By Roos C.F.
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Additional info for A Dynamical Theory of Economic Equilibrium
If the number of different~chniques is finite, then a given technique, if it is applied at all, is applied at every interest rate within a given interval. The border points of these intervals on the r-axis are points at which two techniques (or, in exceptional cases, three and more) are equally efficient in the sense that they can operate at the same maximum wage rate. These border points are called ~itch points. As the rate of interest increases the economy switches at such a point from one technique to another technique.
Thus the value of capital per worker Vt/Lt coincides with the subsistence fund if and only if rand g are equal. We shall refer to this model as the point input point output model or the standard period of production model. We shall refer to the model presented in the first chapter as the standard production function model. In both cases the models have been constructed in such a way that certain concepts can be easily ~pplied and yield the correct results. But the two models already are inconSistent with each other.
E. their specific labour content are then given by n = (n 1 • • • • nn) with or in matrix notation net) = ao(t) + n(t-1) A Now. due to the growth of productivity the value of the commodities declines exponentially through time and we have net) = (1+y)-1 n(t-1) n(t-1) = (1+y) net) It therefore follows net) = (1+y)-t ao net) (I - (1+y) A) net) = (1+y)-t ao or + (1+y)n(t) A = (l+y)-t ao (I - (1+y) A)-1 If z (t) is the vector of final products or consumption and if z (t) - 28 grow. exponentially at rate y we have the equation x (t) = (I -(1+y) A)-1 z (t) = (I _(1+y)A)-1(1+y)t z and the labour requirements are L = = ao II (t) x (t) (t ) (1+y) t z = (1+y) -t = n (y) a o ( I -(1+y) A)-1 -z = z (t) The total value of final products is thus equal to L and hence independent of time.