measure as opposed to the input-oriented measure dis- cussed above. The difference between the output- and input-orientated measures can be illustrated using a simple example involving one input and one output. This is depicted in Figure 4(a) where we have decreas- ing returns to scale technology represented by f (x), and an inefficient firm operating at the point P. The Farrell input-orientated measure of TE would be equal to the ratio AB/AP, while the output-orientated mea- sure of TE would be CP/CD. The output- and input- orientated measures will only provide equivalent mea- sures of technical efficiency when constant returns to scale exist, but will be unequal when increasing or de- creasing returns to scale are present (Fare and Lovell
1978). The constant returns to scale case is depicted in Figure 4(b) where we observe that AB/AP=CP/CD, for any inefficient point P we care to choose.
One can consider output-orientated measures further by considering the case where production involves two o u t p u t s ( y i a n d y ) a n d a s i n g l e i n p u t ( x i ) . A g a i n , i f w assume constant returns to scale, we can represent the technology by a unit production possibility curve in two dimensions. This example is depicted in Figure 5 where the line ZZ’ is the unit production possibil- ity curve and the point A corresponds to an inefficient firm. Note that the inefficient point, A, lies below the curve in this case because ZZ’ represents the upper bound of production possibilities. e
Figure 6 Input- and Output Orientated Technical Efficiency Measures and Returns to Sale
Figure 7 Technical and Allocative Efficiencies from an Output Orientation
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