ise, which educes investment spending. And emembe one o the lessons o Chapte 4: investment spending inceases the capital stock, which ultimately inceases the standad o living. In the long un, inceases in govenment boowing cowd out educe investment spending which, all else equal, slows the county s ate o economic gowth while the economy adjusts to a lowe balanced gowth path. Page 729 Page 730
16 Copyight MHHE 2005 RECAP: Using the Model: What Makes the Real Inteest Rate Change? We can use the gaphical appoach to lowounds equilibium to see that an incease in saving o a decease in investment shits to the ight in the saving cuve o to the let in the investment demand cuve would lead to a all in the eal inteest ate. And a decease in saving o an incease in investment would make the eal inteest ate ise. When the supplyosaving shits, the ultimate change in saving will be smalle than the initial change in saving. When investment demand shits, the ultimate change in investment will be smalle than the initial change in investment. In both cases, this is due to changes in the eal inteest ate which induce movements along the saving and investment cuves that patly osets the initial shits. 7.5 Calculating the Equilibium Real Inteest Rate: Algeba The lowounds gaphs let us igue out whethe inteest ates ise o all in eaction to a change in Notice what happened: The highe inteest ates due to the ist shit in investment led to a subsequent decease in investment that patly but not entiely oset the initial shit. But investment did incease. What made the incease in investment possible? The incease in oeign saving. I saving had not inceased in eaction to the highe inteest ates, investment could not incease. Without an incease in saving, the shit in investment demand would make inteest ates ise so much that investment spending ell ight back to its initial position. Instead, when oeign saving inceases with eal inteest ates, both saving and investment incease in esponse to inceased business optimism. policy o economic envionment that aects investment demand o total saving. But what i we ae policy makes who want to know the pecise value o the eal inteest ate at equilibium, and by how much the inteest ate will change i we implement some policy? To igue out the value o the inteest ate and how much it changes in eaction to a change in policy o economic envionment, we need to do some algeba. What we need ae the equations o total saving S and o investment demand I. Equilibium occus Page 731 Page 732
17 Copyight MHHE 2005 when saving S equals investment I, so we will just set the equations equal to each othe. Then we solve why we gaphed household saving S H and govenment saving S G as vetical lines in Figue 7.6. o the eal inteest ate. What about oeign saving S F? Hee the eal inteest ate plays a ole. (Section 6.3 laid out the details.) It sounds staightowad and it is. But the equations can get quite messy. Don t get discouaged. I the notation and the algeba get to be a bit much, emembe that all we e doing is setting saving equal to investment and solving o The Fomula o the Equilibium Real Inteest Rate Stat with total saving, which is the sum o household saving S H, govenment saving S G, and oeign saving S F. S = S H + S G + S F Household saving is equal to total income Y minus taxes T minus consumption spending C. But since we ae in a wold o lexible pices (that s ou assumption in this chapte, emembe), total income Y is always equal to potential output Y. Consumption spending depends on baseline consumption C 0, the maginal popensity to consume C y, the tax ate t, and potential income Y (peek back at Section 6.2 to Foeign saving is impots minus expots. The deteminants o oeign saving ae thee paametes the popensity to impot IMy, oeignes popensity to buy expots X, and the sensitivity o expots to the exchange ate Xg and thee vaiables oeign incomes Y, domestic total income Y, and the exchange ate ε: S F = NX = (IMyY)  (XY)  (Xεε) And it is the exchange ate that changes when the eal inteest ate changes: ε = ε0  ε(  ) whee the eal exchange ate ε depends upon the baseline value o the eal exchange ate g 0, the sensitivity o the eal exchange ate to changes in inteest ates ε, the domestic eal inteest ate, and the oeign eal inteest ate. eesh you memoy). S H = Y T  C = Y  ty  (C 0 + C y(1  t)y) So, because oeign saving depends on the exchange ate, and because the exchange ate depends on the inteest ate, oeign saving SFdepends on the eal inteest ate. When the eal inteest ate ises, the Govenment saving is equal to net taxes T minus govenment puchases G. As in Chapte 6, let net taxes be a constant popotion o income: T = ty. Govenment saving then equals S G = T  G = ty  G Notice that neithe household saving no govenment saving depend on the eal inteest ate. That is total saving low inceases. Why? Because an incease in the eal inteest ate attacts oeign capital into domestic inancial makets, and inceases oeign saving. We can wite this as: S F () = (IMyY)  (XY)  (X εε0) + (X εε)  (X εε) We wite oeign saving as S F () to emind ouselves that oeign saving depends on the eal inteest ate. Page 733 Page 734
18 Copyight MHHE 2005 the moe amilia statement Y = C + I + G + NX. I you do so, you ll ollow the same plugandchug On the othe side, demand o unds is simply investment spending. Use the investment equation om Section 6.2: When the eal inteest ate ises, investment spending I alls: steps that we use hee. But hee, let s use the lowounds appoach, so we begin with the lowounds equilibium statement SH + SG + SF = I I() = I0 I We wite investment spending as I() to emind ouselves that the level o investment spending depends upon the eal inteest ate. Fist, we need the expession o household saving: SH = Y  T C Substituting the equations o taxes and o consumption gives us The lowounds equilibium is whee supply and demand balance whee the supply o savings is equal to investment spending: At equilibium, S H + S G + S F () = I() So now we solve this equation o, the equilibium eal inteest ate. The details o the deivation ae SH = Y  ty  C0 Cy(1t)Y Next, we need the expession o govenment saving, into which we substitute the equation o taxes SG = T G = ty  G given in Box 7.3. In equilibium, the eal inteest ate will equal I0 = ( Y C0 Cy (1 t) Y ) + G ( IM yy X Y X εε 0 I + X ε ε X ε ) ε Finally, we need the expession o oeign saving SF = NX = IM GX Fist we substitute the equations o impots and o expots Box 7.3 Deiving the Equilibium Inteest Rate Equation To deive the equation o the equilibium eal inteest ate, we stat om eithe the lowooutput o the lowounds equilibium statement. SF = IMyY  (XY + X εε) And then we substitute the equation o the eal exchange ate SF = IMyY  XY X ε (ε0  ε(  ) ) = IMyY  XY X εε0 + X εε  X εε Y = C + I + G + NX o SH + SG + SF = I Because one equilibium statement leads to the othe see Section 7.2 many students like to stat om Page 735 Page 736
19 Copyight MHHE 2005 Remembe the equation o investment I = I0  I But now we can igue out by how much the eal inteest ate will incease. The answe comes om looking at the denominato: I + X εε. The lage the denominato, the smalle the change in when investo s optimism ises. Now plug and chug : Set saving the sum o household, govenment, and oeign saving equal to investment: Y ty C C t Y (1 ) y + 0 ( ty G) + IM Y y X Y X ε + X ε X ε ε 0 ε ε = ( I I ) Notice that ty cancels out. Make that cancellation and also move evey tem that includes the eal inteest ate to the let hand side, and evey othe tem to the ight hand side o the equation: I + X ε = I ( ) ( ) Y C C (1 t) Y G IM Y X Y X ε X ε ε 0 0 y 0 Now isolate the eal inteest ate on the let hand side, and we e done: I0 = ( Y C C (1 t) Y ) 0 y ε y G + IM Y X y I + X ε Y 0 ε X ε X ε ε 0 ε ε Why? The ist tem I captues the change in investment due to a change in the eal inteest ate. The lage the sensitivity o investment to inteest ates I, the latte the Investment demand cuve; the moe quickly investment spending will all in esponse to a ise in inteest ates (the movement along the now latte investment cuve). And the aste investment alls when inteest ates ise, the smalle the ise in inteest ates that is needed to estoe equilibium in the lowounds. The second tem X εε captues the change in oeign saving due to a change in the eal inteest ate. The lage is oeignes sensitivity to the exchange ate X ε o the lage the sensitivity o the eal exchange ate to changes in inteest ates ε, the latte is the Total Saving cuve; the lage is the change in oeign saving when the eal inteest ate ises ( the movement along the now latte S cuve). And the lage the change in oeign saving, the less inteest ates will be pulled up by a ise in investment demand Intepeting the Equilibium Real Inteest Rate Equation What does that equation say? Fist look at the numeato. When I 0 inceases when business people become moe optimistic the eal inteest ate will incease. That is what we ound in Figue Figue 7.12 gives two examples. In panel (a), the sensitivity o investment to changes in the eal inteest ate is vey low. In panel (b), it is vey high. Notice how a decease in saving has a much lage eect on the eal inteest ate when I is small (panel a) than when it is lage (panel b). When G inceases when the govenment uns a lage deicit, deceasing its saving the eal inteest ate will ise. That is what we ound in Figue Page 737 Page 738
20 Copyight MHHE 2005 when saving S equals investment I which is the same thing as aggegate demand AD equals output Y. Box 7.4 is an example o substituting in values o the paametes. Box 7.5 stats om the equations o Aggegate Demand and calculates the value o the equilibium eal inteest ate. Box 7.4 Calculating the Equilibium Real Inteest Rate Fom Paamete Values Assume that the paametes o the model ae: I 0 = 12,000 Baseline investment spending o $12,000 billion pe yea Y = 21,000 Potential output o $21,000 billion pe yea C 0 = 0 C y = 0.8 t = G = 2,000 IM y = 0.3 X = 0.1 Y = 1,000 Baseline consumption spending A maginal popensity to consume o 80 pecent Tax ate o 37.5 pecent o income Govenment spending o $2,000 billion pe yea Impots ae 30 pecent o total spending A $1 billion incease in oeign income inceases ou expots by $0.1 billion Foeign income is $1,000 billion pe yea With the algebaic equations, we can calculate the equilibium value o the eal inteest ate. To do so equies the value o all o those constants in the equilibium equation above. Oten times, howeve, the inomation is given to us not as a list o values o paametes such as the maginal popensity to consume C y and so on, but as equations o the ou components o aggegate demand. Hee again, we can calculate the equilibium value o the eal inteest ate. We just emembe that equilibium occus X g = 600 A 1 point incease in the eal exchange ate inceases expots by $600 billion g 0 = 5 Baseline value o the eal exchange ate is 5 g = 10 A one pecentage point incease in the dieence between domestic and oeign inteest ates () = o ) = 0.01) deceases the eal exchange ate by 0.1 = 0.05 The oeign eal inteest ate is 5 pecent I = 9,000 A 1 pecentage point all in the inteest ate () = 0.01) inceases investment Page 739 Page 740
21 Copyight MHHE 2005 spending by $90 billion a yea. 10,500 and pick out the values o C 0, C y, t, and Y. To ind the equilibium eal inteest ate, we substitute these values into the equation o the eal inteest ate, and then simpliy. I = = = ,000 ( Y C C (1 t) Y ) 0 I X εε ( ( )21000) ( 0.3(21000) 0.1(1000) 600(5) 600(10)(0.05) ) = 0.04 y + G IM + Y y X Y X ε X ε ε 0 ε (10) In this case, we stat om the lowooutput equilibium statement, and then solve o the equilibium eal inteest ate. In equilibium output Y equals aggegate demand AD which is the sum o consumption C, investment I, govenment G, and net expots NX. 21,000 = 10,500 + ( 12,000 9,000) + 2,000 + ( 2,900 6,000) 600 = 15, = When the economy is in equilibium, the eal inteest ate will be 0.04 o 4 pecent. When the economy is in equilibium, the eal inteest ate will be 0.04 o 4 pecent. Box 7.5 Calculating the Equilibium Real Inteest Rate om Aggegate Demand Equations Suppose that we had the same economy that was descibed in Box 7.4, but instead o being given the values o the paametes, we wee given the aggegate demand equations themselves: Y = 21,000 C = ( )21,000 = 10,500 I = 12,0009,000 G = 2,000 GX = 0.1(1000) + 600(510( 0.05)) and IM = 0.3(21,000) which simpliies to NX = 2,9006,000 Now how do we ind the equilibium eal inteest ate? We can t exactly look at the equation C = Detemining the Eect o a Change in Policy on Aggegate Demand With the gaphs o saving and investment, we wee able to igue out whethe the inteest ate would incease o decease. Now we can igue out the eect o a change in policy on the eal inteest ate and on the values o consumption, investment, govenment, and net expots. Let s use a amilia example: an incease in govenment puchases G. Because the equilibium eal inteest ate is I0 = ( Y C C (1 t) Y ) 0 y G + IM Y X y I + X ε ε Y a change in govenment spending G will change the eal inteest ate by X ε X ε ε 0 ε Page 741 Page 742
22 Copyight MHHE 2005 G = I + X εε The size o the change in the eal inteest ate depends on the sensitivity o investment to changes in the eal inteest ate, the sensitivity o expots to a change in the eal exchange ate, and the sensitivity o the eal exchange ate to a change in domestic eal inteest ates. That is, it depends on how much investment and saving change when inteest ates change. Substituting in the change in the eal inteest ate gives us I = I I G + X εε Investment spending will all when govenment spending ises. This is what we call cowding out : The ise in govenment puchases inceases eal inteest ates which cowds out pivate investment spending. The change in investment spending will be equal to the sensitivity o investment to the inteest ate times the shit in the equilibium eal inteest ate. When govenment spending ises, what happens to the components o aggegate demand? Nothing in the intenational economic envionment ou popensity to impot, oeignes popensity to The change in govenment puchases has no eect on consumption. Because potential output does not change, national income does not change. Neithe national income, baseline consumption, the tax ate, no the maginal popensity to consume shits, so thee is no eect on the consumption unction C = C0 + Cy(1 t)y Thus the change in consumption spending is zeo: C = 0 expot changes when domestic iscal policy changes. No does the level o potential output change. But the inteest ate does change. Look back at ou exchange ate equation g = g 0  g (  ) A change ) in the domestic eal inteest ate will change the exchange ate by an amount g ). Looking back at ou expot equation, a change in the exchange ate o g ) will in tun change expots by an amount X gg ). So net expots will shit too: NX = GX  IM = X gg  0 The shit in govenment puchases has an indiect eect on investment. Investment depends on the inteest ate, and the inteest ate will change as a esult o the change in govenment puchases. So om the investment equation: Substituting in the change in the eal inteest ate gives us NX = X ε ε I G + X εε I = I0 I We see that investment spending will change by: I = I Last, eal GDP does not change because potential output does not change, and this is a longun ullemployment model, with eal GDP always equal to potential output: Page 743 Page 744
23 Copyight MHHE 2005 Y = Y = 0 S G = G The change in aggegate demand is the sum o the changes in consumption, investment, govenment, and net expots, so substituting we get G G AD = C + I + G + NX = 0 + I + + G X εε = 0 I + X εε I + X εε Foeign saving is the opposite o net expots, so oeign saving changes by: S F = X ε ε I G + X εε Put all these pieces togethe and we get The change in aggegate demand is 0. The incease in govenment spending G is just oset by the deceases in investment spending and net expots. Aggegate demand does not change when govenment spending changes because this is a longun model in which we have assumed that eal GDP is always equal to its potential value Y. In the long un, a change in one o the components o aggegate demand leads to a eallocation o aggegate demand, but doesn t change the oveall value o aggegate demand. S = S H S = I I + S G + S G + X εε F = 0 + ( G) + X εε I G + X εε The change in total saving just equals the change in investment. This is pecisely what Figue 7.10 led us to expect. The incease in govenment puchases educes the low o saving into inancial makets. The inteest ate ises. The highe inteest ate educed businesses plans o investment spending but also calls oth additional saving om oeignes. And so the highe inteest ate has etuned the low o unds to balance Detemining the Eect o a Change in Policy on Saving What about the eect o an incease in govenment puchases on total saving S? Since neithe household income no consumption changes, household saving does not change. S H = 0 Note that the alls in investment and in total saving ae not as lage as the ise in govenment puchases. This is also what Figue 7.10 led us to expect. The incease in govenment puchases educed the low o domestic saving into inancial makets, but the inceased low o oeignowned capital into the maket patially oset this eduction. The exta oeign saving kept the decline in investment om being Govenment puchases, howeve, do change. Since govenment saving is taxes minus govenment as lage as the ise in govenment puchases, as Figue 7.10 showed. puchases, and since govenment puchases have gone up, the change in govenment saving is: Page 745 Page 746
24 Copyight MHHE 2005 What is the point o the mach though the algeba? It allows us to calculate quantitative eects: to know not just that the inteest ate will go up, but by how much the inteest ate will go up. An example o how to actually calculate the change in the inteest ate is povided in Box 7.6. Box 7.6 A Govenment Puchases Boom: An Example Stat with the same economy that was descibed in Boxes 7.4 and 7.5. We have C y = 0.8 A maginal popensity to consume o 80 pecent C = 0 G $150billion I = I billion I X = 9,000 = $90 + εε 9, G = + $150billion G $150billion NX = X = (600 10) = $60billion I X εε + εε 9, And total saving will change by S = S H + S G + S F = 0 + ( 150) + (60) = $90billion t = X g = 600 g = 10 I = 9,000 Tax ate o 37.5 pecent o income A 1 point incease in the eal exchange ate inceases expots by $600 billion A one pecentage point incease in the dieence between domestic and oeign inteest ates () = o ) = 0.01) deceases the eal exchange ate by 0.1 A 1 pecentage point all in the inteest ate () = 0.01) inceases investment spending by $90 billion a yea. Figue 7.13 illustates the change in eal inteest ate, investment, and saving. Initially we had an equilibium eal inteest ate o 4 pecent, = Suppose that thee is a sudden but sustained incease in govenment puchases o $150 billion a yea. This sustained boom in spending inceases the equilibium eal inteest ate by 1 pecentage point: G 150 = = = I + X εε 9, ,000 = 0.01 = 1% The new inteest ate will be = 0.05 o 5 %. As a esult, the equilibium values o the components o aggegate demand will change by Page 747 Page 748
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