Nonlinear Production, Abatement, Pollution and Materials Balance Reconsidered



21

Maintaining the assumption Xe0 (which implies teA0 owing to (29)) we now wish to
juxtapose alternative scenarios where one, two or all of the (efficient!) tax rates
taA1,taA2 and
tcA may be zero. In view of Ye>0,Re1 <0 and Re2 0 , it is straightforward that (29) and (30)
imply (28). (28) complements (24), in fact, but (28) was derived via (30) rather than via (23)
and thus offers insights in the determinants of the efficient emissions tax rate
te .

Suppose first, pollution is caused by the emission of production residuals only
(Xra1= Xra2= Xrc =0). Then te= Ye is optimal due to (28), i. e. the tax rate te is required to
be set equal to the
conventional marginal costs of abating production residuals. When com-
bined with (29)
te= Ye yields

UiX

-U_ = t = Y                                         (31)

ii ee

Uy

which constitutes the conventional Pigouvian tax rule. Yet in view of possible deviations
from that rule, as described in (29) and (31), (31) is not a trivial result because we specified
conditions under which the
conventional Pigouvian tax rule is valid.

Suppose next that _r > 0 and/or _r > 0 but _r = 0 . In this case the social marginal
ra1                            ra2                      rc

abatement costs of production residuals are Ye-jtaAjRej> Ye. The extra marginal costs,
j taj Rej , accrue because an increase in the abatement of production residuals inadvertently
raises the generation of environmentally harmful abatement residuals. The result
teA Ye is
worth noting: It is now optimal to abate
less production residuals than under the conventional
Pigouvian tax rule. Conversely, if abatement residuals don't degrade the environment but
post-consumption residuals do
(_ra1= _ra2=0 and _rc>0), then the social marginal abate-
ment costs of production residuals are
Ye-tcAYe< Ye. The extra marginal cost savings, tcAYe,
occur because an increase in the abatement of production residuals inadvertently reduces the
amount of post-consumption residuals and consumer goods. Since post-consumption residuals
are (now) pollutants by assumption, curbing
rc reduces that pollution which is, in turn, a
beneficial external effect of abating production residuals. With
teA Ye it is now optimal to
abate
more production residuals than under the conventional Pigouvian tax rule.



More intriguing information

1. The name is absent
2. Optimal Tax Policy when Firms are Internationally Mobile
3. Auction Design without Commitment
4. The Clustering of Financial Services in London*
5. Insurance within the firm
6. Informal Labour and Credit Markets: A Survey.
7. Benchmarking Regional Innovation: A Comparison of Bavaria, Northern Ireland and the Republic of Ireland
8. An Efficient Circulant MIMO Equalizer for CDMA Downlink: Algorithm and VLSI Architecture
9. Disturbing the fiscal theory of the price level: Can it fit the eu-15?
10. GENE EXPRESSION AND ITS DISCONTENTS Developmental disorders as dysfunctions of epigenetic cognition