Economics Dynamics Problems 26

Economics Dynamics Problems 26 - 10 Economic Dynamics...

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10 Economic Dynamics Figure 1.1. period t + 1. Thus x t 1 is the stock at the end of period t 1 and x t is the stock at the end of period t . Now let z t be a flow variable over period t , and involving dimension [ T 1 ]. Of course, there is also z t 1 and z t + 1 . Now return to variable x . It is possible to consider the change in x over period t , which we write as ± x t = x t x t 1 This immediately shows up a problem. Let x t have dimension [ Q ], then by propo- sition (1) so would ± x t . But this cannot be correct! ± x t is the change over period t and must involve dimension [ T 1 ]. So how can this be? The correct formulation is, in fact, ± x t ± t = x t x t 1 t ( t 1) [ QT 1 ] (1.3) Implicit is that ± t = 1 and so ± x t = x t x t 1 . But this ‘hides’ the dimension [ T 1 ]. This is because ± t [ T ], even though it has a value of unity, ± x t t [ QT 1 ]. Keeping with the convention
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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