By Malinvaud E & Bacharach M
Read or Download Activity Analysis in the Theory of Growth and Planning: Proceedings of a Conference held by the International Economic Association PDF
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Extra resources for Activity Analysis in the Theory of Growth and Planning: Proceedings of a Conference held by the International Economic Association
If, as in Fig. 14B, the slope of S is of the same sign as that of S(ft*), then there exist infinitely many feasible sequences of zero-profit activities, that either converge towards, or move away from, z*, depending on whether the slope of Sis absolutely smaller (as in Fig. 14B) or larger than that of S(ft*). This holds regardless of whether z* is an endpoint of S or not. If z* is not an end-point, and if the slope of S is opposite in sign but not equal in absolute value to that of S(ft*), there are again infinitely many value-preserving paths, oscillating on S towards or away from z*, depending on whether the slope of S is absolutely smaller (as in Fig.
A case of this kind is not in any way a result of coincidence. In fact it is likely to arise except for coincidences in any technology with a finite basis. In McKenzie's work (1963b, c, d), cases of this kind are analysed in detail for n-commodity models. The present section is intended only as an intuitive exploration of the possibilities. To avoid still further complications, let us assume that positive prices PI> p 2 can be associated with z*. The situation is then as illustrated in Fig. 12.
Px (P') which implies in turn that (P") fk(X, y) ~ fk* for all activities with a positive input value. Thus the maximal proportional growth factor is at the same time an upper bound for the value growth factors of all feasible activities. Now let (xt, yt), t = 1, ... , T, be a maximal growth path as defined in Section X and illustrated in Fig. 9. Then x1 is the given initial stock, which for simplicity we normalize by x~ +x~ = 1. Furthermore, yt = xt + 1 for all t, and yT = K*h is the maximal final stock having proportions given by h = (h 11 h 2).
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