Walrasian Price Research Articles

Pay More Tribute to Smart Ants: A Note on the Tullockian Environmental Coordination in Non–Human Societies

We show in this short note that the thesis in Tullock (1994) about how the environment coordinates the division of labor in non-human societies can be formulated by the fixed-point argument. As such, both what maybe called the Tullockian environmental coordination and the conventional Walrasian pricing coordination in economics turn out to be special cases of a more general principle, into which further exploration remains to be made.

A model of speculative behaviour with a strange attractor

An asset pricing model for a speculative financial market with fundamentalists and chartists is analysed. The model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms. Speculative bubbles arise as a complex non-linear dynamic phenomenon brought about naturally by the dynamic interaction of heterogeneous market participants. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes, finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists. This model could be a link between two opposite views over the behaviour of financial markets: the theorist's literature view that claims the random motion of asset prices, and the chartist's position extensively adopted by market professionals.

OPTIMAL MONETARY AND FISCAL POLICIES UNDER WAGE AND PRICE RIGIDITIES

We study a structural dynamic monetary economy submitted to technological, monetary, and real demand shocks, and investigate the nature of optimal monetary and fiscal policies under Walrasian or preset wages and prices. If prices and wages are Walrasian, then the optimal policies are both nonactivist and derive directly from Milton Friedman's prescriptions. If prices or wages are preset, however, optimal policies, and, notably, the fiscal part, become activist and countercyclical.

Continua of underemployment equilibria reflecting coordination failures, also at Walrasian prices

In this paper, the existence of unemployment is partly explained as being the result of coordination failures. It is shown that as a result of self-fulfilling pessimistic expectations, even at Walrasian prices, a continuum of equilibria results, among which an equilibrium with approximately no trade and a Walrasian equilibrium. These coordination failures also arise at other price systems, but then unemployment is the result of both a wrong price system and coordination failures. Some properties of the set of equilibria are analyzed. Generically, there exists a continuum of non-indifferent equilibrium allocations. Under a condition implied by gross substitutability, there exists a continuum of equilibrium allocations in the neighborhood of a competitive allocation, when prices are Walrasian. For a specialized economy, a dynamic illustration is offered.

The English Auction with Differentiated Commodities

We study economies (with indivisibilities) that satisfy the gross substitutes (GS) condition. We define an excess demand set with the property that increasing the prices of all goods in excess demand eventually leads to the smallest Walrasian prices. This procedure is a generalization of the auction studied by G. Demange, D. Gale and M. J. Sotomayor, Polit. Econ.94 (1986), 863–872. In our auction, truthful revelation of demand is a perfect Bayesian equilibrium if the smallest Walrasian prices correspond to the Vickrey–Clarke–Groves payments. However, no dynamic auction can reveal sufficient information to implement the Vickrey mechanism if all GS preferences are allowed. Journal of Economic Literature Classification Numbers: D4, D44, D5, D51.

Walrasian Equilibrium with Gross Substitutes

We study economies with indivisibilities that satisfy the gross substitutes (GS) condition. The simplest example of GS preferences are unit demand preferences. We prove that the set of GS preferences is the largest set containing unit demand preferences for which the existence of Walrasian equilibrium is guaranteed. We show that if a GS economy is replicated sufficiently many times, the equilibrium payment of any agent in the Vickrey–Clarke–Groves mechanism is equal to the value of the allocation he receives at the smallest Walrasian prices. The model extended to include production. Journal of Economic Literature Classification Numbers: D4, D44, D5, D51.

Double-edged population monotonicity of Walrasian equilibrium—a note on the nature of competition

We show that extending an economy by admitting new agents of an incumbent type has a double-edged effect on the Walrasian utilities of the original agents so long as substitution effect dominates income effect on the average (i.e. the inner product of price change and the change in aggregate demand is nonpositive) for the original economy at the Walrasian prices of the original and the extended economies: agents of the entrants' type are if anything hurt, and some others are if anything better off. We also show that, if aggregate demand in the subeconomy consisting of incumbent agents whose type is not replenished satisfies the generalized axiom of revealed preferences at these prices, then the converse is also true, so that the double-edged monotonicity in question is then characterized by the mentioned domination of substitution over income effect.

Price-Quantity Adjustment in a Keynesian Economy

In this paper a price and quantity adjustment process in continuous time is considered for an economy with production factors and final goods. We assume that each final good is produced by a constant returns to scale production technology with only factor goods as inputs. The price and quantity adjustments take place on the markets for factor goods only. During the process, the prices in the final good markets adjust instantaneously by setting the price of a final good equal to the production costs. Production adjusts instantaneously to meet the demand and keeping the output markets in equilibrium. The adjustment process consists of three consecutive parts. First, in the short run part of the process the factor prices are assumed to be rigid and only quantity adjustments take place until an out of equilibrium situation is reached in which on each market either equilibrium under supply rationing prevails or excess demand and no supply rationing is observed. Next, in the mid run the factor prices are adjusted upwards in markets with excess demand, while on the other factor markets the supply rationing is adjusted to keep them in equilibrium. This process of adjusting quantity constraints in factor markets with excess supply and prices on factor markets with excess demands is shown to lead to a supply constrained equilibrium. Thirdly, in the long run the factor prices in markets with supply constraints are decreased, whereas supply constraints and prices in all other factor markets adjust to keep those markets in equilibrium. It is shown that eventually a Walrasian price system is reached.

Maximum score estimation of disequilibrium models and the role of anticipatory price-setting

In this paper, a general model of disequilibrium quantity determination under median regression assumptions is combined with weak assumptions on the price adjustment to yield a consistent maximum score estimator. In contrast to Sapra (1986), the supply and demand parameters are separately identifiable and the estimator employs all of the observed data. The price adjustment assumptions can be motivated by the anticipatory pricing model of Green and Laffont (1981). In contrast to the Green–Laffont model, however, our assumptions only require that long-run Walrasian prices have positive probability. As an illustrative application, maximum score estimates of a model of the US commercial loan market are computed and compared to maximum likelihood estimates. Monte Carlo results are also reported.

Market Making by Price-Setting Firms

A model of market making by firms with heterogeneous consumers, suppliers and price-setting intermediaries is examined. Consumers and suppliers engage in time-consuming search for the best price and discount future returns. There exists a unique symmetric equilibrium pricing strategy. In equilibrium, there are non-degenerate distributions of ask and bid prices that straddle the Walrasian price. As the discount rate goes to zero, the ranges of the bid and ask prices, and the total output approach the Walrasian equilibrium values. As the discount rate becomes large, the ask and bid prices approach the monopoly pricing policies. An increase in the discount rate leads to an increase in the equilibrium number of active firms, profit per firm, the mean spread between ask and bid prices, and the variance of ask and bid prices, while lowering the number of active consumers and suppliers. The model is extended to examine the steady-state market equilibrium with continual entry and exit of consumers and suppliers.

Labor Contracts and Business Cycles

This paper investigates the claim, often put forth by real business cycle proponents, that the poor performance of their models in matching real-world aggregate labor market behavior is due to the fact that observed real wage payments do not correspond to the actual marginal productivity of labor but contain an insurance component that cannot be accounted for by the Walrasian pricing mechanism. To test this idea, we dispense with the Walrasian description of the labor market and introduce contractual arrangements between employees and employers. Assuming that employees are prevented from accessing capital markets and are more risk averse than employers, we use the theory of optimal contracts to derive an equilibrium relation between aggregate states of the economy and wage-labor outcomes. This contractual arrangement is then embedded into a standard one-sector, stochastic neoclassical growth model in order to look at the business cycle implications of the contractual hypothesis. The resulting dynamic equi...

Decentralized Markets and Endogenous Institutions

This paper is concerned with decentralized models of market equilibrium in which the primary interest lies in the nature of the institutions that govern trade. There are two separate branches in this literature. In the first, the institutions that govern trade are taken to be given exogenously. The primary motivation for models in this class is essentially the study of comparative institutions. In particular the papers are interested in whether there are specific institutions that will generate Walrasian prices and allocations approximately when transactions costs are small. In the second branch of the literature, the institutions that govern trade themselves are made endogenous. These models characterize the nature of these endogenously generated institutions and examine their efficiency in environments where transactions costs are small.

Incentive-Consistent Matching Processes for Problems with ex Ante Pricing

In a non-stationary matching problem sellers can compete for potential trading partners by making ex ante price offers publicly before the matching process occurs in each period. This paper introduces the concept of an incentive-consistent matching technology in which buyers have no incentive to modify the allocation generated by the matching technology when there is a price deviation. It is shown that when the matching technology is incentive-consistent all trades must occur at prices close to the Walrasian price when transactions costs are small. Journal of Economic Literature Classification Numbers: D46, D83.

Transactional risk, market crashes, and the role of circuit breakers

The authors develop a pair of models that illustrate how imperfections in transfunctional mechanisms can lead to a market crash. Neither market orders nor limit orders allow traders to condition their demands on the full information set needed to achieve a Walrasian outcome. When volume shocks are sufficiently large, the deviations from Walrasian prices and allocations are large also. Properly designed and implemented, circuit breakers may help to overcome some of these informational problems and thereby improve the market's ability to absorb large volume shocks. Copyright 1991 by University of Chicago Press.

On the complexity of simultaneous price-quantity adjustment processes

While the Walrasian price tâtonnement represents the traditional dynamic process in the general equilibrium context with and without production, Walras and other classics designed the process exclusively for pure exchange economies. In productive economies, the short-run output adjustment of existing firms and the entry/exit of firms should be modeled as well. So-called cross-dual processes which represent the classical approach to the dynamics of productive economies are discussed and extended. Complex motion can emerge in a discrete-time version of the original two-dimensional system when the aggregate demand function has a non-standard shape. A simultaneous process of price and short-run quantity adjustment with free entry and exit of competitive firms in a single market with a continuum of firms can generate closed orbits via a Hopf bifurcation when the slope of the demand function is positive at equilibrium. When the continuum economy is replaced by an economy with a finite number of firms, noisy limit cycles and complicated behavior can be observed.

A Disequilibrium Rational Expectations Model with Walrasian Prices and Involuntary Unemployment

A fixprice, non-Walrasian temporary equilibrium which co-exists with the Walrasian equilibrium at Walrasian temporary equilibrium prices, has been called “unsatisfactory” by Hahn. If consumers live, and work, for two periods, expectations of future unemployment easily (in particular with normal goods) generate unsatisfactory Keynesian unemployment equilibria, if these expectations reflect serial correlation in unemployment. Assuming that the choice of temporary equilibrium (Walrasian or Keynesian) is governed by an extraneous, “serially correlated” random variable (sunspots), a long-run equilibrium of an overlapping-generations model is presented which has persistent Walrasian prices, rational expectations and intermittent phases of Keynesian unemployment and Walrasian full employment.

Transactional Risk, Market Crashes, and the Role of Circuit Breakers

The authors develop a pair of models that illustrate how imperfections in transfunctional mechanisms can lead to a market crash. Neither market orders nor limit orders allow traders to condition their demands on the full information set needed to achieve a Walrasian outcome. When volume shocks are sufficiently large, the deviations from Walrasian prices and allocations are large also. Properly designed and implemented, circuit breakers may help to overcome some of these informational problems and thereby improve the market's ability to absorb large volume shocks. Copyright 1991 by University of Chicago Press.

A Dispersed Spatial Price Equilibrium Model

The classical spatial price equilibrium models of Takayama and Jadge was based on trade market of homogeneous goods with perfect information about prices and market, however, as pointed out by many recent literatures, the purchasers are usually spread over several supply regions because of product differentiation, imperfect choice heterogoneity, gravity-type trade models derived from entropy or cost minimization theory have been presented as flow models without a price adjustment mechanism.In the excess supply conditions existing currently in many bulk commodity markets, the producers are increasingly in the position of price-takers. This implies that, in the short run, their main decisions relate to spatial choice of markets and setting of production levels within the currently available capacity.In this paper, at the outset, a random utility theory is introduced to handle dispersion about the profit-maximising choice of markets, then, taking market prices and available production capacity as given, the equivalent mathematical optimization model is presented to deal with dispersion of production levels by suppliers. It is shown that the resultant trade model is consistent with the one derived from the random utility theory. While the model assumes that the producers in the short run set their production levels and choose their markets to maximize profits under conditions of uncertainty, the buyer regions are merely assumed to adjust prices through exogeneous demand functions to equilibrate with the quantities supplied. This Walrasian price adjustment process towards equilibrium is examined and proofs of existense, uniqueness and stability are warranted by decreasing property of the regional demand functions and the spatial supply functions derived from the the mathematical optimization framework being with a finite dispersed parameter.

Undominated prices in the three good model

Any movement away from Walrasian prices will make somebody worse off. We ask: Which other prices share this property? The paper characterizes the set of such prices, called ‘undominated prices’, for the three good economy (output, labor and a nonproduced good) that is now well known from the work of Barro-Grossman, Benassy and Malinvaud. We consider two groups of consumers: workers and shareholders. We show that, under some conditions, there exist prices and wages that generate unemployment and are undominated. This requires that (a) workers be poorly endowed with the nonproduced good, (b) there be little substitution in consumption between the produced and the nonproduced good, and (c) the market for the produced good be balanced (i.e., prices equal marginal costs).

PRE-SET PRICES, DIFFERENTIAL INFORMATION AND MONETARY POLICY

Most studies of the implications of fixed, predetermined or 'disequilibrium' prices have taken resort to some ad-hoc assumption concerning price formation as for instance the anticipatory price setting rule (Green and Laffont, 1981; Brunner, Cukierman and Meltzer, 1983). According to this price rule prices are predetermined equal to the rationally (homogeneously) expected Walrasian price level. However, this approach does not come to issue with the main criticism of the assumption of instantaneous market clearing, namely, that it does not delegate the price-decisions to welldefined agents pursuing well-defined objectives (Arrow, 1959). Prices remain therefore to be set by a third-party or auctioneer, although not a Walrasian auctioneer. In the present study we shall give up the assumption of instantaneous market clearing and propose a way in which an economy with predetermined prices can be constructed such that the identity and objective of price setters are well-defined. The present paper starts out from the criticism made by Arrow (1959) of the instantaneous market clearing assumption by delegating the price decisions to well-defined agents (firms) who pursue well-defined objectives. As forcefully argued by Hayek (1945) most economically relevant information is decentralized, and we analyse the coordination problem which arises when numerous price setters quote prices on differential or decentralized information. The differential information structure arises naturally from the fact that each firm observes its own sales (quantity signal) and costs (price signal). Besides this private information agents have access to aggregate information which becomes available to all agents through price figures (price signals) and output figures (quantity signals). These different sources of information are explicitly considered in the present study.