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

2. D₀ (x, 0) =0 for allx in R₊^N , i.e., inaction is possible. No output is
possible from positive inputs.

3. x'≥x implies that D₀ (x', y) ≤D₀ (x, y), i.e., more the inputs the
less efficient would the production be.

4. D₀(x, μy) = μD₀(x,y) for μ>0, i.e.,positive linear homogeneity.
5. D₀ (x, y) is convex in y.

Of particular interest for our purpose is the disposability
properties of the technology with respect to output, especially the
undesirable outputs. We assume that such outputs are weakly
disposable i.e., a reduction in the undesirable outputs can only be
achieved by simultaneously reducing some of the desirable outputs. We
also assume that the desirable outputs are strongly disposable i.e., it is
possible to reduce the desirable outputs without actually reducing the
undesirable outputs. In other words the outputs are weakly disposable if
y∈P(x) and θ ∈[0, 1], then θ y∈P(x) ; and strongly disposable if we
have ν ≤y ∈ P(x) implies ν∈ P(x) .

Let r = (r₁, r₂,  r_M) denote the output price vector. From the
producer’s perspective, shadow prices of pollutants or the undesirable
outputs are negative in general, and can thus be interpreted as the
negative values of the marginal abatement cost. The revenue function
can now be defined in the lines of Shephard (1970) and Fare and
Primont (1995) as

(iii)KK R(x, r)= max[ry: y ∈P(x)]
^y

Shephard (1970) showed that the revenue function and the output
distance function are dual to one another. So,

(iv)KK R(x, r) = max [ry: D₀(x,y)≤1]
^y

(v)KK D₀(x,y)= max [ry: R(x,r)≤1]
r

<<   <   5   6   7   8   9   10   11   >   >>