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

( xi )......D o( x, У ) = r *( x, У ) * У

*

where, r (x, У) is the revenue maximising output price vector.

Differentiating both sides of equation (xi) with respect to y we get

(^xii)...... ^Vy^D0(x^, y) = r *(x^, y)

Substituting (xii) in (x) we get

(xiii )......r = R (x, r ) * r *( x, y )

Here r (x,y) derived from Shephard’s dual lemma can be interpreted
as a vector of normalised or deflated output shadow prices. The
formulation of equation (xiii) shows that the undeflated shadow prices r
can be computed when the maximum revenue R(x, r) is known.
However, R(x, r) depends on r, which is the vector of shadow prices. In
order to obtain R(x, r) we assume that the market price or the observed
price of one of the output equals its absolute shadow price. Suppose the
observed price of the m^th output r_m^o equals its absolute shadow price

r_m . Then, whenever x and y are known we can compute the revenue
from equation (xiii) as

r^o

( xiv) KK R= ^m _*

r_m(x,y)

In reality one can use the market price (or the observed price) of the
desirable output as the normalising price, since the prices of the
desirable output are market determined and therefore observable. For all
m′ ≠ m , the absolute shadow prices r_m′ are given by

11

<<   7   8   9   10   11   12   13   >>

More intriguing information