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Aggregation of individual demand to total, or market, demand

Given all the assumptions implicit in the economists conception of "rational" behaviour for a consumer, the consumer's demand curve can be derived from an infinite knowledge of the consumer's budget and preferences. The interpretation of this highly theoretical (hypothetical) relationship between price and quantity demanded of a given good is that, given all the other goods and constraints, this set of choices is that one which makes the consumer happiest.

A key step in microeconomic theory is the one which develops the aggregate, or market demand from the large set of individual demands. An important question is to understand the interpretation of the market demand curve. Does the aggregated demand curve show how to optimise the total utility (happiness) of society? Does it show how to optimise something else?

It cannot optimise total utility of society, since:

1) Each person's individual total utility gleaned from purchases depends on the size of her budget, but the distribution of wealth (and thus her budget) is a separate (free) variable in the aggregation. In other words, changing the distribution of wealth (such as giving needy people more resources) will produce a different total for society's utility.

2) Each person's demand curve is a function of her budget, so that if the distribution of wealth changes (by changing the distribution of prices and thus salaries, and so on), all of the individual demand curves change. The aggregate effect of such a change is not simple unless all the consumers have wealth-independent consumption patterns --- that is, unless the pauper and the billionaire spend the same fraction of their budgets on each item.

Given that the distribution of wealth is a function of price levels and is in general a free variable in any attempt at social optimisation, markets cannot be claimed to select by themselves an equilibrium nor an optimum.

It has been known since at least 1953 [Gorman, W.M., "Community Preference "Fields, Econometrica, 21: 63-80] and 1982 [Shafer, W. and Sonnenschein, H., "Market demand and excess demand "functions, in K. J. Arrow and M. D. Intriligator (eds), Handbook of Mathematical Economics (Vol. II), North-Holland, Amsterdam] that no reasonable assumptions can circumvent these problems. The method of this aggregation is typically not discussed at the undergraduate level, but its impossibility entirely invalidates the rest of microeconomic market theory. It tells us that a separate means must be used to choose policy for the distribution of wealth; the market "equilibrium" does not optimise anything if the distribution of wealth is allowed to vary.

Microeconomics ignores the issue of wealth distribution, assuming it to be a separable "political" issue; however, in the context of conceiving of a market demand curve, as in many others (e.g., international trade), microeconomists implicitly assume that wealth distribution is flat -- i.e., that wealth levels between components of society or trading partners are equal.

It is interesting to note that one method of justifying the aggregation of individual demand curves is to split society up into a variety of economic "classes" and to make the assumption that each class has a coherent set of preferences and a relatively inflexible level of wealth. Then different demand curves could be developed not for the entire market, but for different classes. Such an inflexible system is clearly not a "free market", in which prices affect wealth through employment, and economic mobility is in theory unlimited.

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