By Ronald W. Shephard (auth.)
This research is the results of an curiosity within the monetary idea of creation intermittently pursued in past times 3 years. Over this era i've got acquired enormous help from the workplace of Naval learn, first from a private provider consulting agreement at once with the maths department of the workplace of Naval study and secondly from venture N6 onr-27009 at Princeton Univer sity lower than the course of Professor Oskar Morgenstern. thankful acknowledgement is made to the ·Office of Naval study for this aid and to Professor Morgenstern, specifically, for his curiosity within the puolication of this study. The accountability for error and omissions, how ever, rests completely upon the writer. Professor G. C. Evans has given by way of an easy overall expense functionality, based completely upon output price, a remedy of definite features of the industrial concept of creation which has inherent generality and comfort of formula. The classical technique of expressing the expertise of construction via a construction functionality is in all likelihood much less restrictive than using an easy overall expense functionality, however it has now not been utilized in a extra normal shape except to derive the typical stipulations among marginal productivities of the standards of produc tion and their marketplace prices.
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Additional info for Cost and Production Functions
In this coordinate system the production curve 1/I(U,X I X2 } = 1 (U constant) and the Wlit cost curve Q(U,X I X2 ) = 1 (U constant) are approximately sketched. Let Pl', P2' be some arbitrarily given prices of the factors of production. These prices define a direction OR, where the coordinates Pl' P2 of R are proportional to Pl', P2', that is Pl =TP1' and P2 = TP2'· The proportionality factor T i~ taken so that which can be done since Q is homogeneous of degree one in the prices and the point R(Pl' P2} lies on the Wlit cost surface.
Statistical studies of cost funct10ns are generally more access1ble than correspond1ng empirical investigat10ns of production funct1ons, because economic data are most frequently in pr1ce and monetary terms. Under some assumptions of mathemat1cal form, cons1stent with the hypotheSiS of minimum costs, the cost funct10n may be statistically est1mated and transformed by the duality principle to y1eld the corresponding measurement of production functionj and in this calculation certain 1ncidental relat10ns may be found to ex1st on the parameters of the function to be fitted wh1ch serve as an equation system in terms of wh1ch the statist1cal estimation can be made.
Gl. -/\ meters Pl' P2' ••• , PA is needed ~ correspond one-to~ ~ ~ minimum cost values of the independent factor COST AND PRODUCTION FUNCTIONS 37 variables xl' x 2 ' ·:·A xA in terms of eguations like l£2l. The composite prices Pi defined by equations (23) provided such a system of price parameters for the case of linear constraints, but suitable definitions cannot be given in a simple way for non-linear constraints without special assumptions about the functional form of the functions Hr. •. , n) where the P r ~ non-negative constants and the functions Hr ~ homogeneous of degree one.
Cost and Production Functions by Ronald W. Shephard (auth.)