Our aim is to analyse the relationship between market structure and the effects of money of output.

Transcription

1 The assumon of nomnal rgdes s cenral o radonal Keynesan economcs, however such rgdes are no conssen wh erfec comeon. New Keynesan Economcs analyses dearures from erfec comeon ha gve rse o nomnal rgdes. Quesons addressed nclude he lausly of he reured devaons and he effecs of moneary olcy under dfferen yes of rgdy. No all dearures from erfec comeon mly ha moneary shocks have real effecs. For examle, n effcency wage models he roducvy of he workforce deends uon he level of real wages. Increasng he real wage aove he erfecly comeve eulrum level can ncrease ouu dese reducng he level of emloymen. The economy s characersed y nvolunary unemloymen u ecause wages and rces are fully flexle redcale changes n he money suly have no effec on ouu. Wha maers for he effecveness of moneary olcy s ha nomnal merfecons cause ncomlee adjusmen of nomnal rces and wages n resonse o nomnal shocks.. Marke Srucure and rce Seng Our am s o analyse he relaonsh eween marke srucure and he effecs of money of ouu. erfec Comeon and Money We defne he model and show ha under erfec comeon and Raonal Execaons money does no affec ouu. Ths s he key resul of New Classcal Macroeconomcs. Model The economy consss of very many ndvdual reresenave roducer/consumers. Each ndvdual roduce a good usng her own laor, sell her ouu n erfecly comeve markes and use he roceeds o urchase oher goods. All ndvduals are assumed o e he same, hs symmery roery grealy smlfes he model. The man argumens carry over o a more comlex seng. Indvdual Behavour & Suly The Reresenave Indvdual s he roducer of a good. The roducon funcon s, Q L () Indvdual consumon s eual o real ncome, C consumon and laor. Q. Uly s a funcon of γ L U C () γ Where γ > When he aggregae rce level s known he maxmsaon rolem s sraghforward. The key dfference eween erfec and merfec comeon s over he se of choce varales. Wh erfecly comeve markes he reresenave agen s a rce aker and maxmses uly y choosng consumon and laor. Rewrng ()

2 usng he revous wo euaons gves a maxmsaon rolem n L only. Solvng for he omal level of work yelds, Whch can e exressed n logs as, L γ (3) s l γ ( ) (4) Indvdual laor suly and roducon are ncreasng n he relave rce of he roduc. If our ndvdual only worked, hs would read ha work ncreases n he real wage. In general hs ye of ndvdual suly funcon can e raonalsed as follows: If he suler s a roducer only, hen when he real roduc rce ncreases he rce of he roducers own roduc rses relave o he rce of s nus. I follows ha he rof maxmsng level of ouu mus ncrease. Alernavely he suler can e hough of as a consumer/roducer. In hs case when he real roduc rce s hgh, ncreasng sales allows he roducer/consumer o urchase more consumon goods han f he real roduc rce was low. In hs nerreaon he roducer/consumer wll e neremorally susung from erods n whch he real roduc rce s low o hose n whch s hgh. Indvdual and Aggregae Demand The demand for good deends uon references for each good z, he relave rce for good, and he aggregae level of real ncome n he economy. d ( ) y + z η (5) Aggregae real ncome s assumed o eual he average across all goods y. Ths holds ecause of he symmery roery and he z are relave demand shocks. Smlarly he aggregae rce level s jus he average of he ndvdual rce levels,. The aggregae demand sde of he economy s ased on he smle Quany Theory Euaon MV Y. Seng velocy eual o uny, and akng logs yelds he followng aggregae demand curve, y m (6) Eulrum The eulrum reures demand er roducer euals suly er roducer so ha, s d Ths yelds, γ ( ) y + z η( )

3 γ ( y + z ) + + ηγ η (7) Aggregaon of hs euaon yelds, γ y + + ηγ η (The sum of economy wde shocks s zero and ). Ths mles ha ouu s fxed a he naural rae, whch s normalsed o uny. Hence from (6), m Ths s he famous money neuraly resul. Under erfec comeon moneary olcy has no effec on ouu ecause he rce level adjuss one for one. The real level of aggregae demand s unchanged. Ouu s deermned solely y real facors and aggregae flucuaons are eulrum resonses o real shocks as n Real Busness Cycle heory.. Imerfec Informaon -The Lucas Island Model The dearure from erfec comeon a he hear of he Lucas Island model s Imerfec nformaon. In hs model he sgnallng funcon of he marke does no work erfecly causng roducers o over (under) suly n resonse o unancaed ncreases (decreases) n he aggregae rce level. Overvew Suose ha roducers ncrease suly when he rce he roducer s own roduc s hgh relave o he aggregae rce level u crucally, nformaon regardng he aggregae rce level s merfec. In hs case he suly funcon s, Where E [ I ] Y E [ I ] s he execaon of he aggregae rce level y roducer condonal on he nformaon se avalale o roducer, I. As rses so oo does. The suler only knows and may msakenly nerre he rse n as an ncrease n he real roduc rce whereas s ar of a general nflaon. Thus unancaed nflaon can cause an ncrease n ouu. Addng Imerfec Informaon o he Model Frsly we derve he Lucas Surrse Suly Funcon, reresenng he relaonsh eween unancaed movemens n he aggregae rce level and ouu. We hen show ha only unancaed movemens n money cause unancaed movemens n he aggregae rce level and hence n ouu. The corollary of hs s ha redcale changes n money do no affec ouu. 3

4 From euaon (4) ndvdual suly s gven y, l γ ( ) If he aggregae rce level s unknown ndvdual suly ecomes, γ ( E ( I )) (8) For convenence I have used. In decdng how much o suly, he roducer forms a ror dsruon for from whch an execaon of s derved efore s oserved. The ror dsruon s ased on he nformaon se avalale o everyone. I s assumed o e normal, wh varance σ. The second source of nformaon comes from he oservaon of he rce of he roducer s own roduc. The aggregae rce level and he rce of roduc sasfy he followng relaonsh, + z (9) Ths saes ha he rce n marke euals lus a marke secfc shock z. The shock s assumed o e normally dsrued wh varance σ z. Gven hs se u ( ) E( ) E. In general, ( X + Y ) Var( X ) + Var( Y ) + Cov( X Y ) Var, If eher varale s..d, Var X + Y Var X + Var Y ( ) ( ) ( ) Assumng ha he shocks are..d he varance of s eual o he sum of he varances of he marke secfc shock and he aggregae rce level. The es esmae of he aggregae rce level s a weghed-average of he ror execaon of he aggregae rce level and he acual realsaon of. The weghs are; ( ) ( ) ( ) E I φ E I + φ (0) σ φ σ + σ () z The weghs deend on he relave varances of he shocks. σ [ ] Noce ha f 0 φ E I. Susung (0) no (8) and rearrangng yelds, z γ φ ( )( E( I ) 4

5 Aggregang over he sum of ndvdual roducers yelds he Lucas Surrse Suly Funcon. y ( E( I )) () Where, σ z γ σ + σ Noce ha he gger σ z s relave o σ z he gger are he effecs of an unancaed nflaon. Snce mos of he varaly s due o secor secfc shocks raher han general nflaon, an unancaed ncrease n he rce level s nerreed as a rse n he real roduc rce and so frms end o over-suly. Fgure : The Aggregae Suly Curve LRAS SRAS y Aggregae Demand Fgure : Aggregae demand and aggregae suly y m (3) AS AD Eulrum and he effecs of money y 5

6 To solve for he eulrum we smly se AS eual o AD. Ths yelds he followng euaon, m E I Ths mles E( m I ) E( I ) for, Usng (4) n (3) gves, ( ( )). Susung he laer no he former and solvng + + y [ m E( m I )] (4) [ m E( m I )] (5) + Thus unancaed nnovaons n he money suly ncrease oh he rce level and ouu. Ths exlans he correlaon eween money and ouu n New Classcal model. Noce ha snce only unancaed money affecs ouu hen any redcale moneary rule wll have no effec on ouu. Ths s no herefore a argumen for acve moneary olcy. Conclusons Varaons n ouu are he resul of errors. Unlke he Real Busness Cycle model hese varaons are no omal. Only unancaed money affecs ouu. Any olcy resonse ha s redcale wll lead o offseng execaons resulng n rce effecs only. The model mles only shor run varaons n ouu. I has no dynamcs as such and hus n s asc form canno exlan erssen movemens n aggregae varales. Informaon regardng he aggregae rce level s wdely and freely avalale. Exenson: The hlls Curve and Lucas Crue Le he money suly rocess e, m + c + µ m Where µ s a whe nose shock and E m m + c reresens he average rae of money growh. Sung he laer no (4) and (5) yelds, m + c + µ + y µ + Usng he frs euaon and s lag we can wre, 6

7 π ( m m ) + ( µ µ ) π c + µ + + µ c + y + µ + The second lne uses he lag of he money suly rocess. Ouu and nflaon are osvely correlaed. Ths s a hlls Curve. Ouu s only affeced y he unredcale comonen of he money suly. Wha haens f he money growh rae s rased? If he change n unknown here s a erod when µ s hgh and so affecs ouu. Bu once he ncreased rae of money growh s common knowledge unoserved money growh wll agan e zero. Snce c s hgher he sascal relaonsh eween ouu and nflaon s changed. Ths s a verson of he Lucas Crue. In economcs many esmaed emrcal relaonshs, such as he hlls curves are ased on execaons. A change n olcy ha aems o exlo he relaonsh changes execaons and he orgnal relaonsh. For examle n he revous examle we see a relaonsh eween nflaon and unemloymen. One would e emed o nfer ha we need only ncrease nflaon o rase ouu u hs s no he case. Execaons cause he relaonsh o change (shf u). The Lucas crue ales no jus o olcy u also o economc forecass. Imerfec Comeon We now exend he model o merfec comeon u assume erfec nformaon. I s assumed ha frms have rce seng ower u ha rces are se flexly. Indvdual demand s gven y (5) u wh he shock erm se o zero. Uly s as efore u now he model ncludes a comeve laor marke so ha ndvdual real ncome s, ( W ) Q + WL The rolem s o maxmse uly, whch now s, U ( ) + ( ) ( ) γ γ η γ L W Q W L L W Y + W L L C γ γ γ (6) Noe ha Q Y( ) η s he levels verson of (5) wh he shock erm se o zero. The ndvdual s now he sole roducer of hs or her roduc. Our ndvdual s a Monools wh rce Seng ower. The se of choce varales s exanded o nclude. As efore we have elmnaed consumon and so he ndvdual maxmses (6) y choosng how much o work and he rce of her roduc. The F.O.C. wh resec o yelds he followng exresson for he relave rce of he roducer s own roduc, 7

8 η W η (7) Wh marke ower he roducer ses rces as a mark-u of margnal cos. The sze of he mark-u ncreases he more nelasc s aggregae demand for he roducer s roduc. The F.O.C for laor suly yelds, W ( ) L γ (8) Laor suly s ncreasng n he real wage. The eulrum level of naonal ncome can e exressed n erms of (8). Snce all ndvduals are he same follows ha, Q L Y L Snce each ndvdual sasfes (8), Y W ( γ ) The symmery roery means each ndvdual laor marke s exacly he same as he macro marke. Thus he varale Y s eual o he common ndvdual level of ouu, u f you looked a he macro marke and relaced Y Y he real wage would sll e he same. Ths can e used o exress he real wage as a funcon of ouu. Usng hs n (7). In logs hs mles, W Y γ η Y η γ (9) (0) c + φ y () The value of φ s exremely moran. A low value of φ means ha relave rces are no very sensve o changes n aggregae demand. Ths s called real rgdy. I occurs ecause frms may no wan o aler he rces relave o oher frms for varous reasons. If φ 0 he relave rce s consan. Agan ecause of he symmery roery all roducers charge he same rce. From (0) hs means ha, Recall he roducon funcon uses only laour. The laour marke s C so he margnal cos s he real wage. You may have an urge o clam ha hs s mossle ecause he same rce s charged only under erfec comeon. However hey are no sellng he same roduc. They are sellng dfferen roducs, jus haens ha he rce elascy of demand faced y each s he same and so he mark u s he same for each and hey charge he same rce. We jus have very many monoolss sellng dfferen roducs who ehave symmercally. 8

9 η Y η γ () Ths s eulrum ouu. Usng he aggregae demand euaon n levels we fnd ha, M (3) η ( γ ) η Resuls Ouu s su-omal Under Imerfec Comeon a su-omal level of ouu s roduced. To llusrae hs s frs necessary o derve he omal level of ouu. To do hs we make use of he fac ha all ndvduals are alke. Usng euaon () and recall ha n eulrum. Then n eulrum, L Q C. We can now use he fac ha snce all ndvduals are alke o sae ha he omal allocaon s he maxmum of () n erms of L L only. Ths yelds, U L γ L 0 Ths mles ha L. However eulrum ouu gven y () s less han. The rolem s ha roducers face downward slong demand curves, raher han horzonal ndvdual curves under erfec comeon. Ths means ha he Margnal Revenue roduc of Laor s less han he Margnal roduc of Laor. The reason of course s ha as ouu rses he rce of he roduc falls, and hs mles no jus o he margnal un u o revous uns also. The exen of hs effec deends of course on he rce Elascy of Demand. Agan n eulrum, usng hs n (9) and solvng for he real wage gves, W η η And from euaon () he ML s uny. The real wage s lower han he socally omal level, so emloymen s lower and eulrum ouu s lower. From (4) ouu s lower he lower s he ED and when laor suly s more resonsve o he real wage. Tha s when η and γ are lower. A case for nervenon Snce eulrum ouu s neffcenly low hs means recessons make hngs worse whls ooms make hngs eer. Under he heory of Real Busness Cycles all flucuaons are omal. Money Neuraly Fnally as () does no nclude M, money has no effec on ouu n hs Imerfec comeon model. 9