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Such settings are called perfectly competitive markets, which we will discuss in detail

in Chapter 7. For now, note that price and quantity in competitive markets are

determined simultaneouslyby supply and demand. Let’s consider the implica-

tions of this with a simple example.

Suppose both the quantity supplied and the quantity demanded depend

only on price, except for some random terms:

where eand are random variables. The random terms indicate that both the

supply and demand curves jump around a bit. The equilibrium will be deter-

mined by the intersection of the supply and demand curves. Figure 4.2a shows

these curves with random shifts, as well as the price-quantity outcomes that

these curves might generate.

Now, look only at the points in part (a) of Figure 4.2, and imagine try-

ing to use these data to estimate either supply or demand. For this particu-

lar example, the “best line” appears in part (b) of the figure. Is this an

estimate of the supply curve, the demand curve, or what? The problem is

that, because price and quantity are determined simultaneously, we cannot

tell whether two points differ because of randomness in supply, in demand,

or in both; that is, we cannot identify which curve is responsible. Simultaneity

(in the determination of price and quantity) means that the regression

approach may fail to identify the separate (and simultaneous) influences of

supply and demand.

When is identification possible? The easiest case occurs when supply

fluctuates randomly, but demand does not. This leads to a situation like the

one portrayed in Figure 4.2c. In this case, all of the points will be along a sta-

tionary demand curve. Consequently, there is no problem estimating

demand, although estimating supply remains impossible. We say that

demand is identified, but supply is not. In the converse case, where demand

fluctuates, but supply does not, only the supply curve is identified. What if

both demand and supply fluctuate? If the supply or demand functions

depend on other variables, we can use specific statistical techniques to iden-

tify one or both functions. These techniques are beyond the scope of this

book. For our purposes, the lesson is that we must look carefully at the rela-

tionships being estimated and be on the lookout for simultaneously deter-

mined variables.

OTHER PROBLEMS Finally, it is important to recognize that the regression

approach depends on certain assumptions about randomness. To be explicit,

let us rewrite the multiple-regression equation as

QabPcPdYe. [4.11]

QScdP

QDabPe

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