Journal Article Further Comments Get access Lionel McKenzie Lionel McKenzie Rochester, N. Y. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 25, Issue 3, June 1958, Page 200, https://doi.org/10.2307/2295989 Published: 01 June 1958

Journal Article Demand Theory Without a Utility Index Get access Lionel McKenzie Lionel McKenzie Durham, North Carolina Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 24, Issue 3, June 1957, Pages 185–189, https://doi.org/10.2307/2296067 Published: 01 June 1957

The Turnpike Theorem of Morishima Get access Lionel W. McKenzie Lionel W. McKenzie Rochester Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 30, Issue 3, October 1963, Pages 169–176, https://doi.org/10.2307/2296317 Published: 01 October 1963

Journal Article Specialization in Production and the Production Possibility Locus Get access Lionel W. McKenzie Lionel W. McKenzie Durham, North Carolina Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 23, Issue 1, 1955, Pages 56–64, https://doi.org/10.2307/2296152 Published: 01 April 1955

Journal Article Specialisation and Efficiency in World Production Get access Lionel W. McKenzie Lionel W. McKenzie Durham, North Carolina Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 21, Issue 3, 1953, Pages 165–180, https://doi.org/10.2307/2295770 Published: 01 January 1953

[Support prices are derived for weakly maximal paths in an optimal growth model which is time dependent but without uncertainty. The notion of "reachable" stocks and paths is defined and used to derive turnpike theorems by the value loss method. The proofs do not depend on the presence of optimal balanced paths nor on the usual transversality conditions. The theorems are extended to the classical model which has a non-trivial von Neumann facet.]

I SHALL PROVE two theorems using a new method in the problem of stability of equilibrium based upon the second method of Liapounov [4, p. 256ff.]. The novelty of method lies in the selection of the function V(p) whose decrease with time leads to the equilibrium position.2 This is the price weighted sum of the positive excess demands. I shall first prove the existence and stability3 in the large of the set of equilibrium points in the case of cross-elasticities which are nonnegative. The set of equilibrium points is compact and convex, and if the gross substitution matrix is indecomposable at equilibrium, the equilibrium is unique. When a numeraire is not present, it is possible to proceed beyond the limitation of nonnegative cross-elasticities to consider cases where certain weighted sums of the partial derivatives of excess demands with respect to prices are positive. This appears to be a natural generalization. Although the second theorem is primarily of local interest, one hardly need apologize for that. Global stability is not to be expected in general. This type of study was initiated by Walras [8, p. 170) and given its present formulation by Samuelson [5, p. 269]. I shall not elaborate on its limitations. Suffice it to say that, strictly interpreted, the groping for equilibrium which