## Demandandsupply Model

As is well known, the price P of a commodity and the quantity Q sold are determined by the intersection of the demand-and-supply curves for that commodity. Thus, assuming for simplicity that the demand-and-supply curves are linear and adding the stochastic disturbance terms u1 and u2, we may write the empirical demand-and-supply functions as

Demand function: Qf = a0 + a1 Pt + u1t a1 < 0 (18.2.1)

Supply function: Qf = p0 + p1 Pt + u2t p1 > 0 (18.2.2)

Equilibrium condition: Qd = Qf

(Continued)

2These economical but self-explanatory notations will be generalized to more than two equations in Chap. 19.

CHAPTER EIGHTEEN: SIMULTANEOUS-EQUATION MODELS 719

EXAMPLE 18.1 {Continued)

where Qd = quantity demanded Qs = quantity supplied t = time and the as and fS's are the parameters. A priori, a1 is expected to be negative {downward-sloping demand curve), and p1 is expected to be positive {upward-sloping supply curve).

Now it is not too difficult to see that P and Q are jointly dependent variables. If, for example, u1t in {18.2.1) changes because of changes in other variables affecting Qd {such as income, wealth, and tastes), the demand curve will shift upward if u1t is positive and downward if u1t is negative. These shifts are shown in Figure 18.1.

As the figure shows, a shift in the demand curve changes both P and Q. Similarly, a change in u2t {because of strikes, weather, import or export restrictions, etc.) will shift the supply curve, again affecting both P and Q. Because of this simultaneous dependence between Q and P, u1tand Pt in {18.2.1) and u2tand Pt in {18.2.2) cannot be independent. Therefore, a regression of Q on P as in {18.2.1) would violate an important assumption of the classical linear regression model, namely, the assumption of no correlation between the explanatory variable{s) and the disturbance term.