Disequilibrium Trade and Pricing of Durable Commodities

Abstract

The model proposed focuses on trade in disequilibrium with stocks or assets, i.e., durable commodities. Durability implies that the goods have a second hand value and that trade is possible through redistribution of fixed totals of commodity stocks. The first connotation in connection with stocks refers to financial items; bonds, shares, and money, items that only function as stores of value. However, we take a broader perspective, to commodities that also yield services that enter the utility functions. The best example is perhaps items of real estate, apartments and suburb villas, which we can take as the two commodities. Demand naturally shifts over time due to normal demographic change. Retired people move to central apartments, whereas families with children need the space of suburban villas. If real estate prices drift up, everybody becomes nominally more wealthy, so demographic change can cause substantial value drifts without any speculation being involved. Real estate preserves value more than most other durables, yet for most consumers they are just habitations. They also have the property that their total changes very little over time, so that they can be taken as fixed totals redistributed predominantly in disequilibrium. In this chapter we take the case of two agents and two commodities, so that we can use the familiar Edgeworth “box” with the two traders represented in opposite corners. Each agent has a simple Cobb-Douglas set of indifference curves, of opposite concavity. The curve of tangency points between the two sets, the traditional “cont(r)act” curve, provides an infinite set of possible equilibrium states. New is the setting of durable commodities, property distributions represented through points in the box that need not be on the “cont(r)act” curve. An external tâtonnement agent is assumed to devise a price search mechanism based on excess demand. The relative price announced determines the slope of the budget line, but new in the context is that it rotates through the actual property distribution point inside the box. Even if equilibrium cannot be attained at the price announced, the traders may yet find a deal profitable for both. If so, in general the amounts they wish to exchange are different, so it is assumed that the trader wanting to exchange less limits the deal. Then an exchange will take place, though it as a rule will not reach equilibrium, and there will remain some excess supply/demand after exchange. One can object that real estate items are “quantized”, but what is not in reality? It may also be the case that both want to exchange the same commodity for the other, and then no trade can take place. The dynamic system devised then sticks to such a disequilibrium point, while price goes on oscillating, always overshooting equilibrium price. It all depends on the adjustment step, if it is small, an equilibrium will be approached though very slowly, if it is big, approach is faster but price may overshoot equilibrium, and the exchange system stick to a disequilibrium for ever. It is difficult for the external agent to find out these things as the outcome may be very high period oscillation or even chaotic. Other conclusions are that the system may approach different equilibrium or disequilibrium states, depending on the initial point and adjustment step, and that exchange traces are irreversible, i.e., return to a previous price will not make the system return to a previous state. Unlike standard economics, unique demand and supply functions exist as little as do unique equilibria.