By Ronald W. Shephard (auth.)
This research is the results of an curiosity within the fiscal thought of construction intermittently pursued prior to now 3 years. Over this era i've got bought great aid from the place of work of Naval examine, first from a private provider consulting agreement without delay with the maths department of the place of work of Naval examine and secondly from undertaking N6 onr-27009 at Princeton Univer sity lower than the path of Professor Oskar Morgenstern. thankful acknowledgement is made to the ·Office of Naval learn for this aid and to Professor Morgenstern, specifically, for his curiosity within the puolication of this examine. The accountability for mistakes and omissions, how ever, rests completely upon the writer. Professor G. C. Evans has given by way of an easy overall price functionality, based exclusively upon output fee, a therapy of convinced facets of the industrial conception of creation which has inherent generality and comfort of formula. The classical process of expressing the expertise of creation through a construction functionality is possibly much less restrictive than using an easy overall fee functionality, however it has no longer been utilized in a extra normal shape except to derive the typical stipulations among marginal productivities of the criteria of produc tion and their industry prices.
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Extra resources for Cost and Production Functions
It is also possible that factors may be technologically combined in fixed ratios. with an Au zero for some equation (18) and only two of the a Ui not zero. The order of enumeration of factors is unimportant. Some R of the variables xi in illl may be solved in terms of the remaining A n - R. Let (19) (r A + 1. • ••• n) COST AND PRODUCTION FUNCTIONS 31 represent this solution. The coefficients a r' a ri are defined solely in terms of the given coefficients of equations (18). A selection of xl' x 2 ' ...
The homogeneity of r(Pl' ... , Pn ) follows from that of Q(U, Pl' •.. 1) of Section 3. Homotheticity of the production surfaces is ~ necessary ~ well ~ sufficient condition for the factorization of the cost function given El equation i32l. To verify the necessity, suppose that the cost function takes the form (35). Then, because of the duality established in Section 4, the distance function W defining the corresponding production surfaces is the minimum of the expression n L i=l Pi with respect to the variables Xi (39) Pl' ...
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' ... , PAl (29) is satisfied by virtue of (26). 1) corresponding to price parameters 1\ Pl' " ' , P'A satisfying (27). 1\ 1\ Conversely, let Xl' ... 1). •. •. , Pn equation (29) holds. • , xn is characterized by the degrees of freedom of the price variables PI' ••• , Pn in these equations. • , "PA. M solutions (30) (i = 1, 2, ...
Cost and Production Functions by Ronald W. Shephard (auth.)