By Ronald W. Shephard (auth.)
This learn is the results of an curiosity within the fiscal thought of creation intermittently pursued prior to now 3 years. Over this era i've got bought mammoth 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 examine and secondly from undertaking N6 onr-27009 at Princeton Univer sity below the path of Professor Oskar Morgenstern. thankful acknowledgement is made to the ·Office of Naval examine for this help and to Professor Morgenstern, specifically, for his curiosity within the puolication of this study. The accountability for blunders and omissions, how ever, rests solely upon the writer. Professor G. C. Evans has given when it comes to an easy overall expense functionality, based exclusively upon output price, a remedy of yes points of the commercial idea of creation which has inherent generality and comfort of formula. The classical process of expressing the expertise of construction through a creation functionality is possibly much less restrictive than using an easy overall rate functionality, however it has no longer been utilized in a extra normal shape except to derive the conventional stipulations among marginal productivities of the standards of produc tion and their industry prices.
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Additional info for Cost and Production Functions
Then equati9ns (19) take the form (i 1, 2, ... 1) where for some i, Ai = 0, Bi 1. A production function defined in terms of independent factor applications is obtained ~ using the elimination i12l in ill, recalling that ~ ~ ~ considered ~ function of all factor inputs of the process, which results in ~ relationship U= 1\ ~(xl' x 2 ' ... , x A) (20) 1\ and, for any value of U, the surface ~ = U is the locus of alternative applications of the chosen independent factor variables xl' x 2 ' " ' , x A leading to the output rate U.
X A. The duality given in Sections ~ and 2. 2) ££ COST AND PRODUCTION FUNCTIONS 39 l,gll and the "unit cost surfaces" 1\ 1\ 1\ Q(U, Pl' •.. , PAl =1 (28) and the reduced production function (P..!!!. 1) with respect to Pl' ••• , PA restricted to 19§1. 3). A connection must be established "between the two functions ~ Q and Q. •. , x A and Pl' P2' ••. , Pn be any arbitrary system of independent factor variables and prices satisfying equations (24) and (25). •. , PA the equation 1\ 1\ 1\ Q(U, Pl' ...
1) where f(U) is the inverse function of • (q) in (32). (q) and feU). of Section 1, with We may regard the homogeneous function q as a scale ftinction defining the "level of application" of the 42 SHEPHARD factors of production, and corresponding to any level the relation 0'0 (34 ) characterizes the techo10gy of substitution of the independent factor variables xl' •.. , xn to produce an output ~ (0'0) = Uo ' A special geometric relation exists between the members of the family of homothetic production surfaces.