P P P Pp P

Figure 16.2

curve, the price P, will lead to Q2 as the quantity supplied in period 2, and to clear the market in the latter period, price must be set at the level of P2 according to the demand curve. Repeating this reasoning, we can trace out the prices and quantities in subsequent periods by simply following the arrowheads in the diagram, thereby spinning a "cobweb" around the demand and supply curves. B\ comparing the price levels, P0, Px, P2,..., we observe in this case not only an oscillatory pattern of change but also a tendency for price to widen its deviation from P as time goes by. With the cobweb being spun from inside out, the time path is divergent and the oscillation explosive.

By way of contrast, in the case of diagram b, where 8 < y8, the spinning process will create a cobweb which is centripetal. From P0, if we follow the arrowheads, we shall be led ever closer to the intersection of the demand and supply curves, where P is. While still oscillatory, this price path is convergent.

In Fig. 16.2 we have not shown a third possibility, namely, that of 8 = /?. The procedure of graphical analysis involved, however, is perfectly analogous to the other two cases. It is therefore left to you as an exercise.

The above discussion has dealt only with the time path of P (that is, Pt)\ after P is found, however, it takes but a short step to get to the time path of Q. The second equation of (16.10) relates Qdt to Pr so if (16.12) or (16.12') is substituted into the demand equation, the time path of Qdl can be obtained immediately. Moreover, since Qd, must be equal to Qst in each time period (clearance of market), we can simply refer to the time path as Qt rather than Qdr On the basis of Fig. 16.2, the rationale of this substitution is easily seen. Each point on the D curve relates a Pj to a Qt pertaining to the same time period; therefore, the demand function can serve to map the time path of price into the time path of quantity.

You should note that the graphical technique of Fig. 16.2 is applicable even when the D and S curves are nonlinear.

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