The market, commodities, and prices

We developed examples in Chapter 1 of general equilibrium economic systems characterized by N commodities. In Chapter 2 we developed the mathematics suitable for analyzing these economies using RN as the commodity space. A typical point in RN, x = (x1, x2, x3, …, xN), represents a commodity bundle. That is, x is a shopping list, x1 of good 1, x2 of good 2, and so forth through xN of good N. The coordinates xi may be either positive or negative (subject to interpretation). What are these N commodities? That turns out to be rather a deeper question than it appears, so we postpone a full discussion until Chapter 15. Meanwhile, in order to fix ideas, we should give a bit of interpretation.

The market takes place at a single instant, prior to the rest of economic activity. We think of the market meeting, demands being expressed, equilibrium achieved, and allocations decided, all prior to actual consumption or production taking place. This may be unrealistic, but it serves to fix the economic environment.

We think of a commodity as a good or service completely specified by its characteristics. We assume there to be a finite positive integer number of commodities, N. In a model where there are several locations, the same good at different locations will be treated as different commodities. Otherwise identical goods at different locations may then trade at different prices, entering differently in preferences; converting one good to the other requires a production activity (transportation).