ISLM Model 1 C' dy = di


 Phillip Ramsey
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1  odel Solow Assumptons  demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth  Assumptons  supply s rrelevant n short run; assumes economy s operatng below potental (.e., have excess capacty to absorb any ncrease n demand); concerned wth fluctuatons n busness cycle (based solely on aggregate demand) onsumpton Functon  relatonshp between consumpton & those economc varables that determne decson to consume; we only consder t a functon of dsposable ncome: = (  T()) (poor notaton; usng as consumpton and as functon for consumpton) argnal Propensty to onsume (P; ')  amount of ncreased consumpton that results from an ncrease n ncome; dervatve of consumpton functon wth respect to ncome; assume 0 < ' < argnal Propensty to Save (PS)  P + PS = ;.e., PS =  ' Investment  has multple meanngs, but for economsts, t means usng productve capacty to buld captal goods (vs. consumpton goods); for now treat as exogenous (gven) Planned Investment  amount busnesses want to spend on captal goods, ncludng amount they want to add to ther nventores; decde to buy captal goods because they foresee profts accrung to them from usng these captal goods Unplanned Investment  amount busnesses have to add or take away from ther nventores to make up for excess supply or demand Equlbrum  n goods market occurs when unplanned nvestment doesn't exst Smple odel  no taxes, no government purchases, closed economy 2 equatons, 2 unknowns ( and ): = () and = + I Take dervatves: d = 'd and d = d + di Sub d nto d equaton and solve for nvestment multpler: d = 'd + di d = di > 0 Sgn   ' s > 0 because 0 < ' < (assumpton) Graph  plots consumpton (demand, + I) on vertcal axs and producton (supply, ) on horzontal axs; for equlbrum (supply = demand) must be on 45 o lne; 2 has excess supply; 3 has excess demand hange n Investment on Graph  I shfts curve up and ncrease equlbrum ultpler  I by nverse of PS... the more people consume (.e., steeper + I), the larger mpact an ncrease n I wll have on output (see smaller graphs) Addng Fscal Polcy  = + I + G and = (  T) T = net taxes (tax revenues mnus transfer payments) G = government purchases Dsposable Income   T Stll 2 equatons, 2 unknowns of 8 * Demand 3 Supply + I 2 + I 2 45 o lne (Equlbrum) (Keynesan ross) ' + I I 2 + I
2 Take dervatves: d = 'd  'dt and d = d + di + Sub d nto d equaton and solve for nvestment multpler: d = 'd  'dt + di + d = di + + dt > 0 > 0 < 0 Wll get more complcated n a bt * + I + G + I * Tax ut or Government Purchases? lookng at multplers, G has larger mpact on (note that dt s multpled by ' < ); that means, dollar for dollar, government purchases are more effectve than tax cuts because wth cuts, people retan some of the money (determned by PS) whereas money from G goes straght nto Balanced Budget? f you have ncreased taxes to cover ncreased government purchases (.e., = dt), there s no change n... /(  ')  '/(  ') = (  ')/(  ') = Purpose  output and employment are very senstve to changes n nvestment whch s volatle; changes n G and T can be used to stablze output and employment Taxes as Functon of Income  = + I + G and = (  T()) Realstc  ongress sets tax rates and polces for transfer payments, but actually amount collected and pad depends on Automatc Stablzer  net taxes rse as because the government collects more tax dollars and makes fewer transfer payments; f, taxes collected automatcally go down and transfer payments go up; not good for government's fscal poston, but credted wth mnmzng fluctuatons n busness cycle (dfference between peak and trough); want fscal polcy to be automatc because poltcal system s too slow to buld consensus (e.g., decdng whch taxes to cut) T Surplus  T  G > 0;.e., transfer payments plus government purchases are less than taxes: G + Tr < Tx; or look at net taxes: G  T < 0 Defct Defct  T  G < 0;.e., transfer payments plus government purchases are more than taxes: G + Tr > Tx; or look at net taxes: G  T > 0 T ' 2002 Defct  G, T, and at same tme T T T 2 G 2 G Surplus T G 2 argnal Tax Rate (T ')  assume 0 < T ' < ; margnal rate s hgher than you thnk because t ncorporates transfer payments; also called margnal propensty to tax (PT) Stll 2 equatons, 2 unknowns: Take dervatves: d = '(  T ')d  'dt and d = d + di + Sub d nto d equaton and solve for nvestment multpler: d = '(  T ')d  'dt + di + d = di + + dt > 0 > 0 < 0 Poor notaton (agan) Ths s mnus the product of ' and (  T '), not ' evaluated at (  T ') 2 of 8
3 Impact of Taxes  all multplers are smaller now because people have less dsposable ncome (effectvely reduces P) Addng oney  can't talk about fscal polcy wthout lookng at money; wll now look at nvestment as endogenous (explaned by model) Investment Functon  relatonshp between nvestment demand (I) & those economc varables that determne the decson by frms to purchase captal goods; I = I(  π e ) (poor notaton; usng I as nvestment and as functon for nvestment) Real Interest Rate (r)  dfference between nterest rate () and nflaton rate (π = (dp/dt)/p); for model, use expected nflaton (π e ) because decsons made before nflaton s known Investment and Interest  assume ncreased nterest rates reduce nvestment (.e., or I < 0) Back to odel  now have = (  T()) + I(  π e ) + G; and are endogenous so we have equaton and 2 unknowns; need to look at all goodsmarket equlbra ( curve) urve  combnatons of nterest rate () & ncome () that generate goodsmarket equlbrum (.e., [] aggregate supply = aggregate demand; [2] = + I + G; [3] planned nvestment = savngs; [4] unplanned nvestment = 0); downward slopng because hgh nterest rates dscourage nvestment & therefore reduce equlbrum ncome; slope of curve shows how much equlbrum ncome wll change wth change n nterest rate; gets name from planned nvestment (I p ) equals savng (S) Savng  part of ncome that s not used for consumpton; S =  ; condton for goodsmarket equlbrum s savng equals planned nvestment (S = I p ) * + I + G + I 2 + G + I 3 + G an derve curve by usng aggregate expendtures (Keynsan cross) curve above the curve. ne up ncome () for varous values of nterest rate (). 3 2 supply 3 2 Shfts n  (.e., curve shfts to the rght) f T ( ), or π e (I ), or G ; results n larger output () for gven nterest rate () oneyarket Equlbrum  curve doesn't gve a specfc equlbrum, but a set of possble goodsmarket equlbra; to fnd a specfc equlbrum pont, you need to fnd the equlbrum n the moneymarket oney arket  where people ncrease or decrease the amount of money they hold by sellng or buyng shortterm bonds (e.g., Tblls) oney  has multple meanngs: wealth (stock), ncome (flow), etc., but for economsts, t means lqud porton of wealth (cash, checkng balances, etc.)  purely transactonbased defnton; currency plus demand deposts & travelers checks 3 of 8
4 2  purely transactonbased () plus easly transferable savngs accounts (e.g., overnght repurchase agreements, US dollar accounts n Europe, moneymarket mutual funds, savngs deposts, small tme deposts) 3  everythng n 2 plus large tme deposts & other accounts used less frequently for transactons purposes redt ards  affect how much money people want to hold, but are excluded from defnton of money because they re not assets Beneft of oney  certanty that asset can be quckly & readly used to purchase goods & servces ost of oney  holdng money costs because t earns no nterest or has very low nterest rate Demand for oney ()  porton of our wealth we want to hold n the form of money; use for "lqudty preference"; functon of ncome (# of transactons) and nterest rate (cost of holdng money): = (, ) Note: and, so < 0 and > 0 Supply of oney ()  determned by central bank (Fed); treat as fxed n short run onstant Purchasng Power  look at supply of money based on purchasng power by dvdng by prce level, P oneyarket Equlbrum  f there s less or more money demanded than avalable, actons of money holders n tryng to acqure or get rd of money wll brng about a change n nterest rate & hence quantty of money demanded; f excess demand for money then nterest rate s too low (everyone wants more money than s avalable; acqure money by sellng bonds whch drves up nterest rate on bonds) Theater Analogy  only lmted number of seats (fxed supply); demand can t create extra seats, so tcket prces are bd up by those who want to attend untl demand s brought nto lne wth supply urve  combnatons of nterest rate () & ncome () that generate moneymarket equlbrum (.e., [] supply of money = demand for money; [2] (, ) = /P); upwardslopng because hgher ncome ( ) causes hgher demand for money ( ) whch causes hgher nterest rate ( ) to brng money demand back down to equlbrum wth fxed supply; name comes from for money supply & for money demand Interest rate 3 P supply 2 3 supply; P demand; oney Supply & Demand (,) 2 ( 3,) ( 2,) (,) oney supply & demand 2 3 demand Shfts n  (.e., curve shfts to the rght) f, P, or ; results n larger output () for gven nterest rate () 4 of 8
5  Framework  pont of ntersecton of & schedules s one combnaton of nterest rate & ncome common to both schedules pont where both goods market & money market are n equlbrum ultpler Effect  change n ncome that would occur followng a shft n goods market f there were no change n the nterest rate (.e., gnore asset market) InterestRate Effect  followng shft n condtons n goods market, nterestrate effect s change n ncome resultng from change n nterest rate Interest rate 2 Interest rate effect ultpler effect Back to odel  now have 2 equatons, 2 unknowns: = (  T()) + I(  π e ) + G and (, ) = /P Take dervatves: d = '(  T ')d + I 'd  I ' and d + d = d/p  (/P 2 )dp Note: I ' = di/dr, r =  π e Solve for d d = d  T' ) Then sub n d equaton I ' I ' d  + d = d/p  (/P 2 )dp '( T' ) Solve for d [ ] ( d = + ( [ ( + ]P d = d  P 2 dp + P d + 5 of 8 I ' [ ( ] [ ( ] P 2 + < 0 > 0 I ' ( + ( + > 0 > 0 Plug back nto d equaton to get d multplers: d = [ ( + ]P d + [ ( ] P 2 + > 0 < 0 > 0 > 0 ( + Income B A ( + dp + dp +
6 Note, the terms for dπ e and have two terms that need to be combned. The math s ugly, but easy. ultplers above show fnal result. Extra ultplers  note that you can get addtonal multplers from d =  T ')d + d  by recognzng that d = '(  T ')d d = I ' [ ( + ]P d + ( T' ) [ ( ] P 2 + > 0 < 0 I ' T') > 0 > 0 ( + ( + dp + ou can also get addtonal multplers form the d equaton by recognzng di = I 'd  I 'dπ e di = [ ( T' )] ( + [ ] [ ] P 2 ( T' ) d + [ ]P ( + > 0 < 0 I '[ ] ( + I ' > 0 < 0 ( T') ) + ookng at hanges  take d/... No oney: > Wth oney: ( + No money verson treats curve as flat (horzontal); says demand for money s senstve to nterest rates; wth money, multpler s smaller because G causes whch causes so the overall change n s less than t was before consderng the money market Senstve to  note f = 0 (.e., demand for money s nsenstve to nterest rates), curve s vertcal; ncrease n G leaves unchanged and ncreases Implcaton for Fscal Polcy  have to worry about how senstve money demand s to nterest rate ( ); larger means fscal polcy s more effectve (.e., greater change n wth less mpact on ) dp ' ' 2 6 of 8
7 Recap  looked at model three tmes: d = > () T & I exogenous (2) I exogenous & (gven) T endogenous > ( + (3) T & I endogenous () arger P () d/ larger Note: ths concluson s more mportant than the actual value of the multpler (2) arger margnal tax rate (T') d/ smaller Note: concluson form frst model s stll vald n the second. Start smple (or later purposely make thngs exogenous) to make conclusons more obvous. (3) Demand for money more senstve to nterest rate (larger ) d/ larger Note: = 0 d/ = 0 (see graph wth vertcal curve) Note: conclusons form frst and second models stll vald n thrd ore Results  go back to T beng exogenous (.e., T' = 0); ths smplfes the multplers to fnd other conclusons: d = > 0 ( ) + hange n G  Short Verson: 2 G demand for demand for money I 2 ' ong Verson  ncrease n G causes too much demand for goods (.e., excess demand for ); frms ncrease output to elmnate excess demand ( ); as frms ncrease output () ncreases (based on, margnal propensty to consume or the senstvty of consumpton to ncome) and (2) demand for money () ncreases (based on, senstvty of demand for money to ncome); ncreased further ncreases demand for goods (ths goes back to the orgnal d/ multpler) whle ncreased demand for money forces nterest rates () to clmb (based on, senstvty of demand for money to nterest rates); hgher rates elmnate excess demand for money (pulls t back to curve) and ncrease borrowng costs for nvestment so I decreases (based on, senstvty of nvestment to nterest rate); process contnues untl decrease n I soaks up excess demand ("crowdng out") Analyzng omponents  larger d/ larger larger d/ smaller larger d/ larger larger d/ smaller 7 of 8
8 d I ' = d [ ( ) + I ' ]P > 0 ' hange n  Short Verson: supply of money demand I for goods 2 2 ong Verson  ncrease n causes too much supply of money whch drops nterest rates (); lower rates ncrease demand for money (, based on ) and ncrease nvestment (I, based on ); ncreased nvestment ncreases demand for goods so output ncreases; ths ncreases consumpton (, based on ) and ncreases the demand for money (, based on ); eventually the ncreased demand for money from lower nterest rate and ncreased output wll offset the excess supply Analyzng omponents  larger d/d larger (same as wth d/) larger d/d smaller (same as wth d/) larger d/d smaller (opposte of wth d/) larger d/d larger (opposte of wth d/) onetary or Fscal Polcy?  ultplers  sze of multplers not mportant unless one of them s zero because you can always get to potental GDP onventonal Wsdom  monetary s better because t's easer to change than G (less poltcal) Interest Rates  both polces get to potental GDP, but fscal polcy ncreases nterest rates and monetary polcy lowers nterest rates omposton of Output  = + I + G < ; n order to ncreases, one of the components has to ncrease; fscal and monetary polcy target dfferent components; fscal polcy through government purchases ncreases G; fscal polcy through taxes ncreases ; n both cases, fscal polcy results n decreased I; monetary polcy ncreases I Future Growth  recall Solow odel sad I (savngs) has consequences for growth Problem wth "Fact" 3?  sad economy would fx tself, but we've only looked at government nterventon through monetary or fscal polcy; how does economy fx tself? If we're below potental we know we have unemployment, but we gnored the labor market; Prces  we also kept prces constant throughout; that wll change when we add the labor market F ' ' 8 of 8
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