12Economic Dynamicsformqd=a−p. On the face of it this is dimensionally inconsistent.a∈[QT−1]andp∈[MQ−1] and so cannot be subtracted! The point is that the coefficient ofpis unity with dimension [Q2T−1M−1], and this dimension gets ‘hidden’.Example 1.4A typically dynamic version of example 1.3 is the cobweb modelqdt=a−bpta,b>0qst=c+dpt−1d>0qdt=qst=qt(1.5)Here we do subscript the variables since now two time periods are involved. Al-thoughqdtandqstare quantities per period to time with dimension [QT−1], theyboth refer to periodt. However,p∈[MQ−1] is for periodtin demand but periodt−1 for supply. A model that is specified over more than one time period is adynamic model.We have laboured dimensionality because it is still a much-neglected topic ineconomics. Yet much confusion can be avoided with a proper understanding ofthis topic. Furthermore, it lies at the foundations of economic dynamics.
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1 m, Nonlinear system, Multiple Equilibria, Nonlinearities