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Extra info for An Introduction to Efficiency and Productivity Analysis
5. 2. Details are not provided in this chapter, for two reasons. First, we can view transformation functions as special cases of the distance functions discussed in detail in Chapter 3. Second, most applied economists analyse multiple-output technologies in ways that do not involve the specification of transformation functions or their properties. Some simply aggregate the outputs into a single measure using the index number methods discussed in Chapter 4 (and then use the production function to summarise technically-feasible production plans).
10 and suppose the second input is fixed at the value Xi = 100, at least in the short run. 1 with kxi and kx2 and observing what happens to output. 5. Of course, at some time in the future the firm might fmd that the second input is temporarily fixed at another value, say X2 = 150. 84 Ixj''. 5. 4. 3 Transformation Functions We can generalise the production function concept to the case of a firm that produces more than one output. 21) where q = (^P^2>---'^M)' is an M X 1 vector of outputs. 1 expressed in implicit form: T(x,q) = q-f(x) = 0.
4 The Short-Run Cost Function Until now we have assumed that all inputs are variable, as they would be in the long run^^. For this reason, the cost function c(w,^) is sometimes known as a variable or long-run cost function. , buildings). The resulting cost function is known as a restricted or short-run cost function. Let the input vector x be partitioned as x = ( x . , x j where Xf and Xy are subvectors containing fixed and variable inputs respectively, and let the input price vector w be similarly partitioned as w = ( w .