## From Individual to Market Demand

Let us use xl(pi,p2,rrii) to represent consumer z's demand function for good 1 and mi) f°r consumer Vs demand function for good 2.

Suppose that there are n consumers. Then the market demand for good 1, also called the aggregate demand for good 1, is the sum of these individual demands over all consumers:

The analogous equation holds for good 2.

Since each individual's demand for each good depends on prices and his or her money income, the aggregate demand will generally depend on prices and the distribution of incomes. However, it is sometimes convenient to think of the aggregate demand as the demand of some "representative consumer" who has an income that is just the sum of all individual incomes. The conditions under which this can be done are rather restrictive, and a complete discussion of this issue is beyond the scope of this book.

If we do make the representative consumer assumption, the aggregate demand function will have the form X1(pi,p2, M), where M is the sum of the incomes of the individual consumers. Under this assumption, the aggregate demand in the economy is just like the demand of some individual who faces prices {p\,p2) and has income M.

If we fix all the money incomes and the price of good 2, we can illustrate the relation between the aggregate demand for good 1 and its price, as in Figure 15.1. Note that this curve is drawn holding all other prices and incomes fixed. If these other prices and incomes change, the aggregate demand curve will shift.

The market demand curve. The market demand curve is the sum of the individual demand curves.

For example, if goods 1 and 2 are substitutes, then we know that increasing the price of good 2 will tend to increase the demand for good 1 whatever its price. This means that increasing the price of good 2 will tend to shift the aggregate demand curve for good 1 outward. Similarly, if goods 1 and 2 are complements, increasing the price of good 2 will shift the aggregate demand curve for good 1 inward.

If good 1 is a normal good for an individual, then increasing that individual's money income, holding everything else fixed, would tend to increase that individual's demand, and therefore shift the aggregate demand curve outward. If we adopt the representative consumer model, and suppose that good 1 is a normal good for the representative consumer, then any economic change that increases aggregate income will increase the demand for good 1.