Output equals aggregate demand, an equilibrium condition Definition of aggregate demand Consumption function, c
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1 Eonoms 435 enze D. Cnn Fall Soal Senes 748 Unversy of Wsonsn-adson Te IS-L odel Ts se of noes oulnes e IS-L model of naonal nome and neres rae deermnaon. Ts nvolves exendng e real sde of e eonomy (desred n e prevous andou and nrodung a fnanal sde (a nvolves money and ond markes. Te real sde of e eonomy s exended y nrodung and neres sensve omponen of aggregae demand, namely nvesmen. Frs e real sde and e fnanal sde are desred. Tese are en pu ogeer o deermne overall eonom equlrum. Te mpa of fsal and moneary poly s en dsussed, and poly mulplers derved.. Te Real Sde of e Eonomy Eq.No. Equaon Desrpon ( = Z Oupu equals aggregae demand, an equlrum ondon ( Z = C I G Defnon of aggregae demand (3 C = o D Consumpon funon, s e mp (4 D T Defnon of dsposale nome (5 T = Tax funon; s lump sum axes, s margnal ax rae. (6 I = Invesmen funon (revsed (7 G = GO Governmen spendng on goods and serves, exogenous I I Te new parameers are =, and = e neres sensvy of nvesmen. Susung n all e equaons (-(7 no ( yelds: ( = Z = ( ( T ( ( GOo ( = Z = ( ( ( ( GO ( o Equaon ( s a lnear verson of equaon (5.. Sne s lnear, we an solve ou for. Rearrange, solvng for as a funon of, one oans: ( = [ ] ( <IS urve> were ( GO. o Ts equaon an e re-wren as: ( (3 = <IS urve>
2 All pons along e lne defned y s equaon are pons were nome and neres raes are su a aggregae demand equals nome.. Te Fnanal Sde of e Eonomy Eq.No. Equaon Desrpon (4 (5 d s = Equlrum ondon = oney supply s For money demand: d (6 = μ oney demand ( d / Equaon (6 mples a real money demand rses dollar for dollar w real nome, =. ( d / Furer noe a =. Susue (5 and (6 no (4, and rearrange o oan: μ (7 = <L urve> All pons on s lne represen e omnaons of nome and neres raes a equlrae money supply and money demand. 3. Equlrum n IS-L: Algera and Grapal Te IS and L equaons onsue a wo equaon sysem w wo unknowns. Te unknowns an e solved for y susung one equaon no anoer. Te wo equaons are: ( [ ] ( <IS urve> (7 μ = <L urve> One way o solve s sysem s o susue s o (7 n for n (.
3 3 (8 = ( μ Noe a s an e solved for, y rngng e erm n e (. o e lef and sde. (9 ( ( = μ Colle up e las erm on e rg and sde nvolvng o e lef and sde: ( ( μ = Dvdng o sdes y e erm n (. o oan: ( = ˆ μ γ <equlrum nome> Were ( ˆ γ Noe furer a ( ˆ ( γ γ f = Equaon ( ndaes a equlrum nome (w arses from e neraon of o e real and fnanal sdes of e eonomy s a funon of real faors (ow mu auonomous spendng ours and moneary faors (ow mu money e enral ank as prned up. Grapally, equlrum s deped n Fgure :
4 / L,, μ Slope = / ( slope = IS μ Fgure : Equlrum n IS-L 4. oly n IS-L odel Te eases way o see e mpa of poly s o ake e oal dfferenal of (: ( μ = ˆ γ <equlrum nome> ( Δ = ˆ γ Δ Δ Δμ For fsal poly, one as o deermne weer s governmen spendng a s anged, or lump sum axes. Reall ( GO. If e fsal poly nvolves only governmen spendng, en: o Δ Δ = ˆ γδgo = ˆ γ ΔGO If s lump sum axes: Δ = ˆ γ Δ Δ ˆ = γ Δ 4
5 If moneary poly s eng used, e Δ =, so: Δ ˆ Δ = γ Δ = ˆ γ Δ( / How are e effes of ese poles deped grapally? Below are fsal (governmen spendng and moneary poles, respevely. Δ / L,, μ γ ΔGO ΔGO ( IS IS Fgure : Fsal (Gov. spendng oly Noe a fsal poly mg e less powerful n e sense of nreasng nome an was n e Keynesan ross model, and wll e less powerful f = (a s, nvesmen does no depend on nome and <. I s mporan a you undersand e nuon for wy s resul ours: s eause e nroduon of a fnanal seor means a as nome rses, money demand rses (wle e money supply s fxed; rsng neres raes resul n dereased nvesmen and ne expors and ene a lower nome level relave o e ounerfaual level of. ou wll noe, f you expermen w dfferng-sloped urves, a f e IS urve s seep eause e parameers are small, en fsal poly wll e more effeve an wen s fla eause ese parameers are large. ou sould nk aou wy a s e ase. ou wll also fnd a wen e L urve s fla, e fsal poly s also more effeve an wen s seep. 5
6 Now onsder moneary poly. L,, μ L,, μ ˆ γ Δ IS A Δ Fgure 3: oneary oly oneary poly works y dereasng e neres rae, and us spurrng nvesmen. Noe a wen e L urve s seep eause s small, moneary poly wll end o e powerful an wen s large. oneary poly wll also e more powerful, e flaer e IS urve s. ou sould onsder wy ese ouomes our. In news aouns, we don see moneary poly desred as anges n e money sok. Raer, we ear e arge neres rae, Targe (n e US, e Fed Funds rae s eng rased or dropped. How does s f no e model? One way s o nerpre e Fed as angng e money supply as e IS urve sfs around o keep e neres rae a Targe. In Fgure 4 elow, wen e IS urve s a e poson onssen w auonomous spendng level, e enral anks posons e L urve o nerse e IS urve a Targe, w money supply. Wen e IS s sfed ou due o a ger level of auonomous spendng level, e enral ank nreases e money supply o, so a e IS and L urves sll nerse a Targe. Wen e IS s sfed n, e enral ank nervenes agan, pullng n e L urve. 6
7 L,, μ L,, μ L,, μ I Targe Effeve L IS IS IS Fgure 4. L and Effeve L Curve Wen e enral ank underakes s approa o moneary poly, one an nk of a orzonal effeve L urve. Te enral ank n normal mes affes oupu y droppng or rasng e arge neres rae, and erey sfng down or up e effeve L urve. Targe Targe Effeve L Effeve L IS 3 Fgure 5. oneary oly w Effeve L Curve 7
8 As e arge neres rae s lowered, nvesmen rses, erey nreasng oupu. Noe a e enral ank mg nrease e arge neres rae wen oupu rses due o exogenous sfs n e IS urve. Bu for now, we ll assume e enral ank exogenously ses e arge neres rae. 5. Te Lqudy Trap Te IS-L graps are ypally drawn n su a way a e equlrum neres rae s posve. However, n reen years e arge (sor erm neres raes ave delned o zero, and anno go furer downward (sne nomnal neres raes for e mos par anno e negave. Ts s deped n Fgure 6. L,, μ L,, μ IS Fgure 6. oneary oly n e Lqudy Trap In s suaon, equlrum nome s, and e neres rae s a. An nrease n e money supply sfs ou e L urve (o e k dased lne, u anno furer drve down e neres rae. Sne neres raes an delne, en nvesmen anno e spurred y s annel. Noe a fsal poly an nrease oupu (onsder a sf ouward of e IS urve. Hene, n s smple model, moneary poly s ompleely neffeve, wle fsal poly s que effeve. e435_isl_f.dox,4.9. 8
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