2.1.4.2 Output-orientated
measure of technical efficiency
This addresses the question: «by how much can output
quantities be proportionally expanded without altering the input quantities
used?» This can be illustrated using a decreasing returns to scale (DRS)
technology represented by f(x) and an inefficient firm operating at P.
y
D f(x)
A B P
O C
x
Figure 2.3: Decreasing Returns to Scale
(DRS)
The Farrell input-orientated measure of technical efficiency
would be AB/AP while the output-orientated measure would be CP/CD. The two
measures of technical efficiency can only be equal if constant returns to scale
(CRS) exist but will be unequal if both increasing returns to scale (IRS) and
decreasing returns to scale (DRS) exist. The CRS case is presented in figure
2.4 below:
f (x)
y D
A B P
O C
x
Figure 2.4: Constant Returns to Scale (CRS)
case
In the CRS case, we observe that for any inefficient point P
we may choose. One can consider the output-orientated measure of technical
efficiency further by considering a case where production involves 2 outputs
(y1 and y2) and a single input (x). Again if we assume CRS, we can represent
the technology by a unit production possibility curve in 2 dimensions. This
example is illustrated in figure 2.5 below.
y2/x
D
C
Z B B'
.A
D'
O
Z' y1/x
Figure 2.5: Technical efficiency (TE) and
allocative efficiency (AE) from output-orientation
The line ZZ' is the unit production possibility curve. The
distance AB represents technical inefficiency (TIE). That is, the amount by
which outputs could be increased without requiring extra inputs, hence a
measure of output-orientated efficiency is: . If we have price-information,
then we can draw the isorevenue line DD' and define allocative efficiency (AE)
to be: AE0 = OB'/OA which has a revenue increasing interpretation. Further,
one can define the overall economic efficiency (EE) as the product of these 2
measures:
EE0 = OB'/OB = TE0 AE0 = OA/OB OB'/OA. Again, all the 3
measures are bound by 0 and 1. Note that point C is unattainable at the current
level of technology.
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