A Note on a Class of Utility and Production Functions Yielding Everywhere Differentiable Demand Functions.
In a recent article in The Review of Economic Studies, Dhrymes [2] discusses some conditions for the differentiability of demand functions in the case where one does not require knowledge of derivatives beyond those of the second order to determine whether a given stationary point is an extremum. St...
| Publicado en: | Review of Economic Studies Vol. 36; no. 1; pp. 109 - 112 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Oxford University Press / USA
Jan69
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=4622561&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 4622561 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00346527 REM jtl: Review of Economic Studies issn: 00346527 maglogo: N pubinfo: dt: Jan69 vid: 36 iid: 1 pid: 622 pub: Oxford University Press / USA artinfo: ui: 4622561 10.2307/2296347 ppf: 109 ppct: 3 formats: tig: atl: A Note on a Class of Utility and Production Functions Yielding Everywhere Differentiable Demand Functions. aug: au: Barten, A.P. Kloek, T. Lempers, F.B. affil: University of Louvain, Netherlands School of Economics, Netherlands School of Economics su: Production (Economic theory) Utility theory Demand function Production functions (Economic theory) Consumer behavior Mathematical models of economics Mathematical economics Matrices (Mathematics) Mathematical models of consumption Economic models sug: subj: Production (Economic theory) Utility theory Demand function Production functions (Economic theory) Consumer behavior Mathematical models of economics Mathematical economics Matrices (Mathematics) Mathematical models of consumption Economic models ab: In a recent article in The Review of Economic Studies, Dhrymes [2] discusses some conditions for the differentiability of demand functions in the case where one does not require knowledge of derivatives beyond those of the second order to determine whether a given stationary point is an extremum. Starting from production and utility functions with non-singular Hessian matrices, he develops the well-known salient propositions of the theories of the firm and consumer behaviour (see, e.g. Samuelson [3]), using convenient matrix notation to avoid cumbersome properties of determinants. On the one hand, it is well-known (see, e.g., Theil [4]) that the case of constant returns to scale in the theory of the firm involves a singular Hessian. On the other hand, the assumption of a Hessian with rank less than n-1 must be ruled out, since it would contradict the traditional second-order concavity conditions. In this note we shall show that for some propositions of Dhrymes [2] we are still able to derive the same properties if the Hessian is singular with rank n-1. Extension to the other propositions and their conclusions is obvious and hence deleted. We have adopted the notation used by Dhrymes [2] throughout. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 1969 holdings: @attributes: islocal: N |
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