## Q

FIGURE 19.1 Hypothetical supply-and-demand functions and the identification problem.

There is an alternative and perhaps more illuminating way of looking at the identification problem. Suppose we multiply (18.2.1) by X (0 < X < 1) and (18.2.2) by 1 — X to obtain the following equations (note: we drop the superscripts on Q):

(1 — X) Qt = (1 — X)fo + (1 — X)Px Pt + (1 — X)u2t (19.2.9)

Adding these two equations gives the following linear combination of the original demand-and-supply equations:

where

Y0 = Xa0 + (1 - X)ß0 Y1 = Xa1 + (1 - X)ß1 Wt = XU1t + (1 - X)U2t

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