Titlebook: Cost and Production Functions; Ronald W. Shephard Book 1981 Ronald W. Shephard 1981 Cost.Functions.Kosten.Produktionsfunktion.production

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Geometric Interpretation of the Duality Between Cost and Production Functionogeneous of degree one In the prices and the point R(p., P.) lies on the unit cost surface. The amounts x., x. of the factors of production which minimize cost, for given values U, P.’, p.’, define a point P(x., x.) on the production curve ψ(U,X.X.) = 1.

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The Problem of Aggregations of these aggregates. The quantitative expression of such theories of aggregates has been made in terms of index number measurement of the aggregates, defining the prototype variable as some average of the micro-economic components of the aggregate which it represents.

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Dual Determination of Production Function from Cost Functiontechnology. But it is to be expected, in some sense, that the functions . or . and the function Q given by (8) are equivalent statements of production alternatives, assuming that the process is organized for minimum costs. The arguments of this Section are directed to the establishment of the precis

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Geometric Interpretation of the Duality Between Cost and Production Functionfactor space, considering only two factors of production. The coordinate axes X., X. are used Interchangeably for amounts x., X. and prices p., p. of these factors. In this coordinate system the production curve ψ(U,X.X.) =1 (U constant) and the unit cost curve Q(U,X.X.) =1 (U constant) are approxim

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Constraints on the Factors of Productionon functions . and ., and cost per unit time given by (5) was defined without fixed charges per unit time independent of the prices and quantities. These simplifications were made for initial convenience and they may be substantially relaxed without essentially changing the previous analysis.

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The Cobb-Douglas Production Functionith . where x. ., z. . are values at some base time (t) of the factor applications x., z. and . is the value of σ at (t.). We shall think of the variables z. as denoting current rates of application of primary factors of production, e.g. the services of labor and land, and distinguish the rates x. a