John C. Eckalbar

Stable quantities in fixed price disequilibrium

Recent work in the area of non-Walrasian process analysis has focused on three primary deficiencies in the Walrasian tatonnement assumptions. These are the Walrasian neglect of endowment and spillover effects together with the failure to assign a special role for money. In detail: First, it has long been known that if trade takes place during the process of price adjustment, the resulting capital gains and losses coupled with the change in the distribution of commodities will tend to shift the position of the equilibrium. (For an early source, see 18, Book V, Chap. II].) This leaves the system with the problem of trying, so to speak, to close in on a moving target. This is the endowment effect. Surprisingly, Hahn, Negishi, and others (see 17; 1, Chap. 131) h ave found that stability follows in this class of models more readily than in Walrasian models. Second, Clower ]3] and Patikin [ 9, Chap. XIII] have argued that if trade takes place away from equilibrium, we should expect that non-zero excess demands in some markets will influence trading plans in other markets. This is the spillover effect. The classic case is that if a worker on the long side of the labor market cutting his planned consumption below its Walrasian level. Because of spillovers, the demands which actually get expressed in the marketplace can differ significantly, even in sign, from the demands which the Walrasian auctioneer responds to. Initially there was speculation that spillovers would generate instability and/or unemployment equilibria; but thus far the theoretical results are mixed (compare, for example, [ 11, IO]). Finally, Clower [4J has argued that the Patikinesque macromoney-general equilibrium models have not succeeded in formally distinguishing between money and other durables as a means of payment. Noting that the Walrasian budget constraint implicitly allows trading in any pair of commodities, he urges that a tighter restriction be introduced in the interest of enforcing the rule-“Money buys goods, and goods buy money; 302 0022.0531/81/050302-12502.00/O

On the use and misuse of the instantaneous speed of adjustment assumption

Abstract A commonly used simplifying assumption in dynamics is that one of the variables moves infinitely fast to its equilibrium value, given the current values of the slower variables. If a theorist believes that one of his variables is fast relative to the others, how safe is he in setting the system up as if the relatively fast variable were infinitely fast? How do the dynamics of the simplified system compare with those of the true system? In this paper, the notion of adjustment speed is analysed and a new definition is offered. It is found that the simplified system behaves like the true system only in highly unlikely cases.

Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay.

This paper investigates the dynamics of an SIR model of childhood vaccination under the assumption that the vaccination uptake rate depends on past values of disease prevalence. The delay kernel is a high order Erlang function, which allows no instantaneous feedback between prevalence at time t and vaccinations at time t. Multiple types of endemic equilibria are found, as are stable and unstable equilibria, periodic orbits, dependence on initial conditions, and apparent chaos.

Money, barter, and convergence to the competitive allocation: Menger's problem

Abstract This paper explores the propensity of a bilateral exchange economy to get stuck away from the competitive allocation even when the competitive prices have been established. This is Mengers Problem. Necessary and sufficient conditions for a Menger Problem are found to relate to the presence of corner solutions. When money is introduced, convergence can be established.

An Extended Duopoly Game.

Abstract The author shows how principles and intermediate economic students can gain a feel for strategic price setting by playing a relatively large oligopoly game. The author constructs a playoff matrix and discusses various strategies and outcomes. The game extends to a continuous price space and outlines various applications appropriate for intermediate micro students. Finally, to make it easier for others to tinker with the assumptions of the game, the author can provide the Mathematica code used to generate the table and figures.

Inventories in a dynamic macro model with flexible prices

This paper presents a disequilibrium macro model with inventories, rational expectations, and flexible prices. It is found that less than full employment equilibria are possible, even highly likely, in the intermediate term and that wage reductions will cause employment to drop. Increasing aggregate demand will raise employment only if it is done gradually. On a technical level, we have multiple switching lines, disconnected regimes, and a connected equilibrium set which borders on a switching Iline and otherwise lies in a single region.

Profit sharing and employment

Abstract Two disequilibrium macro models are constructed. Each has households and firms exchanging labour, money and storable output. One model has workers compensated by wages only, and the other has a profit sharing scheme. Contrary to earlier findings by Weitzman, both systems are found to be susceptible to a demand shock.

DYNAMICS IN AN SIR MODEL WHEN VACCINATION DEMAND FOLLOWS PRIOR LEVELS OF DISEASE PREVALENCE

This paper investigates an susceptible, infectious, recovered (SIR) model with childhood vaccination demand modeled as a function of prior levels of disease prevalence. Stability conditions for endemic and disease-free equilibria are uncovered, and both Hopf bifurcations and chaos are found with certain constellations of parameter values. Policy interventions directed toward increasing vaccination are explored, and the implied magnitudes of the external benefit of vaccination are modeled.

Profit sharing in a competitive environment

Abstract Nearly all theoretical discussions of profit sharing to date have, following Weitzman, assumed that firms are monopolistic or monopolistically competitive. The present paper investigates the employment effects of a profit sharing scheme in a competitive environment. It is found that profit sharing can actually reduce employment in the long run, since the profit share may produce subnormal profits and exit of existing firms.

Bilateral trade in a monetized pure exchange economy

Abstract A model is constructed having n traders and m commodities, one of which is money and must be used in every trade. Exchange rates are flexible. If bilateral exchange takes place whenever utility increasing trade is possible, the allocation matrix converges to the Pareto locus.