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By Timothy J. Coelli, Dodla Sai Prasada Rao, Christopher J. O'Donnell, George Edward Battese

Softcover model of the second one version Hardcover. encompasses a new writer, Dr. Chris O'Donnell, who brings enormous services to the undertaking within the zone of functionality dimension. a variety of themes are being additional and extra purposes utilizing genuine information, in addition to routines on the finish of the chapters. information units, desktop codes and software program may be on hand for obtain from the internet to accompany the quantity.

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Then the short-run cost minimisation problem can be written <:(w,q,x^) = min w[,x^+w^x^ suchthat r(q,x) = 0. 33) Note that this problem only involves searching over values of the variable inputs. 23. 5 (although the nonnegativity property can be strengthened - the short-run function is strictly positive owing to the existence of fixed input costs). , the function is nondecreasing in fixed inputs). To illustrate these last two properties, suppose the second input in our CobbDouglas production function q = Ix^'^x^^^ is fixed.

L Nonnegativity: x,(p, w) > 0. 2 Nonincreasing in w: dx^(p,yv)/dw^ <0. 3 Homogeneity: qm(kp^kw)='qm(P,yy) for/:>0. 4 Symmetry: ^^. (P, w) / dp^ = dq^ (p, w) / dp^. 0. q^(p, w) > 0. 3). 5). 4) and the result that the first derivative of any linearly homogeneous function is homogeneous of degree 0. 4 follow from the fact that the REVIEW OF PRODUCTION ECONOMICS order of differentiation is unimportant (Young's Theorem). example, 39 This means, for ^•y„(P>w) ^ a';r(p,w) ^ 8V(p,w) ^ dx,„{p,w) Again, these properties can be used to explore the effects of possible changes in economic policy.

CoelU and Perelman (1999, 2000) and O'Donnell and CoelU (2004) provide a discussion of methods for estimating parametric stochastic frontier specification of the distance functions and illustrate their use in an analysis of technical efficiency in European railways. Estimated distance functions have also been used in deriving measures of shadow prices (Fare et al 1989, 1993). 2. 4 Efficiency Measurement using Distance, Cost and Revenue Functions The primary purpose of this section is to outline a number of commonly-used efficiency measures and to discuss how they may be calculated relative to a given technology that is represented by some form of frontier function.

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