By Ryuzo Sato, Karl Shell
ISBN-10: 0126194602
ISBN-13: 9780126194609
This revised version illustrates the undying nature of his contribution to economics. The publication offers with quite a few subject matters in fiscal thought, starting from the research of creation features to the final recoverability challenge of optimum dynamic behaviour
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Extra resources for Theory of Technical Change and Economic Invariance. Application of Lie Groups
Sample text
Setting £ ( L , c) = η(Κ, L), we have the 2. 54 Holotheticity of a Technology canonical variable Ρ and the holothetic technology as P [ L , c(K, L)] = P(K, L) = G(f) + c9 where J d L / ß ( L , c ) = Ρ and } df/H(f) = G(f).
35 Existence o f a Lie T y p e of Technical Progress Proof Since the isoquant m a p is given, the differential equation (10) and an integrating factor (11) are known. Lemma 4 immediately suggests that the differential equation (10) is invariant under U = ξ d/ôK + η d/dL, where ξ and η are given by the integrating factor. However, since ξ and η are subject to the single condition (11), one of them may be chosen arbitrarily, and the other is determined uniquely. Hence there exists at least one U for any given M and N.
L;t0 + ôt) = φ(Κ, L ; δί\ L = φ(Κ, L;t0 + ôt) = φ(Κ, L ; δί\ where t0 is the value of the parameter determining the identical transformation (6-iii), and δί is an infinitesimal. Then we have δΚ = Κ — Κ = ξ(Κ, L) δί, (7) ôL = L — L = η(Κ, L) δί, 2. 28 Holotheticity of a Technology We shall call this an infinitesimal transformation of technical progress. Using 8 the symbol introduced by Lie (Appendix), we shall write this a s I/ = « K , L ) ^ + i K K , L ) ^ - . (70 Lemma 1 (Uniqueness of the Infinitesimal Transformation) type of technical change (5) has one and only one independent transformation (7').
Theory of Technical Change and Economic Invariance. Application of Lie Groups by Ryuzo Sato, Karl Shell
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