Monopolistic competition and menu costs

Transcription

1 Chapter 18 Monopolstc competton and menu costs 18.1 The emergence of New Keynesan economcs John Maynard Keynes General Theory (1936) came out n the mdst of the Great Depresson. It was an attempt to come to grps wth ths economc catastrophe. And to fnd out polces for ts cure and preventon n the future. On the one hand Keynes book revolutonzed the way economsts thought about the economy as a whole. On the other hand, n many respects the analytcal content of the book was ncomplete. Keynes Amercan followers, such as Paul Samuelson, Lawrence Klen, Franco Modglan, Robert Solow, and James Tobn, were pragmatc and polcy-orented. Apart from ncorporatng a Phllps curve (lnkng prce changes to the level of economc actvty), they seemed satsfed wth the basc logc of Keynes theory. They vewed t as the relevant pont of departure for the study of the short run, n partcular when excess capacty and nvoluntary unemployment preval (consdered the normal state of affars). The classcal (pre-keynesan) theory, relyng on market clearng through flexble prces, was conceved applcable for the study of the long run or a state wth sustaned full employment. Ths way of reconclng Keynes and the classcs became known as the neoclasscal synthess or the neoclasscal- Keynesan synthess. We stck to the last label, snce nowadays neoclasscal usually refers to supply-determned models wth optmzng agents and flexble prces. The monetarsts, lead by Mlton Fredman, attacked the polcy actvsm of Keynesansm on the grounds of tme lags n mplementaton, uncertanty 585

2 586 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS about the relevant nterventon, or mere government ncompetence. The monetarsts shared the noton that nomnal rgdtes are of mportance for short run mechansms, although n ther vew the short run was shorter than beleved by Keynesans. Of lastng nfluence was Fredman s emphatc clam that whle there s usually a short-run trade-off between nflaton and unemployment, there s no long-run trade-off. 1 The reason s the endogenety of nflaton expectatons n the long run t s mpossble to fool ratonal people. The new classcal counter-revoluton, started by Robert Lucas, Thomas Sargent, and Nel Wallace n the early 1970s and later joned by Robert Barro and Edward Prescott, rejected Keynesan thnkng altogether and started afresh. Or rather, they revved the classcal or Walrasan lne of thnkng, emphaszng the equlbratng role of flexble prces under perfect competton not only as long-run theory, but also as short-run theory. Lucas epoch-makng contrbuton was the systematc ncorporaton of uncertanty and ratonal expectatons nto macroeconomcs. When combned wth the hypothess of market clearng by prce adjustment, ths gave rse to the polcy-neffectveness proposton clamng that systematc monetary polcy desgned to stablze the economy s doomed to falure. Regardng the explanaton of busness cycle fluctuatons, there were two dfferent strands n ths New Classcal approach. Lucas monetary mspercepton theory (Lucas 1972 and 1975) emphaszed shocks to the money supply as the prmary drvng force. In contrast, the real busness cycle theory of Kydland and Prescott (1982) and Prescott (1986) vews economc fluctuatons as prmarly caused by shocks to real factors, productvty shocks. Yet, the two strands, whch we consder n more detal n Chapter 22, were developed wthn the same type of stochastc modelng approach wth a Walrasan foundaton. Partly n response to the challenges from ths New Classcal Macroeconomcs, partly ndependently, other economsts n the 1970s and the 1980s took a dfferent lne of attack. Ther general concepton was that the Keynesan approach, when extended by some sort of an expectatons-augmented Phllps curve, performed well emprcally; money neutralty seemed a good approxmaton to the long-run ssues, but not to short-run ssues, where nstead refnements of the Keynesan theory along several dmensons were ngreatneed. Atthesametmesuchrefnements were now possble due to new analytcal tools from mcroeconomc general equlbrum theory and the ratonal expectatons methodology. We are here talkng about a qute heterogeneous group of economsts who are called New Keynesans. Ther 1 Fredman (1968). Almost smultaneously the same pont had been made by the more Keynesan orented Edmund Phelps (1967, 1968).

3 18.1. The emergence of New Keynesan economcs 587 endeavour became known as the New Keynesan reconstructon effort. Ths and the next chapters descrbe key elements n ths reconstructon. The IS-LM model and ts dfferent extensons, as presented n the two prevous chapters, consttute a convenent pont of departure. The lmtatons of the old Keynesan theory addressed by the New Keynesans can be summarzed n four ponts: (1) It s not encompassed that nomnal prces and wages do n fact change somewhat over tme n response to events n the economy. (2) It s not made clear why nomnal prces and wages change only sluggshly. (3) The underlyng mcroeconomcs s not elucdated. What are the budget constrants faced by the economc agents? How are demand and supply determned when some agents have market power and are prce setters? If markets do not clear by nstantaneous adjustment of perfectly flexble prces, how do they then clear (reach a state of balance)? What knd of general equlbrum arses under these crcumstances, takng nto account the spllovers across the dfferent markets? (4) The ntegraton of forward-lookng ratonal (unbased) expectatons nto the theory (as n chapters 16 and 17) s only halfway. Shocks are treated n a pecular (almost self-contradctory) way: they can occur, but only as a complete surprse and a once-for-all event. Agents expectatons never ncorporates that new shocks can arrve. Problem (3) was n fact taken up frst, namely by the Amercan economsts Robert Barro and Herschel Grossman (1971) and the French economsts Jean-Pascal Benassy (1975) and Edmond Malnvaud (1977). These contrbutons became known as macroeconomcs wth quantty ratonng. 2 Wth prces and wages predetermned n the short run, the short sde of the market determnes the actual amount of transactons. Ths s called the mnmum transacton rule. And wth prce-settng frms and wage-settng workers (or trade unons) facng downward-slopng demand curves, prces and wages are generally set above the margnal cost of producton and the margnal dsutlty of labor, respectvely. Thus, gven the prevalng prces and wages, frms and workers are actually happy to produce and sell more than expected. In ths way aggregate output tends to be demand-determned. At the same tme the consumpton demand by workers depends not only on wages, prces, and 2 Barro later shfted to the new classcal camp. Hs reasons are gven n Barro (1979).

4 588 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS ntal resources, as n the Walrasan mcroeconomc theory, but also on how much of ther labor supply actually gets employed. In ths way also quantty sgnals play a role and n contrast to the Walrasan demand functon we get a so-called effectve demand functon. In the frst wave of macroeconomcs wth quantty ratonng wages and prces were treated as exogenous, whch s of course not satsfactory. But a path-breakng paper on general equlbrum wth monopolstc competton by Blanchard and Kyotak (1987) made t possble to ntegrate the quantty ratonng framework wth prce settng behavor. At about the same tme Akerlof and Yellen (1985) and Mankw (1985) developed the menu cost theory. Sluggshness n prce adjustment caused by small menu costs can at the aggregate level have large real effects. Ths became an mportant element n the new Keynesan theory of nomnal rgdtes. These developments, whch address problem (2) and (3), are the topc of ths chapter. Later chapters gve an account of how modern macroeconomcs has dealt wth the dynamc ssues, (1) and (4). The reader who does not want to be too nvolved n mcroeconomc foundatons may n a frst readng of ths chapter glance over the rather long Secton Ths wll allow concentraton on the subsequent sectons on dfferenttypesofgeneralequlbrum,themenucosttheory,thenterplayof nomnal and real rgdtes, and the macroeconomc mplcatons The Blanchard-Kyotak model of monopolstc competton In the Keynesan tradton employment and output fluctuatons are vewed as prmarly demand-drven n the short run. The nomnal rgdtes that consttute the bass for ths vew are smply assumed. The new Keynesans havebultaseresofmodelswhchattempttoclarfythecausesandthe effects of nomnal wage and prce rgdtes. To understand what determnes prces and ther movement over tme, we need a theory wth agents that set prces and decde when to change them and by how much. Ths brngs agents wth market power nto the pcture. 3 That s why mperfect competton s a key ngredent n new Keynesan economcs. The challenge s, frst, to explan the behavor of prce-settng supplers on the bass of ther objectves and constrants. Second, clarfyng the nterac- 3 Under perfect competton, nobody sets prces. (Ths s n fact a sgn of a logcal dffculty wthn perfect competton theory. To assgn the prce settng role to abstract market forces or an abstract omnpotent Walrasan auctoneer s not of much help.)

5 18.2. The Blanchard-Kyotak model of monopolstc competton 589 ton between the prce-settng agents and the spllovers across markets wll be a necessary step n the constructon of a theory of the functonng of the economy as a whole. The general equlbrum model wth monopolstc competton by Blanchard and Kyotak (1987) addresses these problems. The model has become one of the cornerstones of new Keynesan thnkng. In contrast to the IS-LM model of chapters 16 and 17, the Blanchard-Kyotak (henceforth B-K) model pays attenton to the supply sde no less than the demand sde. Before gong to the specfcs of the B-K model, let us make clear what s generally meant by monopolstc competton The concept of monopolstc competton Monopolstc competton s a market structure wth the followng propertes: 1. Theresagven,largenumberoffrms and equally many (horzontally) dfferentated goods. 2. Each frm supples ts own good on whch t has a monopoly and whch s an mperfect substtute for the other goods. 3. A prce change by one frm has only a neglgble effect on the demand faced by any other frm. Another way of statng property 3 s to say that frms are small so that each good consttutes only a small fracton of the sales n the overall market system. Each frm, facng a downward-slopng demand curve, chooses a prce whch maxmzes the frm s profts, and then the frm adjusts output to the demand at that prce. Or equvalently, facng a downward-slopng demand curve, each frm chooses an output level whch maxmzes the frm s profts and then the frm sets ts prce accordngly. There s no elaborate strategc nteracton between the frms, and n that respect monopolstc competton s dfferent from olgopoly. Sometmes a fourth property s ncluded n the defnton of monopolstc competton, namely that each frm makes no proft. The nterpretaton s that there s a large set of as yet unexploted possble dfferentated goods, and that there s free entry and ext. But n the B-K model entry and ext are consdered to be costly and tme consumng. In the short run the number of actve frms s thus gven. We therefore make a dstncton between on the one hand short-run equlbrum, here just called equlbrum, and long-run equlbrum under monopolstc competton.

6 590 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS A(short-run)equlbrum under monopolstc competton s defned as a set of prces and quanttes such that: supply equals demand, and each frm s proft s maxmzed, gven the frm s downward-slopng demand curve and gven the other frms prces. Long-run equlbrum refers to a state of affars where, through entry and ext, all profts have been drven to zero. In the B-K model, the monopolstc competton framework s appled not only to frms, but also to households labor supply. Each household s consdered to be a wage settng suppler of ts own specfc typeoflabor, whch s an mperfect substtute to other households types of labor. Overvew ThenextsectonsgontodetalwththeB-Kmodelandtsmanconclusons. Both labor and goods markets are monopolstcally compettve. Thus, both workers and frms have market power and face downward-slopng demand curves on the bass of whch they make ther prcng decsons. It may help the ntuton to thnk of the households as organzed n many small craft unons rather than as ndvdual workers. In any case, n equlbrum each labor suppler sells a bt of hs (her) labor to many frms. 4 To clear the ground, we frst consder the case where there are no forces that nduce nomnal wage and prce stckness. That s, no wage and prce adjustment costs are present. In ths case, called the flexble prce case, n spte of monopolstc competton, money s neutral. But n contrast to perfect competton, monopolstc competton leads to a Pareto-nferor general equlbrum wth underutlzaton of resources. Ths s a smple consequence of the supply behavor of solated optmzng agents wth market power. Next, prce adjustment costs are added. These costs may lead prce setters to abstan from adjustng ther prce when demand changes. In ths setup money s not neutral. Itturnsoutthatevensmalladjustmentcostscanhave large real consequences at the aggregate level The agents behavor There are m frms, =1,..., m, and m goods, one for each frm. The goods are mperfect substtutes (thnk of dfferent knds or brands of cars, beers, 4 Thus, monopsony s absent.

7 18.2. The Blanchard-Kyotak model of monopolstc competton 591 toothpaste etc.). Further, there are n households (or craft unons), j = 1,..., n, each supplyng ts specfc typeoflabor. Thesen types of labor are mperfect substtutes as nputs n the frms producton. Money s the only fnancal asset and s the numerare. The model s essentally statc n that only one perod s consdered and there are no explct ntertemporal consderatons. The reason that money s demanded s not made explct. Dfferent nterpretatons of are possble. Money holdng just appearsasanargumentntheutltyfuncton. Thsmayreflectthatmoney holdng yelds lqudty servces or that there s an mplct savng motve. There s no prvate bankng sector. There are many frms and many households (m and n are large). The two basc decson problems The decson problem of frm s to choose a vector (P,Y, (N j ) n j=1), where P s prce, Y s output and N j s labor nput of type j, j =1, 2,..., n, so as to maxmze V = P Y nx W j N j s.t. (18.1) j=1 Y = Y d (P,...), (18.2) Ã nx! σ 1 σ 1 α Y =, (18.3) j=1 N σ 1 σ j where Y d (P,...) s the demand functon faced by the frm and the rghthand sde of (18.3) s the producton functon. 5 The parameters descrbng the producton functon satsfy the nequaltes σ>1, α 1. The parameter σ s the constant elastcty of substtuton between the dfferent types of labor nput, and α sthedegreeofdecreasng returns to labor. When α > 1, there are decreasng returns and when α =1, constant returns. Other nputs than labor are not consdered. The decson problem of household j s to choose a vector ((C j ) m =1,Mj,W 0 j,n j ), where C j s consumpton of good, =1, 2,..., m, Mj 0 s money holdng, W j 5 After havng solved at least part of the households decson problem below we shall be able to specfy the demand functon Y d (P,...).

8 592 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS s wage rate and N j s labor supply, so as to maxmze à m! γ X U j = m 1 1 C 1 1 j ( M j 0 P )1 γ N β j =1 s.t.(18.4) N j = Nj d (W j,...) (18.5) mx mx P C j + Mj 0 = M j + W j N j + V j I j, (18.6) =1 where Nj d (W j,...) s the labor demand functon faced by household j,(18.6)s thebudgetconstrantwthi j denotng total wealth of the household, consstng of the ntal endowment of money, M j, labor ncome, W j N j, and profts, V j, from frm, =1, 2,...,m. 6 The parameters descrbng the preferences satsfy the followng nequaltes: 0 <γ<1, > 1,β 1. The parameter s the constant elastcty of substtuton between the dfferent consumpton goods, the parameter γ ndcates the relatve weght of consumpton vs-a-vs money holdng n the utlty functon. The coeffcent m 1/(1 ) n (18.4) just reflects a convenent normalzaton. The parameter β s 1+ elastcty of margnal dsutlty of work. When β>1, there s ncreasng margnal dsutlty of work. The symbol P denotes the deal consumer prce ndex correspondng to household j s preferences. Snce the relevant sub-utlty functon, nvolvng the m consumpton goods and money, s homogeneous of degree 1, such an ndex exsts. The ndex s some functon ϕ(p 1,..., P m ) of the prces of the consumpton goods. Ths functon (to be determned below) s closely related to a certan Lagrange multpler and wll depend on the parameters n the utlty functon. For now t suffces to note that P wll be a knd of average of the actual prces the general prce level. Solvng the problem of household j It s convenent to defne a consumpton utlty ndex C j by C j m à m 1 m X =1! C 1 1 j =1 = m 1 1 à m X =1! C 1 1 j. (18.7) Such an ndex s called a CES ndex (CES stands for Constant Elastcty of Substtuton). The ndex s normalzed such that f the consumpton basket 6 After havng solved at least part of the frms decson problem below, we shall be able to specfy the labor demand functon N d j (W j,...).

9 18.2. The Blanchard-Kyotak model of monopolstc competton 593 contans equally much of each good,.e., C j = C j,= 1, 2,..., m, then consumpton utlty s C j = m C j. A handy way of solvng household j s decson problem s to dvde the soluton procedure nto three steps. In the frst step the choce between consumpton expendture and carryng money over to the next perod s made. In the second step t s decded how to dvde the consumpton budget between the dfferent consumpton goods. And n the thrd step a decson on the supply of labor and the wage rate to clam. As a preparaton for step 1, let B j be the consumpton budget of household j,.e., mx B j P C j. (18.8) =1 Then, by defnton of an deal consumer prce ndex P, cf. Box 1, n the optmal plan we must have PC j = B j. (18.9) Box 1. An deal prce ndex Let the prce vector (P 0 1,...,P0 m) be such that P 0 = ϕ(p 0 1,...,P0 m)=1so that P 0 Cj 0 = C 0 j= P m =1 P 0 Cj= 0 B 0 j,where(c0 1j,...,C0 mj) s the demand vector, gven (P 0 1,...,P0 m) and the budget Bj 0. Then, magne that some of the prces change and the new prce vector s (P 1,...,P m ).Bydefnton, the deal prce ndex s the mnmum factor by whch the orgnal budget, here Bj 0, must be multpled f the consumer s to be fully compensated for the prce change,.e., the deal prce ndex equals the compensatng budget multpler. Hence, f the new value of the deal prce ndex s P = ϕ(p 1,..., P m ), then a new budget equal to B j = PB 0 j= PC 0 j leaves the consumer as happy as before. The CES utlty functon (18.7) s homogeneous of degree 1 n C 1j,..., C mj, reflectng that preferences are homothetc. That s, gven the prce vector (P 1,...,P m ), the correspondng demand vector (C 1j,...,C mj ) s proportonal to the consumpton budget B j. It s ths property that wll allow the constructon of a meanngful prce ndex, P = ϕ(p 1,...,P m ), ndcatng the mnmum expense per unt of consumpton utlty, gven the prces P 1,..., P m. 7 If there were > n (18.9), then the consumer has got hgher utlty than she can afford wthn the budget B j, whch s mpossble; and f there were < n (18.9), then the consumer could ncrease utlty wthn the gven budget B j. Step 1 (j) :Choosng between B j and M 0 j (consumpton versus holdng money). 7 Because of the homogenety of degree 1 of the CES utlty functon, t can be seen as an ndcator of utlty as well as quantty.

10 594 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS Consder the sub-utlty functon Ũj C γ j (M j/p 0 ) 1 γ =(B j /P ) γ (Mj/P 0 ) 1 γ = B γ j M 01 γ j /P and the problem: gven the wealth I j, choose B j to maxmze Ũ j s.t. B j +Mj 0 = I j. After nsertng the constrant and takng logs (assumng an nteror soluton), we solve the equvalent problem: FOC: whch mples and, from B j + M 0 j = I j, max B j f Ũj = γ ln B j +(1 γ)ln(i j B j ) ln P. dũ f j = γ 1 1 +(1 γ) =0, db j B j I j B j B j = PC j = γi j M 0 j =(1 γ)i j. It follows that the ndrect utlty functon for consumpton and money holdng can be wrtten Λ j = B γ j M 01 γ j /P =(γi j ) γ [(1 γ)i j ] 1 γ /P μi j /P, (18.10) where μ denotes the constant margnal utlty of wealth, μ γ γ (1 γ) 1 γ ). Step 2 (j) :Choosng C j,=1, 2,..., m (the consumpton bundle), gven the consumpton budget. Gven B j, max C j = m 1 1 C 1j,...,C mj mx P C j = B j. =1 Ã m X =1! C 1 1 j s.t. For solvng ths problem, we shall apply the Lagrange method because t delvers a Lagrange multpler whch has a useful economc nterpretaton. We ntroduce the Lagrangan L = C j λ( where λ s the Lagrange multpler. mx P C j B j ), =1

11 18.2. The Blanchard-Kyotak model of monopolstc competton 595 FOCs: L/ C j =0, =1, 2,..., m,.e., From the defnton of C j we have C j C j = m 1 1 = m 1 1 C j C j = λp, =1, 2,...,m. (*) Ã X m 1 0 =1 Ã X m 0 =1 = m 1 Cj 1 m 1 1 C 1 0 j! C 1 0 j 1 1 1! 1 1 C 1 j = m C 1 j (from (18.7)) = λp (from (*)) so that from m 1 C j C m 1 j 1 = m 1 C j 1 C j 1 C j 1 Ã X m 0 =1! C j follows m 1 C j =(λp ), C j or C j =(λp ) C j, =1, 2,...,m. (18.11) m Snce we consder maxmzaton andthelagrangefunctonl s concave, the frst-order condtons (18.11) are both necessary and suffcent condtons forannteroroptmum. We see from (18.11) that 1 C 1 j µ C j P = = C hj P h µ Ph That s, s the elastcty of substtuton between goods and h. Interestngly, the Lagrange multpler λ s closely related to the consumer prce ndex P. Indeed: P. Clam 1. λ =1/P.

12 596 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS Proof. Multply by C j n (*) to get C j C j = λp C j C j mx C j mx C j = λ P C j C j =1 C j = λ =1 mx P C j =1 = λb j (from (18.8)) = λp C j (from (18.9)). Hence, snce C j > 0,λ=1/P. (from Euler s theorem on homogenous functons) Note that n vew of Clam 1, we can wrte (18.11) as C j = µ P P C j, =1, 2,..., m. (18.12) m In ths expresson the factor C j represents total real spendng on consumpton by household j and thus the factor C j /m represents average real spendng per consumpton good. Ths wll equal the actual demand for each good f the m prces are the same. But f for example P <P,we get C j >C j /m so that consumpton of good exceeds average consumpton per good. But how s the prce ndex, P, determned? Clam 2. Ã 1 mx P = m =1 Proof. From (18.9), (18.8) and (18.12), P 1! 1 1. (18.13) PC j = B j = P = P 1 = 1 m mx P C j = =1 µ 1 X m P =1 mx P 1, =1 P 1 mx =1 1 m µ P C j P P m

13 18.2. The Blanchard-Kyotak model of monopolstc competton 597 from whch follows (18.13). Note that the prce ndex n (18.13) s a knd average of the m prces n the sense that t s homogeneous of degree 1 and has the property that f P = P for all, then P = P. Makng use of the ndrect utlty functon Λ j n (18.10), we are now ready to set foot on the thrd step, the decson on the wage rate and the supply of labor gven the labor demand functon Nj d (W j,...). However, ths decson problem s not well-defned untl we have specfed the labor demand functon. Ths requres that we frst turn to the frms behavor. Solvng the problem of frm It s convenent to defne an effectve labor nput ndex L symmetrcally to the consumpton utlty ndex C j above: L n à n 1 nx j=1! σ N σ 1 σ 1 σ j = n 1 1 σ à nx j=1! σ N σ 1 σ 1 σ j. (18.14) If N j = N for all j, then the defnton mples L = n N. The producton functon (18.3) can now be wrtten Y =(n 1 σ 1 L ) 1 α. (18.15) A convenent way of solvng frm s decson problem, see (18.1) - (18.3), s to dvde the soluton procedure nto three steps that are n prncple symmetrc wth the three steps for the household. In the frst step we fnd the requred effectve labor nput, gven the desred level of output. In the second step t s decded how many unts of the dfferent types of labor to use n order to make up the desred effectve labor nput. And n the thrd step the prce and output supply are decded. Step 1 () :Fndng the effectve labor nput, L, requred to obtan a gven output level, Y. Gven Y, fnd the requred effectve labor nput L. From (18.15) we get the soluton L = n 1 1 σ Y α. (**) Step 2 () :Choosng N j,j=1, 2,..., n (the labor type mx), gven the desred effectve labor nput L.

14 598 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS Gvenadesredeffectve labor nput L = L, frm solves the problem: mn (N j ) n j=1 n 1 1 σ à nx j=1 nx W j N j j=1! σ N σ 1 σ 1 σ j s.t. = L. Agan, for solvng such a problem, the Lagrange method s convenent because t delvers a Lagrange multpler whch has a useful economc nterpretaton. Therefore, we ntroduce the Lagrangan L = nx W j N j η j=1 n 1 1 σ à nx j=1! σ N σ 1 σ 1 σ j L, where η sthelagrangemultpler.focs: L/ N j =0, j =1, 2,..., n,.e., W j = η L, N j j =1, 2,..., n. (***) From the defnton of L we have L = n 1 σ 1 σ N j σ 1 so that from follows or = n 1 1 σ à nx j 0 =1 à nx j 0 =1 N σ 1 σ j 0! σ σ 1 1 σ 1 σ! 1 N σ 1 σ 1 σ j N 1 0 σ j = n 1 1 σ N j à nx 1 = n 1 L σ 1 1 σ N σ n 1 j (from (18.14)) 1 σ = W j, (from (***)) η n σ 1 σ L N n 1 j 1 = n 1 L 1 σ N j n 1 L N j =( W j η )σ, σ 1 σ 1 j 0 =1! σ N σ 1 σ 1 σ j 0 1 σ N 1 σ j N j =( W j L η ) σ, j =1, 2,..., n. (18.16) n

15 18.2. The Blanchard-Kyotak model of monopolstc competton 599 Snce we consder a mnmzaton problem and the Lagrange functon L s convex, the frst-order condtons (18.16) are both necessary and suffcent condtons for an nteror optmum. We see from (18.16) that N j N k = µ Wj W k σ = µ Wk W j σ. That s, σ s the elastcty of substtuton between labor types j and k. Let W denote the deal wage level ndex,.e., the mnmum cost per unt of effectve labor. Then, n the optmal plan, WL = nx W j N j. j=1 By the same method of proof as wth Clam 1 and 2, t s easy to show that η = W =( 1 nx Wj 1 σ ) 1 1 σ. (18.17) n Now, (18.16) can be wrtten j=1 N j = = σ L W n µ Wj µ Wj W σ n σ 1 σ Y α, j =1, 2,..., n. (18.18) by (**). In the expresson (18.18) the factor L represents total effectve employment n frm and thus L /n s average employment per labor type. Ths wll be the actual employment of each labor type f they demand the same wage. But f for nstance W j < W, we get N j > L /n. That s, employment n frm of labor type j wll exceed average employment per labor type. Note that the deal wage level ndex and the labor demand functon are symmetrc to the consumer prce ndex and the consumpton demand functons, respectvely, found above. 8 8 In step 2 for the household, we maxmzed utlty for a gven budget, whle n step 2forthefrm, we mnmzed costs for a gven output level. Therefore, n the frst case we got λ =1/P, whle n the second case we got η = W. In fact, also n the household s problem one could formulate step 2 as a mnmzaton problem, namely that of mnmzng consumpton expendture, P m =1 P C j, for a gven utlty level C j. The correspondng Lagrange multpler, say λ 0, would satsfy λ 0 = P.

16 600 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS We are now ready to look at frm s thrd step: Step 3() :Settng the prce P and the supply of output Y. The problem s: max V = P Y WL s.t. P,Y nx µ Y = Y d P γ P n j=1 = C j = I j, P mp j=1 L = n 1 1 σ Y α, (**) that s, maxmze profts subject to the demand functon (from (18.12) and step 1(j)) and the nverse of the producton functon. For ths decson problem t s mportant that m s large so that the effect of P on the average prce level P s neglgble. Before solvng the problem t s convenent to ntroduce the dependence of demand on natonal ncome. We defne (as usual for a closed economy) natonal ncome, Y, as aggregate value added n real terms,.e., Y = P m =1 P P m Y =1 = P ( P n j=1 C P m P n j) =1 j=1 = P C j P P P n P m j=1 =1 P P n C j j=1 = B j = γ P n j=1 I j, (18.19) P P P where the last equalty comes from the soluton for B j n step 1(j). By settng Y = P n J=1 C j, =1,...,m, we have here assumed equlbrum n the goods markets. In vew of (18.19), the demand functon faced by frm can be wrtten µ Y = Y d P Y = P m. (18.20) We are now ready to solve the supply and prce settng problem of frm. Let P (Y ) denote the maxmum prce at whch output Y can be sold; ths P (Y ) s gven as the nverse of the demand functon (18.20). Now, after nsertng ths and (**) nto the objectve functon of frm, the problem s: max V = P (Y )Y Wn 1 1 σ Y α = TR TC, Y where TR s total revenue and TC s total cost.

17 18.2. The Blanchard-Kyotak model of monopolstc competton 601 FOC: dv dp = P + Y Wn 1 1 σ αy α 1 = MR MC =0. Now, dy dy MR = P (1 + Y dp dy )=P (1 + 1 P P dy )=P (1 1 ) Y dp = MC P = (by (A5)) MC. (18.21) 1 Ths s the standard prcng prncple from monopoly theory: the proft maxmzng prce s a mark-up on margnal cost. The mark-up s hgher, the lower s the substtutablty between the consumpton goods as measured by. We have assumed >1 because otherwse no equlbrum wth prce setters can exst. When α>1, there are decreasng returns to labor, hence, MC s tself endogenous: MC = Wn 1 1 σ αy α 1 = Wn 1 1 σ α " µp P # α 1 Y (from (18.20)). m Insertng nto (18.21), dvdng through by P, and solvng for P /P gves P P = " 1 µ # 1 α 1 1+(α 1) W P n 1 1 σ Y α, =1,..., m. (18.22) m Ths s the prce rule for frm. It reflects that a hgher W mples a hgher MC, whch mples a hgher optmal prce, gven the constant markup, /( 1), cf. Fg Smlarly, an ncrease n the general prce level P mproves the compettve poston of frm. Ths nvtes an ncrease n P but notallthewayupfα>1. Thats,P /P falls, because part of the mproved compettve poston s taken out as hgher supply of output. 9 Fnally, an ncrease n natonal ncome Y mples, ceters parbus, an outward shft n the demand curve faced by the frm; satsfyng the hgher demand mples hgher MC (when α>1), hence, hgher P, gven the constant mark-up. Hereby, we have fnshed the soluton of frm s problem. We are now ready to solve the thrd step n household j s problem. h 9 W To see ths notce that, from (18.22), P = P 1 P n 1 1 σ α Y α (α 1) m, so that 1 the exponent on P on the rght hand sde s 1 1+(α 1) (0, 1), when α>1.

18 602 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS Fgure 18.1: markup. The relatonshp between elastcty of substtuton and frms Back to the household decson on labor supply and wage clam The problem for household j (j =1,...,n) s: max U j = μ I j W j,n j P N β j s.t. mx µ σ P m N j = Nj d Wj =1 = N j = L µ σ Wj N = W n W n,(18.23) =1 mx I j = M j + W j N j + V j, (****) =1 where μ s the margnal utlty of wealth, cf. (18.10). At the rght-hand sde of the constrant (****) only the term W j N j s endogenous. The constrant (18.23) comes from (18.18) and our defnton of aggregate labor demand, N : P n j=1 N W P jnj d n j=1 = W j( P m =1 N P n P m j) j=1 =1 = W jn j P W W W m P n =1 j=1 = W P m jn j =1 = WL mx = L. W W By settng N d j = P m =1 N j, j=1,...,n,we have here assumed equlbrum n the labor markets. The second last equalty holds, n vew of the defnton of L and W, when frms optmze. For ths decson problem t s mportant that n s large so that the effect of W j on the average wage rate W s neglgble. Step 3(j) :Settng W j and N j (the wage clam and the supply of labor). =1

19 18.2. The Blanchard-Kyotak model of monopolstc competton 603 To solve the problem above, let W j (N j ) denote the maxmum wage rate at whch the labor supply N j can be sold; ths W j (N j ) s gven as the nverse of the demand constrant (18.23). Now, after nsertng ths and the constrant (****) nto the objectve functon of household j, the problem s: max U j = μ W j(n j )N j + constant N β j N j P = TR TC, where TR s total revenue of labor and TC s total cost, both n utlty terms. We may call TC total dsutlty of labor. FOC: du j = μ dn j P (W dw j j + N j ) βn β 1 j = MR MC = MR MDL =0, dn j where MDL denotes margnal dsutlty of labor. We have MR = μ P W j(1 + N dw j j dn j )= μ W j P W j(1 + 1 W j dn j )= μ P W j(1 1 ) σ N j dw j (by (8 )) = MDL W j = σ P MDL. σ 1 μ (18.24) Ths s the standard wage settng prncple for a monopolst suppler of labor: the utlty maxmzng wage rate s a mark-up, σ/(σ 1), on margnal dsutlty of labor. The markup s hgher, the lower s the substtutablty between the dfferent types of labor as measured by σ. We have assumed σ>1 because otherwse equlbrum wth wage setters cannot exst. When β>1, MDLtself s endogenously ncreasng n labor supply: MDL = βn β 1 j = β " µwj W # σ β 1 N (by (18.23)). n Insertng nto (W j ), dvdng through by W, and solvng for W j /W gves " W j W = σ P σ 1 W β μ µ # 1 β 1 1+σ(β 1) N, j =1,..., n. (18.25) n Ths s the wage rule for labor of type j. Itreflects that a hgher P makes consumpton more expensve, whch mples substtuton towards more lesure,.e., less labor supply, so that a hgher wage rate W j can be clamed. Smlarly, an ncrease n the general wage level W mproves the compettve poston of

20 604 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS household or craft unon j. Ths nvtes an ncrease n W j but not all the way up f β>1. Thats,W j /W falls, because part of the mproved compettve poston s taken out as hgher supply of labor. 10 Fnally,anncreasenaggregate demand for labor, N, mples, everythng else equal, an outward shft n the demand curve faced by the household; to satsfy the hgher demand, ahghermdl must be accepted (when β>1) and to compensate for ths, gven the constant mark-up, a hgher W j s demanded. Hereby, we have fnshed the analyss of the decson problems of the agents General equlbrum wth flexble wages and prces A general equlbrum wth flexble prces and wages s a prce-wage vector (P 1,..., P m,w 1,..., W n ) and a quantty vector (Y 1,...,Y m,n 1,..., N n ) such that (a) the prce and wage rules are followed and (b) demand equals supply on all markets. We shall call such an equlbrum a flex prce-flex wage equlbrum. As we shall see, n a flex prce-flex wage equlbrum money s neutral. Later we wll see that f prce adjustment costs are operatve on both output and labor markets, then, when a change n aggregate nomnal demand occurs (brought forth by a change n the money supply), the prce and wage rules are suspended. As long as margnal cost s below the prce and margnal dsutlty of labor (measured n equvalent money unts) s below the wage, output and employment respond to changes n aggregate nomnal demand, whle prces and wages are kept unchanged. Ths knd of equlbrum wll be called a fx prce-fx wage equlbrum. It has many features n common wth smple Keynesan models. But back to the flex prce-flex wage case. The flex prce-flex wage equlbrum Aggregate demand for money can be wrtten M 0 nx Mj 0 =(1 γ) j=1 nx j=1 I j = 1 γ PY, (18.26) γ from step 1(j) and equlbrum n the goods markets, (18.19). When we also take equlbrum n the labor markets together wth the budget constrants h 10 σ P β To see ths notce that, from (18.25), W j = W N β σ(β 1) σ 1 W μ n, so that the 1 exponent on W on the rght hand sde s 1 1+σ(β 1) (0, 1), when β>1.

21 18.3. General equlbrum wth flexble wages and prces 605 (****) nto account, we fnd that M 0 must equal the aggregate supply of money, whch s P n j=1 M j, that s, M 0 = nx M j M. (18.27) j=1 Ths reflects Walras law: equlbrum n the goods and labor markets, together wth the budget constrants, mply equlbrum n the last market, the money market. We use ctaton marks because n ths model money s the only asset and so the correspondng market has very lmted smlarty wth the money market n a setup where money s traded for other other fnancal assets. Substtutng (18.27) nto (18.26), we see that P = γ M 1 γ Y. (18.28) Ths tells us that n general equlbrum the varables P and Y are lnked n averysmpleway.itremanstofnd the soluton for Y. In the absence of prce adjustment costs, prces and wages are flexble and follow the prce rule and wage rule, respectvely. Snce all frms have the same prce rule, (18.22), they all set the same prce, say P. Then P = P for all. Hence, also the prce ndex P equals P, n vew of (18.13). Usng P /P =1for all n (18.22), we can solve for P/W to get P W = 1 n 1 1 σ αm 1 α Y α 1. (18.29) Ths s the aggregate prce rule, whch gves the prce-wage rato consstent wth frms prcng and producton decson. By nvertng and takng logs n (18.29), we get the downward-slopng sold lne wth slope 1 a 1 n Fg A hgher level of aggregate output s assocated wth hgher MC = W/( Y/ N) because of a lower margnal product of labor. Gven the mark-up, ths leads to a hgher prce-wage rato and a lower W/P. In the lmtng case of α =1, the aggregate prce rule s represented by a horzontal lne. The analogue aggregate wage rule can also be formulated as a relaton between W/P and aggregate ncome Y, snce there s a lnk between aggregate

22 606 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS labor demand and aggregate ncome (output). Indeed, we have N = mx =1 = n 1 1 σ L = n 1 1 σ =1 mx =1 Y α (by (**)) " mx µp # α Y (by (18.20)) P m = n 1 1 σ m µ Y m α (snce, n vew of symmetry between the frms, P = P, ) = n 1 1 σ m 1 α Y α. (18.30) Insertng nto (18.25) gves W j σ W = σ 1 P W β α(β 1) 1 μ n σ 1 σ (β 1) m (1 α)(β 1) 1+σ(β 1) Y, (18.31) for j =1,..., n. Now, snce all households have the same wage rule (11), they all set the same wage, say W. Then W j = W for all j. Hence, also the average wage, W, s equal to W, n vew of (18.17). Usng W j /W =1for all j n (18.31) we can solve for W/P to get W P = σ β σ 1 μ n σ 1 σ (β 1) m (1 α)(β 1) Y α(β 1). (18.32) Ths s the aggregate wage rule, whch gves the real wage consstent wth households wage settng and labor supply decson. By takng logs n (18.32) we get the upward-slopng sold lne wth slope (β 1)/a n Fg A hgher level of aggregate output requres hgher employment and therefore hgher margnal dsutlty of labor and, gven the mark-up, ths leads to a hgher real wage. In the lmtng case of β =1(.e. perfectly elastc labor supply), the aggregate wage rule s represented by a horzontal lne. Invertng (18.29) and usng (18.32) gves the equlbrum level of aggregate output, 1 Y = 1 σ 1 σ (K pk w ) 1 αβ 1 for a>1 or β>1, (18.33) where K p n 1 1 σ αm 1 α and K w β μ n σ 1 σ (β 1) m (1 α)(β 1). Insertng ths nto (18.32) and (18.28), respectvely, gves the equlbrum real wage W P =( σ σ 1 ) α 1 αβ 1 K α 1 αβ 1 w ( 1 K p 1 ) α(β 1) αβ 1,

23 18.3. General equlbrum wth flexble wages and prces 607 and the equlbrum prce level P = γ γ M σ 1 σ (K pk w ) 1 αβ 1. A unque equlbrum exsts f ether β>1or α>1 (a <1). In case β = a =1, generally no equlbrum exsts because frms markup clams are ncompatble wth households wage clams. 11 Unless otherwse ndcated, we wll from now assume α 1, but β>1, so that there s a unque flex prce-flex wage equlbrum. Results We see that n the absence of prce adjustment costs the model has the classcal features: The real varables (output and the real wage) are determned by technology and preferences ndependently of the supply of money. The prce level s proportonal to the supply of money. In short: n the flex prce-flex wage equlbrum money s neutral. Yet, we see from Fg. 18.2, comparng wth the correspondng equlbrum under perfect competton, that monopolstc competton leads to underutlzaton of resources. Theeffectofmarketpowerstomovetheeconomyfrompont A 0 n Fg to pont A. The reason s that market power gves an ncentve to wthhold supply. The underutlzaton of resources shows up as underemployment (labor s the only nput). In any case, the degree of underutlzaton can be large. Indeed, under perfect competton n goods and labor markets frms and households are prce takers. By elmnatng the markup factors /( 1) and σ/(σ 1) from (18.33) we fnd the correspondng aggregate output level to be Y pc =(K p K w ) 1/(αβ 1). Hence the dstorton measured n forgone output s µ 1/(αβ 1) Y σ = < 1. Y pc 1 σ 1 We see that the Y/Y pc rato s an decreasng functon of the market power of frms, as measured by the markup /( 1), as well as of workers, as measured 11 In the knfe edge case ( 1) 1 n 1/(1 σ) = σμ 1 /(σ 1) there exst nfntely many equlbra. Indedd, for W/P = σμ 1 /(σ 1) the (Y,W/P) wll be an equlbrum for any Y>0.

24 608 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS log W P Prce rule Wage rule } log σ > 0 σ 1 A A } log > 0 1 logy mc logy pc log Y Fgure 18.2: Monopolstc competton equlbrum and perfect competton equlbrum compared (the case α>1, β>1). by the markup σ/(σ 1). The hgher these markups are, the hgher the degree of underemployment. But whereas the real wage s lowered by ncreased market power of frms, t s rased by ncreased market power of workers. Therefore, gong from perfect competton to monopolstc competton n all markets has an ambguous effect on the equlbrum real wage. Sometmes a smplfed verson of the B-K model s used, where monopolstc competton rules only n the goods markets, whereas there s perfect competton n the labor market and usually only one type of labor. Then the stppled wage-rule curve n Fg becomes a labor supply and as long as t s not vertcal (nelastc labor supply), the underutlzaton-of-resources concluson agan comes true. Ths s because frms wll stll set prces wth a mark-up. But wthout the addtonal monopolstc behavor on labor markets, the degree of underutlzaton wll be less. 12 The underutlzaton-of-resources pont can also be llustrated as n Fg. 18.3, whch depcts equlbrum from the perspectve of product lne. For fxed M and P = P mc ( mc for monopolstc competton), the demand curve faced by frm s shown as the downward-slopng sold curve D(P /P, M/P mc ) to whch corresponds the margnal revenue curve, MR. For fxed P and W, 12 An analogue concluson would appear n a model wth only monopolstc competton n the labor markets. In any case, when t comes to the ncorporaton of menu costs, a model wth monopolstc competton n both goods and labor markets works best (see below).

25 18.3. General equlbrum wth flexble wages and prces 609 P P MC 1 A B C MR P M D, P P pc D P M, P P mc 0 mc pc Y Y Y Fgure 18.3: Equlbrum from the perspectve of product lne. the margnal costs faced by frm s shown as the upward-slopng margnal cost curve, MC (notethatbothmr and MC are measured n real terms,.e., relatve to the general prce level P ). All prces and wages are set optmally n accordance wth the rules derved above. Hence, MR = MC and P /P =1. Under perfect competton, however, frms produce up to the pont C, where margnal costs equal prce. Thus Y wll be hgher. Ths results n a lower general prce level P pc ( pc for perfect competton), cf. (18.28), and s reflected n a hgher real money supply. To ths corresponds the dashed demand curve n Fg To the addtonal producer and consumer surplus dsplayed as the hatched areas n Fg corresponds the addtonal welfare, gong from monopolstc competton, Y mc Y pc. 13, to perfect competton, ThePareto-nferorunderemploymentthatarseundermonopolstccompetton s an example of coordnaton falure. Any agent does the best, gven what the others do, but the outcome s socally neffcent. A coordnated acton could mprove the outcome for everybody lke n the prsoners dlemma (see Cooper 1999, Benassy 2002). 13 In ths model the margnal utlty of wealth s constant, as noted n connecton wth equaton (18.10). Hence, the sum of the producer surplus and consumer surplus for the representatve producer s ndeed an approprate measure for welfare.

26 610 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS 18.4 Menu costs The neutralty of money n the above analyss derves from assumng the prce and wage setters face no costs when they change prces and wages, respectvely. Now, we ntroduce such costs. Two types of prce adjustment costs The lterature has modelled these prce adjustment costs n two dfferent ways. Menu costs refer to the case where there are fxed costs of changng prce. Another case consdered n the lterature s the case of convex adjustment costs, where the margnal prce adjustment cost s ncreasng n the sze of the prce change. Menu costs should not be understood n ts narrow lteral sense. Rather, menu costs should be vewed as a parable ncludng, n addton to costs of reprntng of prce lsts, costs of: 1. nformaton-gatherng, 2. recomputng optmal prces, 3. conveyng the new drectves to the sales force, 4. offendng customers by frequent prce changes, 5. search for new customers wllng to pay a hgher prce, 6. renegotatons. Thus, menu costs nduce frms to change prces less often than f no such costs were present. And some of the factors mentoned under pont 2, n partcular pont e and f,may be relevant also at the dfferent labor markets. When convex prce adjustment costs are present, the stuaton s somewhat dfferent. Suppose, the prce change cost for frm s c t = α (P t P t 1 ) 2,α > 0. Then the frm wll want to avod large prce changes, whch means that t tends to make frequent, but small prce adjustments. Ths theory s related to the customer market theory. Customers search less frequently than they purchase. A large upward prce change may be provocatve to customers and lead them to do search on the market, thereby perhaps becomng aware of attractve offers from other stores. The mpled knked demand curve can explan that frms are reluctant to suddenly ncrease ther prce For detals n a macro context, see McDonald (1990).

27 18.4. Menu costs 611 In lne wth B-K we wll now embed the frst knd of prce adjustment costs, menu costs, n the monopolstc competton setup. The menu cost theory The menu cost theory orgnated almost smultaneously n Akerlof and Yellen (1985) and Mankw (1985). It s one of the mcrofoundatons provded by New Keynesans for the presumpton that nomnal prces and wages are stcky n the short run. For smplcty, here we shall talk mostly about prces and prce-settng frms. To summarze the mportant theoretcal nsght of the menu cost theory: There are menu costs assocated wth changng prces. Even small menu costs can be enough to prevent frms from changng ther prce n response to a change n demand. Ths s because the opportunty cost of not changng prce s only of second order,.e., small ; ths s a reflecton of the envelope theorem (see below). But, due to mperfect competton (prce > MC), the effect on aggregate output, employment, and welfare of not changng prces s of frst order,.e., large. When tryng to relate menu costs to the B-K model, we frsthaveto face the dffculty that ths model s essentally statc. To be able to dscuss money supply changes, prce change decsons, and barrers to prce changes, we have to renterpret the model n a quas-dynamc framework. We magne the agents are actve n several perods, but ther decson makng remans myopc. As to the way changes n the money supply are brought about, open market operatons are ruled out because there are no other fnancal assets n the model than money. We magne that a change n M occurs n the form of a lump-sum helcopter drop at the begnnng of a perod. The proft functonoffrm s µ P γ V = P P 1 γ V (P,P,W,M), M mp Wn1/(1 σ) µ α µ P γ P 1 γ M mp wherewerememberthatp = the output prce of frm, P = the general prce level, W = the general wage level and M = the money supply. Facng a downward slopng demand curve, frm chooses P wthavewtothe maxmzaton of proft. Suppose that ntally, P = P, where P s the prce that maxmzes V, gven P, W, and M. Thus, maxmum proft s V (P,P,W,M) V, Let money supply shft to the new level M 0 >M.Intally, suppose no other agents change prce (or wage). Then P and W are unchanged. In ths

28 612 CHAPTER 18. MONOPOLISTIC COMPETITION AND MENU COSTS stuaton the opportunty cost to frm of not changng prce tends to be small because we have: dv dm (P,P,W,M)= V (P,P,W,M) P P M + V M (P,P,W,M) (18.34) =0+ V M (P,P,W,M). The frst term on the rght-hand sde of (18.34) vanshes at the proftoptmum because V P (P,P,W,M)) = 0,.e., the proft curvesflat at the maxmzng prce P. An llustraton s shown n Fg The result reflects the general prncple, called the envelope theorem: nannteroroptmum, the total dervatve of the maxmzed functon wrt. a parameter s equal to the partal dervatve wrt. that parameter; 15 the relevant parameter here s the aggregate money supply, M. Hence, the effect of a change n M on the proft s approxmately the same (to a frstorder)whetherornotthefrm adjusts ts prce. Indeed, due to the envelope theorem, for an nfntesmal change n M, the proft offrm sthesamewhetherornotthefrm adjusts ts prce n response to the change n M. For fnte changes n M ths s so only approxmately. Indeed, gven a fnte change M, the opportunty cost of not changng prce s of second order,.e., proportonal to ( M/M) 2, see Appendx A; ths s a very small number, when M/M s small. Therefore, n vew of the menu cost, say c, t may be advantageous not to change prce. Indeed, the net gan (= c opportunty cost) by not changng prce may be postve. Each ndvdual frmsnthesamestuatonaslongastheother frms have not changed prce. The outcome that no frms changes ts prce s thus an equlbrum. Snce there s no change n the general prce level n ths equlbrum, a hgher output level results. These consderatons presuppose that the households do not ncrease ther wage demands n response to the ncreased demand for labor. But ths rases no new problem because, n prncple, a smlar argument apples to the wagesettng households (or crafts-unons) n the B-K model. 16 As we have seen, each worker faces a downward-slopng demand curve for her specfc typeof labor and each worker sets the utlty maxmzng wage takng the demand curve nto account and supples then the amount of labor demanded at that wage level. If there are menu costs assocated wth changng the wage clam and they are not too small, an ncrease n demand need not have any effect onthewageclams. Aganthsfollowsfromtheenvelopetheorem. The utlty curve n a (W j,u j ) dagram s flat at the utlty maxmzng wage Wj. 15 See Appendx A to Chapter The motvaton for the provso n prncple wll become clear below.

29 18.5. Fx prce-fx wage equlbrum 613 V V * V( P, P, W, M ') V( P, P, W, M ) P P *' * P Fgure 18.4: The proft curvesflat at the top (P and W are fxed, M shfts to M 0 >M). Thus, all n all, no agent n the economy may want to change prce or wage, gven that none of the agents change prce and wage. And nstead, output, employment and socal welfare respond. Ths takes us to the next secton Fx prce-fx wage equlbrum When menu costs are operatve on both output and labor markets, the prce and wage rules are suspended. Output and employment adjust to demand, whle prces and wages are constant. Note that the demand functons for goods and labor, and the relaton between aggregate demand and real money balances, were derved wthout use of the prce and wage rules. These functons and relatons therefore stll hold. Consder agan the money market where aggregate demand s nx nx M 0 Mj 0 =(1 γ) I j = 1 γ γ PY, j=1 from (18.26). Aggregate supply of money s M = P n j=1 M j. In the flex prceflex wage equlbrum the general prce level, P, satsfed P = {γ/[(1 γ)y ]} M andrespondednproportontoachangenm. Butnthefx prce-fx wage equlbrum, snce P s gven, t s natural to wrte Y = γ M 1 γ P. (18.35) Thus, as long as menu costs are operatve, aggregate output s proportonal to aggregate nomnal demand, whch s proportonal to the money supply. j=1