Estimation of marginal abatement costs for undesirable outputs in India's power generation sector: An output distance function approach.

∂D₀ (x, y)

__________/^УУт’m

^d D 0( ^x, У )/
∕∂y_n

As shown in equation (xv), the shadow price of т ′ output is
given by the product of the marginal rate of transformation and the
market price of the m^tt^h output. If one considers the m′ output to be the
undesirable output (i.e., the pollutant) and the т ^th output as the
desirable output then, from equation (xv) the shadow price of the
undesirable output is given by the product of the marginal rate of
transformation and the market price of the desirable output. This, in turn,
is equivalent to the value of the foregone desirable output associated
with the reduction in one unit of the undesirable output. In the above
equation the ratio of the output shadow prices reflects the relative
opportunity cost of the output in terms of the revenue foregone. In other
words, it is equivalent to the marginal rate of transformation. Thus the
shadow prices reflect the trade-off between the desirable and
undesirable outputs at the actual mix of outputs. Derivation of the
shadow prices of undesirable output as given by equation (xv) is based
on the assumption that the production is occuring at the frontier of the
output set. But if the production firms lie within the output set and not on
the frontier (i.e., for such firms the value of the output distance function is
less than one), then there might be some problem in estimating the
shadow prices. To resolve the problem of estimating the shadow prices
for such inefficient firms, we proportionately increase all the outputs so
that they are on the frontier. Such proportionate scaling of the outputs
will have no affect on the shadow prices as we have assumed that the
output distance function is homogeneous of degree one in outputs and
therefore its derivatives with respect to the outputs as shown in equation
(xv) are homogeneous of degree zero. To put it differently, regardless of
the location of the observed production combinations, the shadow prices
can be derived through an estimated output distance function by using

12

<<   8   9   10   11   12   13   14   >>

More intriguing information