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This has concerned me for some time: basic economic concepts such as preference relations and equilibrium, and the law of one price derived from them, are often misunderstood. Today, @takuyakitagawa said something like, “Yesterday I wanted wine, but today I feel like sake, so I suppose the preference relation does not hold.”

kitagawa-utility

I suspect this misunderstanding arises because economics’ concept of a good has not been properly conveyed. So, accepting some slight inaccuracy, I will explain it boldly and simply.

In economics, a good means the state at a particular time and place of something having certain physical properties. Thus there is no good called “wine.” Even Chateau Margaux 1992 in the same glass is treated as a different good at this moment and the next. If we accept the assumption that one object cannot simultaneously exist in 2 places, an object with given physical attributes can be represented, with t as the time index, as xi = {xit | ∀t ∈ Z}. Here each xit is 1 good.

The law of one price says that when a transaction in a specific xt occurs, there is only 1 transaction price. This seems almost self-evident, though on reflection it is not. It emphatically does not mean that xt and xt+1 are identical, nor that the prices of 2 goods in the same category, such as taxis in different locations, are identical.

Preference relations are similar. Introductory economics textbooks often explain them by asking whether one prefers tea or coffee, but as the above shows, the actual comparison is between a particular cup of tea at a particular time and a particular cup of coffee at a particular time. Thus, in @takujikitagawa’s example, yesterday’s wine and today’s wine are different goods, so there is no contradiction in wanting wine yesterday and sake today. More precisely, an actual preference relation compares entire bundles of goods, xi and x‘i , rather than single goods, so quantities of other goods also matter. Preference relations may differ among individuals; indeed, they must differ. To dispense with the assumption that individual preference relations are convex, preference relations must vary among individuals and income must also be dispersed. Otherwise an equilibrium may not exist. Conveniently, our actual preferences and income distribution satisfy these conditions.

Economics thus models reality under assumptions extremely close to the circumstances in which we actually live. That is why it is useful. If it assumed that everyone had identical preferences, it would be so remote from reality as to be frankly useless.

General equilibrium theory proves that an equilibrium exists under such general assumptions, and further proves that the equilibrium is Pareto optimal. This serves as a benchmark. Various market failures are then introduced to derive non-optimal equilibria, and one considers what additional assumptions—policies—should be introduced to bring them closer to an optimal equilibrium. Often these policies are not obvious and are frequently counterintuitive. Economics is useful precisely because it teaches us such counterintuitive things.

Oops, it is already half past nine, Munich time. This is serious. I need to hurry out for dinner!

Well then!

 

 

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