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Nonclearing Markets: Microeconomic Concepts and Macroeconomic Applications Author(s): Jean-Pascal Bénassy Source: Journal of Economic Literature, Vol. 31, No. 2 (Jun., 1993), pp. 732-761 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2728514 . Accessed: 11/06/2011 18:49

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http://www.jstor.org Journal of Economic Literature Vol. XXXI (June 1993), pp. 732-761

Nonclearing Markets: Microeconomic Concepts and Macroeconomic Applications

By JEAN-PASCAL BE'NASSY CNRS and CEPREMAP,Paris

I want to thank the anonymous referees for the numerous improve- ments they brought to this article. All remaining deficiencies are my sole responsibility.

I. Introduction equilibriumin its modern reformulation (Leon Walras 1874; Kenneth Arrow and THE LAST TWENTY YEARS havewitnessed Gerard Debreu 1954; Debreu 1959). Im- the development of a new body of perfect , on the other hand, theory, in both micro and macroeconom- was dealt with in a "Marshallian"partial ics, aimed at generalizing traditional equilibrium framework,1 in line with the Walrasian theory to cases where not all pioneering works of Augustin Cournot markets clear. This generalization was (1838) and Edward Chamberlin (1933). achieved through a synthesis of three im- As for , it had been portant paradigms: Walrasian, Keynes- for many years dominated by the ian, and imperfect competition. The pur- Keynesian paradigm, particularly in its pose of this article is to give a simple IS-LM version ( and self-contained account of these de- 1936; 1937). It was then clear velopments for both micro and macro- to most economists that the Keynesian economists. model had no and that its long existence was due to the fact that, A. Early Motivations and Scope unlike the Walrasian model, it could deal explicitly with such important problems An early and continuing motivation as involuntary employment and the asso- for this theory was the desire to give seri- ciated policy problems. ous microeconomic foundations to mac- A number of authors tried to bridge roeconomics. When this research pro- the gap between and gram started there was indeed a profound Keynesian macroeconomics: The stimu- split between the two. The microeconomics of perfect compe- tition was built from rigorous principles 1 With of course one importantexception, Takashi in a general Negishi's (1961) formalizationof imperfect competi- equilibrium framework, and tion with subjective demand curves in a general equi- culminated in the notion of Walrasian librium framework. 732 Benassy: Nonclearing Markets 733

lating contributions by Don Patinkin to quantity signals as well as to sig- (1956), Robert Clower (1965), and Axel nals, and secondly by endogenizing Leijonhufvud (1968) made clear that the in a way that resulted from explicit Keynesian paradigm could make sense maximization by private agents. The re- only in a world where agents were quan- sulting concepts enable us to treat price tity constrained (for example the involun- formation schemes ranging from full ri- tarily unemployed in labor markets) and gidity to full flexibility, including a thor- where quantity adjustments would partly ough treatment of imperfect competi- replace price adjustments (as in the vari- tion. Moreover each may have ous versions of the Keynesian multi- its own specific price determination plier). In a well-known article, Robert scheme, which allows the model builder Barro and Herschel Grossman (1971) great flexibility, as we shall see especially constructed an aggregated fixprice model in the macroeconomic applications of giving some choice theoretic foundations Part IV. to the basic Keynesian model, and point- Generalizing the Walrasian model to ing out the existence of other regimes cases where markets do not clear was not as well. At that stage, however, both a the only avenue to reconcile micro and full general equilibrium formulation of macroeconomics. In the early 1970s a the Arrow-Debreu type, and a descrip- new macroeconomic school, the "new tion of rational price formation in various classical" school, took the opposite route markets were obviously missing. by rejecting both Keynesianism and im- The goal of the research program de- , and constructing scribed in this article was to fill these macroeconomic models based on the as- gaps and produce a framework of analysis sumption of full market clearing at all which would encompass simultaneously times. This school met with quite a large the three lines of work described above success, due to the fact that it combined by using their most interesting insights. the market clearing hypothesis with a From the Walrasian paradigm it retained very popular assumption, the "rational the full general equilibrium setting; from expectations hypothesis" (John Muth the Keynesian one the possibility of non- 1961). It has become clear, however, that clearing markets, quantity signals, and the distinguishing feature of new classical partial quantity adjustments; and from macroeconomics is not so much the ra- the imperfect competition paradigm the tional expectations hypothesis as the explicit formalization of price making by Walrasian market clearing one. As this agents internal to the system.2 More spe- will be the main focus of this article, we cifically the synthesis between these are now naturally led to examine why three lines of thought was achieved we want to have a general theory of non- through a generalization of Walrasian clearing markets. theory, first by allowing agents to react B. Why Study Nonclearing Markets 2 Though this endogenous price setting aspect will be obvious in what follows, it may be useful to dispel We begin our argument with the sim- at this early stage a widespread misconceptionof the ple observation that on only a fraction domain, in which this reduces solely to the treatment of completely fixed prices. Althoughthe first models of real world markets, such as the stock endogenizing prices in such a frameworkappeared market which inspired Walras, is the in the mid-seventies (Benassy 1976, 1978), this mis- equality between demand and supply en- representationpersists in some circles. Two recent examples are Olivier Blanchardand, Stanley Fischer sured institutionally by an actual auc- (1989) and Gregory Mankiw(1990). tioneer. For all other markets where no 734 Journal of Economic Literature, Vol. XXXI (June 1993) auctioneer is present, there is, as Arrow C. The Necessity of a General (1959) himself perceptively noted Equilibrium Approach

a logical gap in the usual formulationsof the One might agree with the preceding theory of the perfectly competitive economy, arguments, but still be satisfied with a namely that there is no place for a rationaldeci- partial equilibrium approach to nonclear- sion with respect to prices as there is with re- ing markets. In this case market imbal- spect to quantities. (p. 41) ances would be studied at the level of each single market, while the Walrasian Although quantity actions by all agents structure would be kept for general equi- result from rational maximizing behavior, librium and macroeconomics, the basic market clearing is assumed axiomati- idea being that, as far as policy is con- cally. cerned, demand-supply imbalances can As we demonstrate below, our method be dealt with on a market by market ba- allows us to build a consistent theory of sis. We shall show here that, at least from price (and quantity) determination on a general equilibrium and macroeco- markets without an auctioneer, mainly nomic point of view, this is not a sound because it enables us to derive the poten- position. Indeed one of the main insights tial quantity consequences of any price of the models we shall study is the impor- choices, whereas Walrasiantheory allows tance of " effects" through which such a description of quantity conse- disequilibrium in one market can actually quences for the Walrasian equilibrium be provoked by causes originating in an- prices only. Furthermore, the explicit other market. We shall illustrate this by in the determina- use of quantity signals a simple example where, in spite of a tion of demands, supplies, and prices by fully flexible wage, in the agents makes our representation private labor market is caused entirely by the of the functioning of markets much closer malfunction of the market. to what is observed in real world decen- tralized markets. The Example From a more macroeconomic and em- Consider an economy with two agents: pirical point of view it is clear to most One firm whose production function is people that a number of historical epi- y = F(f), and one supplying sodes, such as the massive unemploy- inelastically units of labor and with a ment or idleness of productive capacities eo function: observed during the or the recent crisis, seem extremely diffi- U = a log c + (1 - a) log(m/pe) (1) cult to reconcile with a general market where c is current good consumption, clearing view of the world. m the quantity of saved and pe Finally on the theoretical side, recent future expected price.3 We assume the developments in industrial economics, household has a quantity of money labor economics, or financial markets (in mo to start with and receives from the firm particular credit markets) all point to the all profits ur = py - we. Its budget con- of non-market clearing situa- possibility straint is thus: tions, due to informational imperfections or to the game theoretic nature of the pc+m=w4+ir+mO=py+mO. (2) price formation process. Thus a theory is needed that can accommodate in a gen- 3The quantity rn/pe should be thought of as ex- eral equilibrium setting the possibility of pected future consumption, the implicit assumption these non-market clearing situations. being that the household expects no future income. Benassy: Nonclearing Markets 735

Maximization of the firm's profits sub- manding a quantity of labor F'-l(w/p). ject to the production function F(s) yields Rather it will curtail production to the the Walrasian demand for labor ed = level demanded (y = cd) and demand F't'(w/p). Equating this with the inelas- the quantity of labor needed to produce tic supply e0 gives us the Walrasian real it, i.e., e= F-1(y). Using the consump- wage: tion function (3), these two equations yield: * = F'(eo). e F p a mo am1[ ] (5) Employment is thus equal to e0, and production to yo = F(0). Maximization We see that with p > p* we shall al- of the household's utility function (1) un- ways have e< e0. If the labor marketis der budget constraint (2) yields a con- competitive, the wage would go down sumption demand: to zero, and unemployment would re- main at the e0 - e, where e is cd = a + (3) given by formula (5). We see that unemn- p ployment in the labor market is due en- With total real income equal to yO, the tirely to the malfunctioning of the goods equality of demand (cd) and supply (yo) market! Of course this is only an example on the goods market yields the Walrasian but we must keep in mind the extreme price: importance of the interactions across markets, which is a major reason why a is p*= aLmO . (4) full general equilibrium analysis (1a)yO needed. The traditional view on unemployment D. The Structure of the Article is that it is due to too high real wages, i. e., wlp > F'(eo). This in turn may come The article will be organized as fol- from a "real wage rigidity" wlp > F'((0), lows: Part II will describe in a simple or a "nominal wage rigidity" w > w*. manner the basic concepts of the theory. We shall see that this need not be the Part III will give a number of non-Walra- case by experimenting with a totally dif- sian equilibrium concepts, which gener- ferent cause. alize Walrasian equilibrium to nonclear- Assume indeed that w is perfectly flexi- ing markets. Part IV will derive ble, but that for some reason p is rigidly macroeconomic applications using a uni- fixed at a level above p*. Let us now fied model under various assumptions consider a wage level w such that wlp about the price mechanism, and Part V ' F'((o) (if this were not the case the will conclude. excess supply of labor would make w go Because the field under review aims down until the inequality holds) so that at synthesizing different currents of mi- unemployment cannot come from a too croeconomic and macroeconomic theory, high real wage. With p > p* we see that, the structure of this article has been cho- even if a real income yo is distributed sen such that people with specific inter- to the household, consumption demand ests can take shortcuts in their first read- will be below yo (equations 3 and 4). ing of the paper. For example the micro- Faced with a consumption demand cd < oriented reader will find the sequence yO' F[F'-'(wlp)], it is clearly not profit of Parts II and III of most , maximizing for the firm to continue de- whereas the macro-oriented reader can 736 Journal of Economic Literature, Vol. XXXI (June 1993)

go through Part II and move directly to which he will receive PhSih units. Let us the macroeconomic applications of Part note in passing that it is only in a mone- IV. However, as the purpose of the arti- tary economy that the notion of a "market cle is to synthesize these different cur- for good h" unambiguously exists, as the rents, the article should be read in full counterpart is always money. In a barter so as to exploit fully the positive external- economy there would be e - 1 markets ities between the various parts. where good h would be traded, against (- 1 different counterparts. II. MicroeconomicConcepts Demands and Transactions We are now ready to study the basic microeconomic elements of the theory. We must make an important distinc- We shall show successively how transac- tion, which by nature is not made in mar- tions and quantity signals are formed in ket clearing models, that between de- a decentralized fashion on a nonclearing mands and supplies on the one hand, and market, how quantity signals affect de- the resulting transactions on the other. mand and supply, and finally how we can They will be distinguished by different build a consistent theory of price making notations. Demands and supplies, de- by agents internal to the system. noted dih and ?ih, are signals sent by each agent to the market (i.e., to the other A. Nonclearing Markets and Quantity agents) before exchange actually takes Signals place. They represent as a first approxi- A Monetary Economy mation the exchanges agents wish to carry, and thus do not necessarily match An often neglected issue in Walrasian on a market. Transactions, i. e., pur- general equilibrium models is the prob- chases and sales of goods, are denoted lem of the actual institutions of exchange. dt*hand s*. They are exchanges actually In his initial model Walras himself (1874) carried on markets, and as such are sub- referred to a barter economy, with a mar- ject to all traditional accounting identi- ket for each pair of goods. Other authors ties, such as budget constraints. In par- assume that all exchanges are monetary. ticular in each market h aggregate Barter exchange is almost never ob- purchases must be equal to aggregate served nowadays, and thus for evident sales. If there are n agents in the econ- reasons of realism we shall from here on omy this will be written work in the framework of a monetary economy.4 Money is the medium of ex- change. It is also the numeraire and a Dh = dhi Si5h = h. 6 i=l i=l reserve of value. There are ( markets in the period con- As we indicated no such equality holds sidered where nonmonetary goods, in- a priori for demands and supplies. dexed = 1, . . . by h , e, are exchanged Schemes against money. The money price of good h is Ph. An agent i may make a purchase We shall now study the functioning of dih on market h, for which he will pay a market for a particular good h, where Phdih units of money, or a sale Sih, for a price Ph has already been quoted by some price setter. This price being given, we shall, until Section II.C where 4Non-Walrasian theory has been developed in price nonmonetaryexchange structures as well; see notably making is explicitly studied, treat price Benassy (1975b, 1982). makers and price takers symmetrically. , Benassy: Nonclearing Markets - 737

Because the price Ph is not necessarily change agents are naturally classified in a market clearing one, we may have: two categories: Rationed ones (for which < n n d* < djh or Sih ?ih) and nonrationed which = or s5h = Dh=> dih # ih = Sh ones (for dih dih Sih). i=l i=l We shall now say that a rationing scheme on a market h is or fric- From any such set of possibly inconsis- efficient tionless if there are not both rationed de- tent demands and supplies the exchange manders and rationed suppliers on mar- process must generate consistent transac- ket h. The intuitive idea behind it is that tions satisfying equation (6) above. Evi- in an efficiently organized market a ra- dently, as soon as Dh # some demands Sh tioned buyer and a rationed seller should and supplies cannot be satisfied in the be able to meet, and would exchange un- exchange process and some agents must til one of the two is not rationed. To- be rationed. In real life this may be done gether with the voluntary exchange as- through a variety of procedures, such as sumption, this implies that agents on the uniform rationing, queueing, propor- "short side" of the market (i.e., deman- tional rationing, priority systems, etc., ders in case of excess supply, suppliers depending on the particular organization in case of excess demand) can realize of each market. We shall call rationing their desired transactions: scheme the mathematical representation of the exchange process on market h. Dh 2 Sh D Sih = Sih for all i This rationing scheme gives the transac- : = tions level of good h for each agent as a Sh Dh => dih dih for all i. function of the demands and supplies of This also yields the "rule of the mini- all agents present in that market (this will mum,, implicit in many macroeconomic be formalized more rigorously in Section models, which says that the aggregate III.A). We shall now study successively level of transactions is equal to the mini- a number of properties of rationing mum of and supply: schemes in general, which will lead us naturally to the notion of quantity signals. D* = Sh = min(Ih,?h). Voluntary Exchange and Market We should note that the market effi- Efficiency ciency assumption may be somewhat un- realistic if we consider a fairly wide and The first property we shall require decentralized market. We shall use this from rationing schemes is a very natural property for its convenience in the mac- one in a free market economy, namely roeconomic examples of Part IV, but we that of voluntary exchange, according to should keep in mind that most of the which no agent can be forced to purchase concepts that follow do not depend on more than he demands, or to sell more it. than he supplies. This will be expressed We may finally note that, though these by: properties are never explicitly discussed in the Walrasian literature, the "ration- h dih Sih C 8ih ing schemes" implicit in Walrasian the- This condition is quite natural and ac- ory satisfy both voluntary exchange and tually verified on most markets (except market efficiency, so that our theory of maybe for some labor markets which are markets appears as a natural generaliza- regulated by more complex contractual tion of the Walrasian one to cases where arrangements). Under voluntary ex- markets do not clear. 738 Journal of Economic Literature, Vol. XXXI (June 1993)

Quantity Signals d7ih Now it is quite obvious that at least rationed agents must perceive a binding quantity constraint in addition to the price signal. To get a first intuitive ap- dih - - - - - proach on these quantity signals, we shall / pdt/ begin with a simple example, where there are only two agents in market h. Agent 1 demands dlh, agent 2 supplies Figure la. Nonmanipulable ?2h* In this case the rule of the minimum and scheme is: applies, the rationing d7ih

dlh = 2h= min(dh,2h). At the same time as transactions take place, quantity signals are sent across the market: Faced with supply ?2h and under voluntary exchange, demander 1 knows that he will not be able to purchase more than ?2h* Symmetrically supplier 2 knows that he cannot sell more than dlh. Each agent thus receives from the other one a "quantity signal," respectively denoted dlh and ?2h, which tells him the maximum Figure lb. Manipulable quantity which he can respectively buy and sell. In this example: of the other agents on the market. The dlh = 52h ?2h = dlh relation between demand dih and pur- * so that the rationing scheme can be alter- chase d looks thus as in Figure 1. natively expressed as We may note that under the represen- tation given by (9) and (10), the rationing dlh = min(lh, dlh) (7) scheme displays obviously voluntary ex- change, but also another important prop- S2h = min(?2h,?2h). (8) erty, that of nonmanipulability. A It turns out that many rationing scheme will be called nonmanipulable if, schemes, and actually all those we will once rationed, an agent cannot increase in what the study follows, share simple his transaction by increasing the size of representation given by equations (7) and his demand. This assumption will be (8). Each agent i receives in market h a maintained in what follows.5 Of course, quantity signal, respectively dih or Sih on even though the trader cannot "manipu- the demand or supply side, which tells late" through the size of his demand (or him the maximum quantity he can buy supply), he can modify his quantity con- or that sell, so the rationing scheme can straints in his favor by other (costly) be written simply:

ih= min(h,dih) (9) 5We thus exclude manipulable schemes (Figure lb), like the proportionalrationing scheme. Typi- sih = min(?ih,?ih) (10) cally, unless exogenous constraintsare imposed, ma- nipulable schemes lead, in case of non-marketclear- where the quantity signals dih and ?ih are ing, to divergent demands or supplies and no functions of the demands and supplies equilibrium (see Benassy 1977, 1982). Benassy: Nonclearing Markets 739 means, such as for example arriving ear- ory via our definition of effective de- lier in a queue. As we shall see in Sec- mand. This we shall further see by study- tions II.C and III.C, price setting is a ing a well-known example. particularly important way to "manipu- late" the quantity constraints an agent The Employment Function is faced with. The first illustrative example of our Now it is clear that the quantity signals definition is the employment function perceived by the agents should have an due to Patinkin (1956) and Barro and effect on demand, supply, and price for- Grossman (1971): Consider a firm with mation. This is what we shall explore a to scale production next. function y = F(() faced with a price p and wage w. The Walrasian labor de- B. and Supply mand is equal to F'-'(wlp). Assume now A Definition that the firm faces a constraint y on its sales of output (y is of course equal to We must now discuss how demands the total demand coming from the other and supplies are formed when markets agents). According to the above defini- do not clear, and for that develop a the- tion the effective demand for labor, id, ory of effective demand and supply, is the solution in ( of the program: which will be functions of both price and - quantity signals. When formulating these Max py we such that effective demands and supplies, agent i Jy= F(e) knows that his transactionswill be related to them by equalities (9) and (10) above. Maximizing the expected utility of the solution of which is: these resulting transactions may lead to id = min {F'-(wlp), F-`(g)}. (11) complex calculations, especially if con- straints are stochastic (see for example We see that the effective demand for Benassy 1977, 1982). In the case of deter- labor may have two forms: The Walrasian ministic constraints, which is what we one if the sales constraint is not binding, shall consider throughout, there exists a or, if this constraint is binding, a more simple and workable definition which "Keynesian" form equal to the quantity generalizes Clower's (1965) original of labor just necessary to produce the "dual-decision" method: Effective de- output demand (this last form was actu- mand (or supply) on one particular mar- ally the one operative in Section I.C). ket is the trade which maximizes the We see immediately in this example that agent's criterion subject to the usual con- effective demand may have various func- straints and to the quantity constraints tional forms, which explains intuitively on the other markets. This definition thus why non-Walrasian models often have naturally includes the well-known spill- multiple regimes, as we shall see indeed over effects: We say indeed there is a in Part IV devoted to macroeconomic ap- spillover effect when an agent who is con- plications. trained to exchange less than he wants C. The Formation of Prices in a market because of rationing modifies his demands or supplies in other mar- We are now ready to address the kets. These spillover effects, which un- problem of price making by agents inter- derlie the surprising result of Section nal to the system, and we shall see that, I. C, will be present throughout the the- as in demand and supply theory, quantity 740 Journal of Economic Literature, Vol. XXXI (June 1993)

signals must play a fundamental role. The this seller faces a constraint ?ih which is general idea relating the concepts of this equal to the sum of all other agents' de- section to those of the previous ones is mands on the market h: thus that price makers change their ?ih = >dh = Dh. (12) prices so as to "manipulate"the quantity joi constraints they face (that is, to increase But if we or decrease their possible sales or pur- consider the market h before i chases). As a result of this introduction agent has set price Ph, we see that he will of quantity signals into the price-making not, contrary to a price taker, con- sider ?ih process, the theory will bear some re- as parametric. Rather, and this is semblance to the traditional theories of how the price making theory devel- here links imperfect competition (see notably oped with what we saw previ- Chamberlin 1933; Negishi 1961). ously, he will use the price Ph to "manip- Various modes of price making inte- ulate" the quantity constraint ?ih he faces, grating the above ideas can be envi- i.e., to increase or decrease the demand sioned. We shall deal here with a particu- addressed to him. The relation between the maximum lar (and realistic for many markets) quantity seller i expects to sell and the organization of the pricing process where price he sets on the market is called the agents on one side of the market (usually perceived . the sellers) quote prices and agents on If expectations are deterministic (which we the other side are price takers.6 shall assume in all that follows) it will We shall moreover, as in the tradi- be denoted gih(Ph,Oi)where Oiis a vector tional theories of monopolistic competi- of parameters which integrates all infor- tion, characterize a good not only by its mation available to the price maker. In physical and temporal characteristics, view of equation (12), this perceived de- mand curve can also be but also by the agent who sets its price. written: Each price maker is thus alone on his Sih(Ph,Oi) = Dh(Ph,1i) side of the market, and appears formally where is as a monopolist (or a monopsonist). This l6h(Ph,Oi) what the price maker expects the aggregate effective de- does not imply, however, anything as to mand of his degree of monopoly power, as there the rest of the agents to be, con- ditional on the price he sets and on may be competitors' markets where Ph all other agents sell or buy goods that are information contained in the vector We see on what extremely close substitutes. Oi. that, depending the price maker knows about the rest of the PerceivedDemand and Supply Curves economy, several forms of perceived de- mand curves can be Consider thus the seller i who sets the considered: price Ph on a market h (the exposition * In the objective demand curve ap- for a demander would be symmetrical). proach it is assumed that Oicontains As we saw above, once he has posted all relevant information and that the his price, demands are expressed, and price maker knows the exact form of the function ])h. This assumption is the one usually made in partial 6Other modes of pricingcould be studiedwith our tools but have not yet been integratedin this equilibrium analysis and in indus- line of workat a generalequilibrium level. Interest- trial organization. We shall see in ing alternativeconcepts have been studieddirectly Section III.C how to use the con- at the macroeconomiclevel by JoaquimSilvestre (1988, 1989), Hans-JorgenJacobsen and Christian cepts developed here to construct Schultz(1990). rigorously the objective demand Benassy: Nonclearing Markets 741

curve in a full general equilibrium first order condition the traditional "mar- system. ginal cost equals marginal revenue" con- * In the subjective demand curve ap- dition, which is written here: proach, the price maker is assumed evaluation of to make a subjective =pi I -I the demand curve addressed to ct(Yi) him. Note however that subjective demand curves are not fully arbi- in which we see that the firm will choose a price high enough, so that it will want trary, as each realization (ph'SAh) is a point on the "true"demand curve, not only to serve the demand forthcom- and the subjective demand curve ing, but would be willing even to serve must "go through" this point (Don- more at the price it has chosen: in fact, ald Bushaw and Clower 1957). The the firm would be happy to serve demand functional form and the elasticity up to C- '(pi). There is thus in our sense may be wrong, but at least the posi- "excess supply" of the good, even though tion must be right. this excess supply is fully voluntary on the part of the price maker. Of course The important point to keep in mind which level of output and price will be is that the perceived demand curves rep- chosen will depend on the exact value resent the effective demands (and not, of the estimated Oi. This will be deter- for example, the Walrasian ones) of the mined, as we already indicated above, agents. For applications of this point, see by the effective demands of the other for example, Benassy (1988, 1989, agents. An example of this will be seen 1991b), Huw Dixon (1987b), and the ref- in the fully closed model of Section IV. C erences therein. below. Price Making III. Non-WalrasianEquilibria Once the parameters of the perceived demand curve, objective or subjective, We shall now describe in a more formal are known, price making proceeds along way than in Section II a number of non- lines that are traditional in the theories Walrasian equilibrium concepts that em- of imperfect competition: The price body all the notions seen above in a full maker will maximize his objective func- general equilibrium framework. In order tion, subject to the constraint that de- not to burden the exposition, we shall mand be smaller than the amount given describe these concepts in a pure ex- by the perceived demand curve on the change economy. The concepts de- markets he controls (in addition to the scribed extend naturally to economies usual constraints). Consider as an exam- with production, though at the cost of a ple a firm with a cost function Ci(yi) and heavier notation. assume it faces an isoelastic perceived demand curve of the form Si(pi,O0)= A. The Economy Oipi-, where the elasticity parameter I is given. The program giving the optimal Markets and Agents of the firm is thus written: price We shall thus consider a monetary Max piyi - CQ(yi) such that exchange economy. There are in the pe- riod considered ( markets where non- a Yi' Oipi monetarygoods indexed by h = 1,. . . . This well-known program yields as a ( are exchanged against money at a price 742 Journal of Economic Literature, Vol. XXXI (June 1993)

Ph* We call p the (-dimensional vector Zih(p), h = 1, . , e. A Walrasian equi- of these prices. librium price vector p* is defined by the Agents are indexed by i = 1, . condition that all markets clear, i.e.: n. Agent i has initial endowments Wih of n good h and hi of money. He may pur- >Zih(p*) = 0 h=1, chase a quantity dih > 0, or sell a quantity i=l1 Sih >0 of good h. In what follows it will The transaction of good h realized often be more convenient for notations by agent i is to work with the net transaction of agent Zih(P*). i on marketh, Zih, defined by: Demands, Transactions, and Rationing Schemes Zih = dih - Sih. Call zi the (-dimensional vector of net As we indicated in Section II.A, one transactions of agent i, wi his vector of must make a clear-cut distinction be- initial endowments. His final holdings of tween demands and supplies, dih and ?ih, nonmonetary goods E Re and of on the one hand, and transactions, d* xi * money mi > 0 are given respectively by: and s on the other hand. Let us define net demand Zih and net transaction Zih xi = Oi+ zi mi = 'hi - pzi. by: We shall assume that the agent has a Zih=dih -Sih Zih =dih h-. utility function on these. final holdings: A rationing scheme converts possibly Ui(xi,mi) = Ui(wi + zi, mi) inconsistent demands and supplies into which we shall assume throughout con- consistent transactions. The rationing tinuous and strictly concave in its argu- scheme in market h is described by a ments. Note that, at least because of the set of n functions presence of mi as a in the utility functions, everything we shall say Zi = Fih(Zlh, * nh) is conditional on the prevailing expecta- such that: tions scheme. Because expectations are n not the subject of the article, and our Fih(Ztlhl * Znh)-? approach allows us to deal with rational i=l1 and nonrational expectations as well, we for all Zih, . * * Znh. shall leave this expectations issue totally implicit in this section (for explicit treat- We shall generally assume that Fih is ments see Benassy 1975a, 1982, 1986, continuous, nondecreasing in Zih, nonin- 1990, 1991a). creasing in the other arguments. The property of voluntary exchange on mar- Walrasian Equilibrium ket h translates here into: For every price vector p, agent i deter- I Zi Zih 2 0 mines his Walrasian net demands by IZihl Izihl and for all i. maximizing his utility subject to the bud- The assumption that a market h is effi- get constraint: cient or frictionless is written here: Maximize Ui(wi + zi, mi) such that ;Zih) * Zih ? => ZZih= Zih for all i. pzi + mi = mi This yields a vector of Walrasian net As we indicated in Section II.A, we demand functions zi(p) with components will always assume voluntary exchange, Benassti: Nonclearinng Markets 743 whereas frictionless markets will not be Maximize Uj(i + zi, mi) such that assumed unless explicitly specified. [PZi + mi = 'hi Quantity Signals - sik Zikj dik for all k = h To express the way quantity signals are which yields an effective demand func- formed in an easier way, let us rewrite tion Ch(p,di,?i).Call t;(p,di,?) the vector the rationing scheme on market h as: of all thesedemands, Eih, h = 1, . . . , ( for agent i. It has two good properties: ih = Fih(Zih,Z-ih)13) The first is that, as it is easy to check where Z-ih is the set of all net demands (or see Benassy 1977, 1982), it leads to on market h, except that of agent i, i.e.: the best transactionvector taking account ,of all constraints di and ?i. Secondly, Z-ih = {ZjhI # i}@ whenever a constraintis binding on a As we indicated in Section II.A we marketh, the effectivedemand or supply shall work with nonmanipulable ration- on this marketis greaterthan the corre- ing schemes which can be written under spondingquantity constraint, which thus the form seen above: "signals"to the market that the agent trades less than he wants. Such a signal d= min(dih,d1h) (9) is actuallyuseful to avoidtrivial equilibria Sih = min(?ih,?ih) (10) where nobody would trade because no- body else signalsthat he wants to trade. where the quantities dih and &ih are func- tions of all demands on the market, ex- B. Fixprice Equilibria cept that of agent i himself, which is writ- ten: We shall now begin with a first con- cept of equilibrium, somehow polar to dih = Gih(Z-ih) > 0 (14) 2 the Walrasianone, that of fixpriceequi- Sjh = G6h(2-ih) 0. (15) libriumassociated to a given price vector For compactness of notation, equations p. This concept is interestingfor several (13), (14), (15) will be rewritten in vector reasons:First it will give us a very wide form as: class of logicallyconsistent market alloca- tions, as we shallfind out that undervery ZL Fi(ii,zi (16) standard conditions a fixprice equilib- di= Gi(Z_i) (17) rium exists for all strictly positive price ?i= G!(_i) (18) vectors and every rationingscheme (we where: may note also that Walrasianallocations are part of these allocations,as they are -i= {ijj $ i} simply those correspondingto a Wal- Effective Demand rasianprice vector).Secondly, as we shall see in SectionIII.C below, fixpriceequi- As we indicated in Section II.B the libriaare a very useful buildingblock for effective demand Zih is obtained by maxi- constructingother non-Walrasianequi- mizing the utility function Ui subject to libriumconcepts with flexibleprices. We the budget constraint and to the quantity shall now study two different fixprice constraints on the other markets, i.e., it equilibriumconcepts. will be the solution in Zih (unique because The firstconcept we shalldescribe was of strict concavity) of the following pro- developed in Benassy (1975a, 1977, gram: 1982). It derives straightforwardlyfrom 744 Journal of Economic Literature, Vol. XXXI (June 1993) the definition of effective demand func- * D Agent B tions and the equations describing trans- 0 actions and quantity signals (equations 16, 17, 18).

DEFINITION 1: A fixprice equilibrium is characterized by a set of vectors of effec- tive demands Zi, transactions z* and quantity signals di and ?i such that: (a) 2i = Ji(p,di,) for all i (b)z* = Fi(ii,2_i) for all i Agent A (c) di = G'(&i-) for all i Figure 2. ?i = Gs(&_i) for all i. Equilibria defined in this way exist for Point 0 corresponds to initial endow- all positive price systems, and for all ra- ments, DC is the budget line of the two tioning schemes satisfying voluntary ex- agents at price points A and B are change and nonmanipulability (Benassy p, the tangency points of the indifference 1975a, 1982). The "exogenous data" are curves with this budget line. Of course, the price system and the rationing because there are only two we schemes It was shown by Norbert agents, Fih. assume that the market is frictionless. Schulz (1983) that for a given price sys- the level of tem and rationing scheme the equilib- Measuring exchanges along the line OC, we see that A demands a rium is unique provided that the "spill- quantity OA, B supplies a over effects" from one market to the quantity OB. They exchange the minimum of these other are less than one hundred percent two quantities, i.e., OA, and B is in value terms. For example in the sim- agent rationed. Perceived constraints are, re- plest Keynesian model this would as- spectively, OA for agent B and OB for sume a propensity to consume strictly agent A. Agent B is constrained on his smaller than one, a fairly intuitive condi- supply, while A is not. tion. In what follows, we shall assume that An Alternative Concept the Schulz conditions hold, and we shall The concept we shall now describe is denote by Z*(p), Di(p), Si(p) the 2j(p), from Jacques Dreze (1975, 1991).7 This functions giving the values of Zi, Zi, di, concept does not differentiate between ?i at a fixprice equilibrium corresponding demands and transactions, and thus deals to p (the market organization, and thus directly with quantity and trans- the rationing schemes being assumed in- signals actions. The variant). quantity signal structure is very simple, with uniform rationing on A Simple Example all markets. Each agent i receives on every market h signals dh and Sh repre- As a simple example of fixprice equilib- senting the maximum quantity he can re- rium, consider the traditional Edgeworth box example (Figure 2), which represents a single market where agents A and B 7 The original paper dealt with the more general case of prices variable between preset bounds, or exchange a good (measured horizontally) indexed on each other, an issue pursued in Gerard against money (measured vertically). van der Laan (1980), Pierre Dehez and Dreze (1984). Benassy: Nonclearing Markets 745 spectively purchase and sell, so that his traditional concavity assumptions for the transactions on market h are limited to utility functions. The concept can be eas- the interval: ily extended to nonuniform bounds dih and ?ih (Jean-Michel Grandmont and Guy -8h < Zih s dh Laroque 1976), but in this last case it is We are now ready to give the defini- not specified in the concept how short- tion of a fixprice equilibrium in the sense ages are allocated among rationed de- of Dreze: manders and rationed suppliers, so that there are usually a large number of equi- DEFINITION 2: A fixprice equilibrium for libria for a given price vector. a given set of prices p is characterized At this stage the reader may wonder by transactions Z*h, i = 1, . . . n, if there are connections between the two h = 1,. . . , X, and quantity constraints concepts we described. It was proved by dh and h', h = 1, . . ., , such that: Silvestre (1982, 1983; see also Antoine n D'Autume 1985) that one obtains the (a) z*i= for all h same set of equilibrium allocations for definition 1 (assuming all rationing schemes to be frictionless) and definition (b) The vector z is solution in zi of the 2 for nonuniform in following program: (extended bounds), both exchange and production econo- Maximize Ui(wi + zi, mi) such that mies. These allocations have a number JPZi + mi = mi of suboptimality properties which we {-Sh Zih' dh h=1, ... , shall not study here, but which are devel- (c) if Z = dh for some agent i, then oped in Benassy (1975a, 1982, 1990), ih Dreze and Heinz Muller (1980), and Sil- > ?h for all agents j. Zjh vestre (1985). If Zih = -Sh for some agent i, then Zjh < dh for all agents j. C. Equilibria with Price Makers Let us now interpret these conditions. We shall now construct a non-Wal- Condition (a) simply says that transac- rasian general equilibrium model where tions should balance on each market. prices are explicitly set by agents internal Condition (b) says that transactions maxi- to the system. This will show that, as a mize utility subject to the budget con- "by-product," our theory provides a sim- straint and the quantity constraints on ple and natural solution to the (heretofore all markets, a natural individual rational- unsolved) problem of defining an objec- ity condition. We may note that the uni- tive demand curve for price makers in a form rationing procedure used here dis- general equilibrium situation. the two properties of voluntary plays The Framework exchange and nonmanipulability that we discussed earlier. Condition (c) says ba- As we indicated in Section II.C, we sically that rationing may affect either shall consider the case where agents on supply or demand, but not both si- one side of the market (demanders or multaneously. We recognize here the suppliers) set prices and agents on the assumption of efficient or frictionless other side act as price takers. Call Hi markets, which is thus "built in" to this the (possibly empty) subset of goods definition. whose prices are set by agent i. As said The existence of such an equilibrium above goods are distinguished not only was proved in Dreze (1975) under the by their physical characteristics, but also 746 Journal of Economic Literature, Vol. XXXI (June 1993) by the agent who sets their price. As a to the idea that there are many price set- result, the sets Hi are disjoint: ting agents, as in monopolistic competi- tion. Each agent chooses his price vector =1{0} j # i Hi nHj pi, taking as given the prices decided by and each price maker is alone on his side others, which we shall denote by p .: of the market. Subdivide further Hi into H (goods supplied by i) and Hd (goods P-i = {pjIj# i}. demanded by i). Agent i appears formally The idea behind the objective demand as a monopolist on markets h E Hs, as curve approach is that the agent knows a monopsonist on markets h E Hd. Con- the economy well enough to be able to sequently the constraints he perceives compute the quantity constraints he will have the simple form: face under all circumstances. In particu- lar he must be able to compute the dih Sih->djh heHE (19) joi or ?ih of equations (19, 20) for any value of the prices p-i and pi that others and dih =>Sjh hEHd. (20) himself may set. This is actually quite joi Now the basic idea of the concept we easy to do given the results of Section shall present is that the agent i uses the III. B where we saw that, for any given prices he controls to "manipulate" his market organization, we could notably constraints. Call pi the set of prices con- compute demands, supplies, and quan- trolled by i: tity constraints as functions of the price vector p = (pi,p-i) These were denoted Pi = {PhI hE Hi}. Di(p), Si(p), Di(p), Si(p). The objective In order to pose the problem of the demand curve for a good h E Ht is thus: optimal price choice by the firm, all we need to know is how he perceives the E Djh(P) = Sih(P) j#i quantity constraints in equations (19) and (20) to vary with pi. We shall now de- and symmetrically the objective supply scribe here the objective demand curve curve for a good h E Hid: approach, as developed in Benassy = (1988).8 The subjective demand curve ap- E Sjh(p) Dih(P). joi proach will be treated by way of example in Section IV.C.9 Price Making and Equilibrium The Objective Demand Curve Once it is assumed that agent i knows The equilibrium structure we shall the exact functions Di(p) and Si(p), the consider is that of a Nash equilibrium program yielding his optimal price pi is in prices, which corresponds implicitly very naturally written Maximize + such that 8 Earlierworks on the objective demand curve ap- Ui((.i zi, mi) proach are found in Jean Gabszewicz and Jean-Phi- [PZi + Mt =Mt lippe Vial (1972), Thomas Marschakand Reinhard Selten (1974), HukukaneNikaido (1975), FrankHahn -Sih(P) Zih(P)< Dih(p) h = 1, . . .e (1978). 9 For an applicationof this methodologyto subjec- which gives the optimum price decision tive demand curves in general equilibrium, see B& of agent i as a function of the prices cho- nassy (1976, 1978, 1982, 1990), which link the ap- proach described here with Negishi's (1961) seminal sen by the other agents: work on general equilibriumwith subjectivedemand curves. Pi= i(P-i) Benassy: Nonclearing Markets 747

We can now describe the equilibrium * ~~~~~~~~~~AgentB as a Nash equilibrium in prices as fol- 0 Agent A's lows: demand curve DEFINITION 3: An equilibrium with price makers is characterized by a set of,prices p*, net demands Zi, transactions zi, and quantity constraints di, si such that: w (a) p* = *i(p*i) for all i (b) ;zi,z*, di, ?i (i = ,. n) form a fixprtce equilibrtumfor the price vec- tor p*, i.e., they are equal respec- Agent A tively to Z4(p*), 2i(p*), Di(p*),i(p*). Figure 3. Further discussion, conditions for exis- tence, and inefficiency properties can be found in Benassy (1987, 1988, 1990, 1991b). For an explicit modeling of ra- IV. MacroeconomicApplications -tional expectations in that framework, In this part we shall show how the con- see for example Benassy (1991a). cepts studied above allow the construc- At this stage we clearly see that the tion of a wide variety of macroeconomic method we described, far from being models. We shall thus study successively confined to fixed prices, allows us on the a Walrasian equilibrium model, a fix- contrary to treat the endogenization of price-fixwage model, a model with im- prices in a rigorous manner, because it perfect competition on the goods and allows us to derive the quantity conse- labor markets, a model with real and quences (i.e., demands, supplies, trans- nominal rigidities, and an extension of actions, and quantity constraints) of any that model to . All price choice. these models -will be studied in the framework of the same economy, which An Example we shall now quickly describe.'10 For a simple example of an equilibrium A. The Economy and Wairasian with price makers, consider again the Equilibrium Edgeworth box seen above. Assume now Markets and Agents that agent B (the seller) sets the price. The "objective demand curve" is then We shall consider here a very simple agent A's demand, and corresponds thus monetary economy with three goods to the locus of tangency points between (monev, output, and labor) and three various lines and A's indifference budget 0 We shallconcentrate in thispart on the standard curves. This is depicted as the curved threegoods model and the problemsof employment line OMW in Figure 3, where W is the andpolicy. Other problems have been treatedwith Walrasian The this methodology,including foreign trade (Avinash point. equilibrium point Dixit1978; Peter Neary 1980; John Cuddington, Per- is then simply point M, the tangency Olov Johansson,and Karl-GustavLofgren 1984), point of this curve with B's indifference growth(Takatoshi Ito 1980;Pierre-Yves H6nin and which agent B the highest PhilippeMichel 1982; Pierre Picard 1983; D'Autume curve, yields 1985),business cycles (Benassy 1984, 1986),as well possible utility, given A's objective de- as the specificproblems of plannedsocialist econo- mand behavior. mies (RichardPortes 1981). 748 Journal of Economic Literature, Vol. XXXI (June 1993)

agents: An aggregate firm, an aggregate d = _ _ household, and the government. at+ + - There are two markets where output + IT + - and labor are exchanged against money [wC0 MO PT1 (23) at the price p and wage w respectively. p1 We assume that these markets are fric- p ts= t _ tionless, so that transactions on each one - are equal to the minimum of supply and ? a+ + demand. We shall denote by y and f re- + Tr + [u)eo[w U)+IT+m0-PT]mO -v (24) spectively the transactions on output and labor. The aggregate firm has a production The equations giving the Walrasian function F(e) which we shall assume price and wage are: strictly concave. The firm maximizes profits rr = py - wie, which are fully ys = y = cd + g redistributed to the household. e s = = The household has an initial endow- e ed. ment of labor and of money It to mo. Simple manipulations of the above consumes a quantity c of output, works equations yield the following equations an amount X, saves an amount of money for the values of e, y, w in Walrasian m, and its budget constraint is: p, equilibrium (if it exists):

pc + mi= W# +r mO+-PT+ (21) F'(e)(e0 e) = [F(e) - g] (25) where T is the real value of taxes levied at by the government. The household will = be assumed to have the simple utility y F(e) (26) function -=F(e) (27) U = at log c + (3log(eO - e) p + atmo y log(m/pe). (22) P =y( )~(m ) (28) 'Y(Y - g) - Ot(g - T) Finally the government taxes an amount T in real terms from the house- From (25) and (28) we see that the con- hold. He also has a demand for output g. ditions for the existence of a Walrasian equilibrium are: Walrasian Equilibrium g < F(eo) Let us first compute the Walrasian de- mands and supplies on the output and Ot(g - T) < y(Y - g) (29) labor markets. Maximization of the firm's profits under the production function where y is that given by equations (25, F(f) yields: 26). The first condition is obvious. The second says that the real deficit of the t' = F'-(w/p) ys = F[F'-'(w/p)]. government should not be too high. From these equations we see a few Maximization of the household's utility things; first money is neutral (i.e., price function (22) subject to the budget con- and wage are proportional to mo, y and straint (21) yields: i do not depend on it). Further: Benassy: Nonclearing Markets 749

sumption demand Cd is the value of c U < < 1'V ag ag that solves the following program (cf., Clower 1965): on which we see that there is crowding out of private consumption by govern- Maximizea log c + 13log( '-e) ment expenditures, though less than one + y log(m/pe) such that hundred percent. {pc+ m = mo + w(t + ir- pr f?? P B. Fixprice-FixwageEquilibria yielding, as the second constraint is bind- We shall now study the above model ing: under the assumption, somehow polar to the Walrasian one, that the price p and Cd = (X[MO+wes+ - P] wage w are completely rigid in the period considered. We shall obtain the famous "fixprice"model originally developed by which can be rewritten, using the defini- Barro and Grossman (1971, 1976). " As tion of ir and the fact that is is equal to is well known, this model has three possi- the actual sale of labor: ble regimes.12 p * Keynesian unemployment with ex- ot + -P + cess supply for both output and la- in which we recognize a traditional bor, very Keynesian function. Be- * Classical unemployment with ex- consumption cause of excess in the mar- cess supply of labor and excess de- supply goods transactions are to total out- mand for goods, ket, y equal put demand: * Repressed with excess de- mand for both labor and output. d otx[i0 yY Cd=5+9=~ g + ^wt MOy-T]+gY ] We shall study these three regimes in =oa [P turn. yielding: Keynesian Unemployment O y* = +g-T) +g=Yk (30) This regime displays excess supply in both markets. In particular the house- hold faces a binding constraint is in the a most traditional Keynesian labor market, so that its effective con- formula where (a + y)Iy is the multiplier. Labor transactions are equal to the firm's demand, which, as the firm is con- " The fixprice macromodelwas further developed in Benassy (1978, 1982), Edmond Malinvaud(1977), strained in its output sales to Yk, is (as Werner Hildenbrandand Kurt Hildenbrand (1978), we saw in Section II. B) equal to the John Muellbauer and Portes (1978), Seppo Honka- quantity of labor just necessary to pro- pohja (1979), Neary and Joseph Stiglitz (1983), Tor- sten Persson and Lars Svensson (1983). The adapta- duce Yk, i.e.: tion presented here is that of Benassy (1978, 1990). *= F-'(yk) = 12 Note that this terminologyof the regimes, which Ek. (31) is Malinvaud's(1977) contributionto the field, is not fully satisfactoryas it tends to associate the idea of We may also compute private con- classical unemployment to an excess demand for sumption c* = -g: goods. This clearly need not be the case, as we shall see in $ection IV.D. However, we still keep this terminologyhere, as most people aware of the field C= + g - T). pl are accustomed to it. P 750 Journal of Economic Literature, Vol. XXXI (June 1993)

Let us make a few observations: The able policy instrument. Note that this first is that money is not any more neu- time crowding out does not occur tral, but that increases in mo will increase through prices, but by a direct rationing production, employment, and private mechanism. The only variable which af- consumption. These will also be in- fects the level of employment and pro- creased by decreases in taxes or increases duction is the level of real wages, thus in government spending. The traditional validating the "classical" presumption results of "Keynesian" analysis are thus that there is unemployment because valid in this regime. "real wages are too high." Maybe the most striking fact is that Repressed an increase in government spending will Inflation increase not only production and em- In this regime there is excess demand ployment, but also private consumption. in both markets. In particular the house- There is thus no crowding out, quite the hold is faced with a binding constraint 5 contrary, as even though the government (actually equal to its purchases c* in the collects real output from the private sec- goods market). Its supply of labor iS is tor, more of it is available for private con- thus given by the solution in f to the sumption, a remarkable by-product of following program: the inefficiency of the Keynesian multi- Maximize aolog c + 13log(0 - plier state. 13 ) + -ylog(m/pe) such that Classical Unemployment {pc+ m = mo + we + iT-pT In this case there is excess supply of labor and excess demand for goods. The firm, being on the "short" side in both where the last constraint is binding. The markets, is able to carry out its Walrasian solution to this program (assuming labor plan, so that: supply is strictly positive) is: -* = F' l(w/p) = Ec (32) s_ 1 y* = F[F'-'(w/p)] = Yc. (33) - We see immediately that "Keynesian" Pe P-]MO + we0 +1T - policies have no impact on employment and production. In fact it is easy to check In this formula we see a new spillover that their main effect is to aggravate ex- effect: Rationing on the goods market cess demand on the goods market. If we leads the household to reduce its supply further assume that government has pri- of labor. Now assume again that govern- ority in the goods market, then the actual ment has priority on the goods market, is to: consumption equal and production is high enough to satisfy c* = y* - g = Yc- g. g (the reader can easily work out the case where it is not). Then: There is a one hundred percent crowd- ing out effect of government expendi- c= c* = y- g. tures, which thus appears as an undesir- Because there is excess demand for la- bor, the transaction f* is equal to fS. Combining this with the definition of 1 For furtherdevelopments on these inefficiency properties, see for example Benassy (1975a, 1978, profits and the two above equations, we 1982, 1990). obtain: Benassy: Nonclearing Markets 751

*= e_13 (mc + pg - PT) (34)

Output transactions are equal to the supply, which is equal (as the firm is con- strained in its labor purchases) to the maximum quantity producible with avail- able labor supply, i.e.:

y* = F(er) = Yr-

We may now note that the economic K policy variables have effects completely opposite to those in the Keynesian re- R gime. In particular, increases in the quantity of money or in government spending diminish employment and pro- duction! Furthermore, under the above mO + assumptions, private consumption is g_ equal to: Figure 4.

c* = Y* - g = Yr - g. ble employment levels computed above (equations 30 to 35), i.e.: Because an increase in g reduces Yr, it reduces c* by a quantity even greater ,e= min(ek,eC, r) than g. There is thus a more than one min(yk,yc,yr). hundred percent crowding out effect! y*= The mechanism at work in this regime We can depict the three regimes, de- is some kind of "supply multiplier" (Barro noted K, C, and R in the space (mjp + and Grossman 1974), by which a reduc- g - T, wlp), with g being parametric. tion in the amount of goods available for Figure 4 has been drawn for g equal to consumption reduces the supply of labor, zero. The triangles are iso-employment which itself reduces further the amount or iso-output lines. For a given g, the of goods produced, and so on . highest level of employment and produc- tion occurs at W, the Walrasian equilib- The Complete Picture rium point. As g increases, point W slides down the dashed line, and the frontier As we have seen above, the three re- between regime K and the two other re- gimes of our model display strikingly dif- gimes moves accordingly. ferent properties concerning the deter- On this diagram we see particularly mination of employment and activity and well that the spillover effects from the the response to policy variables. It is goods market to the labor market do mat- therefore important to know for which ter a lot: Even if the real wage is "right" values of the "exogenous" parameters mo, (i.e., equal to its Walrasian equilibrium p, w, g, and T, each of the three regimes level, which corresponds to the horizon- obtains. As the reader may easily check, tal line going through W), we may have both the employment level and the na- inefficiently low values of employment ture of the regime are determined by due to insufficient (or excessive) demand finding out the lowest of the three possi- in the output market. 752 Journal of Economic Literature, Vol. XXXI (June 1993)

C. An Imperfectly Competitive Model14 not to be rationed on the labor market, so we shall simply ignore this nonbinding now endogenize the price We shall constraint. The first order conditions for in a framework of imperfect and wage this program yield, after elimination of 0: competition similar to those of Sections II.C and III.C. It will be assumed that F'(e) = -W (36) the firm sets the price, and the household 71- l p sets the wage. In order to make exposi- tion more compact, and because we have and of course the production relation al- a model with aggregate representative ways holds: agents, we shall use the subjective de- y = F(f). (37) mand curve approach. It turns out that the same results are obtained with objec- Assume now that the household simi- tive demand curves (Benassy .1987, 1990) larly perceives demand curves for labor and with both objective demand curves of the form Ow-- where E > 1 is given, and rational expectations (Benassy and 0 is again a position parameter. The 1991a). program yielding the household's opti- mal actions is: The Equilibrium Maximize a log c + 13log(e'-e) In order to characterize the equilib- + -ylog(m/pe) such that rium, we shall successively consider the optimal actions of the firm and house- fpc + m-mO + we +T -pT (A2) hold. Consider first the firm, and assume 1 -? OwTh. that it perceives demand curves for goods The first order conditions yield, calling of the form Op-', where X > 1 is given X the " of income," and 0 is a variable "position" parameter; and after elimination of 0: the optimal actions of the firm are given by the program: au au = - =Xp (38) Maximize py - we such that am ac - {y cop s. (1 a(fo ) Aw(1e)@ (9 Note that in all rigor we should add a With our particularCobb-Douglas util- quantity constraint on e since the firm ity function, these yield, defining ,B' = is a wage taker on the labor market. But E3/(E-1): we know that the household will always choose a wage high enough for the firm pc = aX + PI + y (weo + 'r + mO-pT) (40)

14 Macroeconomicmodels with imperfectcompeti- - W(,eo-e)= = +P++ + tion were developed notably in Benassy (1978, 1982, P' -y 1987, 1990, 1991), Negishi (1978, 1979), Yew-Kwang Ng (1980, 1986), Oliver Hart (1982), Martin Weitz- (wto + r + mO-PT). (41) man (1982, 1985), Dennis Snower(1983), Torben An- dersen (1985a, 1985b), Kiyohiko Nishimura (1986, We may note that these equations re- 1992), Svensson (1986), Blanchardand Nobuhiro Ki- semble the competitive ones (equations yotaki (1987), Huw Dixon (1987a, 1991), Henri 23 and 24 in Section IV.A), with ,3 re- Sneessens (1987), Silvestre (1988, 1989), Jacobsen and Schultz(1990), MarcoPagano (1990). This section placed by ,3'. Of course we must add is adapted from Benassy (1978). the budget constraint of the household: Be'nassy: Nonclearing Markets 753

pc + m= mO + wte + - P. (42) Secondly, we may remark that we are somehow in a "general excess supply" be- Finally we still have the equality regime. Indeed program A1 and equation tween production and total demand (36) show that the firm would be willing, y = c + g. (43) at the equilibrium price and wage, to sell more goods (and hire more workers), if Solving the system of equations (36, the demand was forthcoming. Similarly 37, 40-43) we find that the values of y, program A2 and equation (39) show that e, p, w in equilibrium (if it exists) are the household would like to sell more given by: labor at the going price and wage, if there Ft(f)(o - e) was more demand for it. In the diagram of Figure 4, the equilibrium w and p = 6 * X X [F(e)-g] (44) would yield a point within region K. e-1 Xg-lox There is and under- y = F(e) (45) production, even though both are volun- tary and individually rational. -= F(e) (46) Now let us come back to equation (44) p 'ii which gives the level of employment at p = otmOam(47)( equilibrium. We see that it is smaller - - than Walrasian employment, and actu- *yy- g) ot(g T) ally a decreasing function of the "market We may first note that the Walrasian power" of both firms and (the equilibrium is a limiting case of our equi- "Lerner indices" of market power are librium when both X and e go to infinity equal respectively to 1M on the output (compare equations 44 to 47 with equa- market and 1/e on the labor market). Fur- tions 25 to 28). Secondly the conditions ther, and though it is arrived at by fully for the existence of the equilibrium are rational behavior, this level of employ- again ment is inefficiently low in the following g < F(eo) sense: Assume that some "benevolent dictator" makes the household work t(g - ) < - g) (48) *Y more (say by de > 0) and gives the extra where y is given by (44) and (45). Though production dy = F(e) de > 0 to the they look the same, condition (48) is a household. Considering first the firm, we bit more stringent than condition (29) in see, using equation (36), that the varia- the competitive case, as the level of em- tion in its real profits would be: ployment given by equation (44) is smaller than the one given by (25). d('w/p)=- > 0. (49) Properties of the Equilibrium We shall now show that the allocation Considering now the household, we at our imperfectly competitive equilib- can compute the variation in its utility rium has properties similar to those of a as: "Keynesian" allocation, as described in au au Section IV. B above. Let us note first that dU=- dc +- de equation (47), inverted to give y as a func- dc ae tion of p, yields exactly formula (30) giv- ing Yk in the Keynesian regime when p which, using equations (36), (38), and (39) is exogenously given. yields: 754 Journal of Economic Literature, Vol. XXXI (June 1993)

point of view, one should include explic- dU=L 1- -l -d) 71 E1) itly government spending as an argument of the household's utility function. For -dy > o. (50) dc such a normative analysis, see Benassy (1991a). We see that both the firm (equation All in all, we see that this model yields 49) and the household (equation 50) an allocation which has very "Keynesian" would gain from the move. It can further inefficiency properties, but reacts to gov- be shown (Benassy 1987, 1990) that the ernment policy in a way which is some- household gains both as a wage earner what similar to that of a Walrasian model. (if LIE# 0) and as a profit earner (if 1/k D. Real and Nominal Rigidities15 # 0). Of course, and even though it is Pareto improving, it is very difficult to We shall now study briefly another envision such a "benevolent dictator" so- version of our , lution in a free market economy. More- which will allow us to throw some light over the complexity of actual exchanges, on the issue of "real" versus "nominal" and notably the lack of "double coinci- rigidites. If we consider the fixprice-fix- dence of wants," would make these addi- wage model of Section IV. B above, it is tional Pareto improving trades almost indeed not clear what kind of rigidities impossible to realize in a real world de- are actually at work: It might be that both centralized economv (Benassy 1990). We p and w are nominally rigid, or p nomi- shall thus examine..whether more tradi- nally rigid and the real wage (wlp) rigid, tional policies can bring about this in- or w nominally rigid and the "real crease in employment and production. markup"(plw) rigid (we may remark that, from this point of view, the imperfectly Government Policy competitive model of the preceding sec- We shall now try to find out whether tion displays two "real" rigidities). We government policies which were success- shall thus make things a little more ex- ful in the regime of Keynesian unemploy- plicit, and study a simple model with one ment are still so in this imperfectly real and one . We shall competitive framework. Studying first assume that both the nominal , we see that it is fully and the real wage are rigid downwards, neutral: An increase in mO will bring but flexible upwards, which we will rep- about an equiproportionate rise in p and resent by the conditions: w, and y and e will not move. Considering now a tax decrease, we p 'po W/p>-W. see that it does not have any impact on We may note that the first inequality y and e, but increases prices (equation implies that the household will never be 47) and thus wages (equation 46). In view rationed on the goods market. Consump- of condition (48), a too large tax decrease tion rationing clearly made the fixprice- might actually be inflationaryto the point fixwage model a bit unrealistic for free of jeopardizing the existence of an equi- market economies, as rationing on goods librium. If we finally consider an increase markets is seldom observed in such econ- in government spending g, we see that omies. As a result we shall always be "on it will increase employment and produc- the demand curve" (in a sense that will tion, but actually crowd out private con- sumption. In order to see whether this 5 The model in this section is adapted from B& would be desirable or not from a welfare nassy (1986). Be'nassy: Nonclearing Markets 755 become clearer below). In spite of this so that we have on the demand side of we shall still observe three regimes with the goods market: markedly different properties in this y = model (if an equilibrium exists): K(p,m^,g,r). The firm is unconstrained on the goods * Excess supply of labor and goods market (which clears) and on the labor (Regime A), market (where it is on the short side). * Excess supply of labor with the It carries thus its Walrasian plan, which goods market cleared (Regime B), yields, taking into account that wlp = : * Both markets cleared (Regime C) Regime A ("Keynesian") e* =F'F-1( With excess supply on both markets, the price will be blocked at pO and the We see here that only a reduction in real wage at o. the real wage X can cure unemployment, as in the "classical" regime of Section P = Po W/p = (0. IV. B. As we already emphasized, this oc- Output level will be determined by curs without any rationing on the goods demand in exactly the same way as in market. the "Keynesian" case of Section IV.B, yielding: Regime C ("Walrasian") y*= -(MO+g-_T +g Because both markets clear, we are in Y P the Walrasian case, described in Section IV.A (see equations 25-28). We shall not and comment on policies, which were dis- ,e*= F-'(y*). cussed there, but simply note for the se- quel that equation (28), inverted to give These are exactly the values found in y as a function of p, yields: the Keynesian unemployment regime of the fixprice-fixwage model, and employ- y = K(p,m.,g,r). ment will be increased through the same policy measures:An increase in mo, g, The General Picture or a decrease in T. For what follows it If we look at the systems of equations will be convenient to define a "demand similarin to giving the equilibrium values of y and p curve"K(p,mo,g,), spirit in each of the three regimes (as well as the "aggregate demand curve" of macro- the inequalities they must satisfy, which economic textbooks, by: are left to the reader), we see that they can be determined as the intersection in K(p,MO, g T) =g - T + g. (p,y) space of a "demand curve" and a "supply curve" (Figure 5), The "demand With this definition y* in this regime curve" has for equation: is simplyequal to K(pO,MO,g,T). y = K(p,mO,g,T). Regime B ("Classical") The "supply curve" consists of two real is blocked at o, Here the wage parts: A vertical part with equation p = but the price is now determined by the po. A horizontal part with equation: equality of . As in the previous regime, y is equal to demand, y = min{F[F''1((x)], yw} = min(yc,yj) 756 Journal of Economic Literature, Vol. XXXI (June 1993)

y we have seen that the economy can still have several regimes where it behaves as if mainly nominal rigidities were pres- ent (Regime A), mainly real rigidities were present (Regime B), or none was (Regime C). From that we deduce that interesting insights can be gained by an adequate combination of the two types

K(p,mo,g,T) of rigidities; and secondly that the same p system may react in a totally different P0 manner to different shocks, so that appar- Figure 5. ent "discontinuities" in observed behav- ior of economic series may come from a "change of regime" within the same eco- nomic system as well as from changes where is the yw, Walrasian value of y, in the system itself. given by equations (25) and (26) above. In Figure 5 (as well as from the above E. Rational Expectations and the formulas) we see immediately that the Multiplier16 equilibrium it will values (if exists) yield We shall finally describe an intertem- of y* and (*: poral extension of the model of the previ- y*= min{ K(po,mo,g,r), F [ F`1()], yw} ous section with explicitly rational expec- tations. This will e* =F-'(y*). be useful in several respects: Figure 5 also gives us the condition * It will demonstrate in the most sim- for the existence of an equilibrium, which ple manner that our is simply that the "demand"and "supply" approach is fully consistent with rational expec- curves intersect, i.e.: tations. * It will show that spillover effects lim K(p,M,,,g,T) < min(yw, y,) P2-3*00 work not only through current quantity constraints, but through Or: expected ones as well. If these inter- Ot(g - T)/y + g < min[yw(g), yj(w)] temporal spillovers are correctly taken into account, the multiplier a condition which is more stringent than the one for the existence of a Walrasian in Keynesian regimes will be higher than what we would expect from the equilibrium (equation 29) if w > value of the propensity to consume To summarize, this model with real out of current income (which may and nominal rigidities, although ex- be fairly low if one has a "permanent tremely simple, has taught us a few income" view things: The first is that one could obtain of consumption). both Keynesian type (Regime A) and clas- Our model will be a direct extension sical type (Regime B) unemployment of that in Section IV. D, but this time with the demand for consumer goods al- taking explicitly into account a sequence ways satisfied. The usual association of of periods indexed by t = 1, . . , k. "classical unemployment" with an excess In each period the price Pt and the real demand for goods is thus-clearly invalid. Secondly, even though both real and 6The model in this section derives from Neary nominal rigidities are present in all cases, and Stiglitz (1983), Benassy (1986). Benassy: Nonclearing Markets 757

wage wW/ptare flexibleupwards but rigid (regime A), and thus that Pi is blocked downwards. The aggregate household at its floor value. Equation (53) immedi- has a utility function ately yields a multiplier on current gov- ernment expenditures equal to + -y)/ U = Y. at log + Z log( - (ac, ct Pt et) -y. We see that, with expectations cor- + -y log mipe rectly taken into account, the multiplier where m is the quantityof money saved is the same as it would be in a one period and pe the price expected after the last model where the propensity to consume period (which may be thought of as the would be ac,/(ac,+ -y), whereas the pro- retirement time). Assuming the house- pensity to consume out of current income hold does not have any binding"liquidity is actually equal to (cf. equation 52): constraint,"its budget constraintsfor pe- a1 riods t = 1, . . . , k can be merged into the single followingone: X tt + -Y which may be much lower than acl/(acl Y, PtCt+ m = Y, PtYt+ mO -Tt + -y)if there are many periods. We thus where Tt is the nominal value of taxes see that not taking expectations into ac- in period t. We assume that the govern- count and considering only the propen- ment spends Gt in nominalterms in pe- sity to consume out of current income riod t,17 so that we will have might lead us to seriously underestimate the multiplier effects in a Keynesian re- = + t. PtYt PtCt Gt forall (51) gime. Because prices are flexible upwards, demandfor goods will alwaysbe satisfied. V. Conclusions It is then easy to check that, whatever the regime in each periodt, the following As compared with the Walrasian ap- equationsalways hold: proach, we have described in this article a more general and realistic view of the Ott market process, where the exchange of PtCt= E [mO+ ZpPtt-Z Tt] information consists not only of price sig- for all t. (52) nals, but also of quantity signals gener- ated in a decentralized fashion in each Putting together equations (51) and market by the agents' demands and sup- (52) for all t and solving the correspond- plies. All agents, including some explic- ing system we find: itly modeled price makers, take these sig- nals into account for their price-quantity ptyt =-[mO + Y Gt-Z Tt] + Gt decisions. The result is a more general formulation of demand and supply the- for all t. (53) ory, as well as of price making, that takes These equations are the multiperiod full account of the intermarket "spill- generalizationof the "demandcurve" in overs" generated by the quantity signals. Section IV.D. Note that these equations In particular we endogenized prices in hold whatever the regime (A,B,C) the a framework with fully rational price economy is in during period t. Assume markers. now that the economy is in a state of We saw that the Walrasian general Keynesian unemployment in period 1 equilibrium concept may be generalized to non-market clearing situations, gener- 17 Taking both taxes and government spending in ating consistent allocations for any posi- nominal terms is made only to simplify calculations. tive price system. This permits to build 758 Journal of Economic Literature, Vol. XXXI (June 1993) an equilibrium concept with fully flexible such as the one we provided. Thus it (though non-Walrasian) prices by deriv- would certainly be worthwhile to inte- ing rigorously an "objective demand grate the most relevant "New Keynes- curve" in a general equilibrium situation ian" insights into the general equilibrium with price makers. The concepts so ob- approach developed here. tained link the Walrasian, Keynesian, There are several prospective future and imperfect competition theories in a developments for research in the field manner that allows us to treat the corre- we have surveyed. On the theoretical sponding issues in a unified way, as dem- side, various theories of price formation onstrated in the macroeconomic applica- without an auctioneer can be developed tions of Part IV. Although the role of and integrated within the general equi- expectations is not at all the focus of this librium framework presented here. (So article we indicated, and emphasize far only imperfect competition under again, that our framework is consistent complete information has been fully inte- with both rational and nonrational expec- grated.) Insights should come not only tations. This leaves maximal flexibility to from macroeconomics, but also from mi- the model builder. croeconomic studies, particularly in the Some readers may be curious about fields of , labor, the relation between the approach devel- and financial markets. The methodology oped in this article and the currently and framework we outlined will permit popular "New ." the derivation of the micro and macro- Rather than a school of thought, New economic consequences of these new de- Keynesianism, recently described in the velopments, as well as the potential insightful survey by Robert Gordon consequences of economic policy pre- (1990), is a collection of contributions de- scriptions. signed to describe non-market clearing Though we did not discuss the empiri- price making derived from rational mi- cal literature, important work remains to crofoundations, the ultimate aim being be done on the empirical side. Our con- to rationalize Keynesian-type situations. cepts apply to various sorts of market This literature covers a wide range of economies, whether of the U.S. type or topics: Labor contracts, unions, insider- of the planned socialist type. But clearly outsider theory, efficiency wages, and the type of market imbalances observed menu costs, to name only a few. While will differ widely across countries, de- many of these ideas are worth pursuing, pending on the underlying economic and a problem with this literature (noted by institutional organization of markets. Gordon 1990) is that for the most part Further development of econometric these insights are of a partial equilibrium methods should allow us to choose the nature.18 But, as we have seen in this most relevant hypotheses for each coun- article, many interesting results (and cer- try and to characterize specific historical tainly most of the "true Keynesian" in- episodes. 19 sights) come from the "spillover" effects All this shows that this article, and the between several non-clearing markets in a full general equilibrium framework, 19Econometric work in this area is actuallya lively research domain. A bibliographycirculated by Rich- 18 There are of course exceptions to this qualifica- ard Quandtof PrincetonUniversity contained around tion, for example Russell Cooper and Andrew John 400 empiricalstudies in June 1990. For recent contri- (1988). Gordonhimself, though more empiricalthan butions see, for example, Dreze and Charles Bean the current article, is distinctly general equilibrium (1991), Jean-Paul Lambert (1988), Quandt (1988), oriented in his approach. Sneessens and Dreze (1986). Benassti: Nonclearing Markets 759

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