Optimal Tax Policy and Environmental Externality: A General Equilibrium Analysis
3. The harmfulness of externality
3.2 Interpretations for the terms in the shadow price
The first term in the brackets, Cd, describes the direct harmful effect of the externality on consumers. It is a sum of the marginal willingnesses to pay to avoid the externality. Resulting from its definition, the sum is positive as the externality is assumed to affect the utility of the households negatively.
The shadow price is affected by the self-selection constraint through the indirect effect of the externality on consumers, term Ci. Its sign depends on the
3See Edwards, Keen and Tuomala (1994) for a proof.
difference in valuation of the externality between mimicker and true type 1 household. Since the mimicker is of the high ability type, he can do the work of type 1 in a shorter time than a true low ability type worker, and thus he has more leisure. When environmental quality and leisure are complements (substitutes), the marginal willingness to pay is the greater the more (less) leisure household has. Thus, it can be concluded that when environmental quality and leisure are complements (substitutes), MWPEB is larger for the mimicker than for the low productivity household and the term has a negative (positive) effect on the shadow price of the externality.
When environmental quality and leisure are complements, mimickers are willing to pay more to avoid the externality than true low ability type workers.
Thus lowering the level of the externality raises the desirability of mimicking. In order to reduce the incentive to mimic back to the level where mimicking does not give higher utility for the high ability type than revealing their true type, government needs to increase the taxation of the low ability households. This in turn changes the level of the income redistribution towards wider income differences, which contradicts government’s redistribution objective. Thus income distribution target and the objectives to promote environmental quality are not in accordance with respect to these two consumer side terms4. The case where environmental quality and leisure are substitutes proceeds analogously. In this case promoting environmental quality is in accordance with redistributional aims, as decreasing the level of externality makes mimicking less desirable and thus, by mitigating the self-selection constraint, allows a more equal income distribution.
4 On the consumer side there are actually two indirect effects: impacts of the self-selection constraint and the labour market influencing through wage adjustment. In the next section it is shown that the sign of the labour market effect is most plausibly positive, so these two effects have opposite signs and as a whole the impact of the indirect effect on the shadow price on the consumer side remains ambiguous.
59 The third term inside the brackets in Eq. (11), Pd, is the marginal cost of the externality in production. Thus this term can be interpreted to be the direct effect on the producers. Pd increases the shadow price as the derivative of the production function with respect to the externality was assumed to be negative. The indirect effect on the producer side arises from labour markets. As wages are not constant, their adjustment affects the valuation of the externality. This effect appears in the second last term in Eq. (11), called the labour market term LM, due to the fact that the wage adjustment affects both consumers and producers.
The sign of the LM term depends on the partial derivative of the wage ratio with respect to the externality as *, L1 and VˆB2are positive and VˆL2 is negative.
Since the wage ratio can be defined with the help of marginal productivities, it
can be written as
( )
determined by 1E and 2E, the elasticities of wages with respect to the externality.Assuming pollution to have a negative effect on productivity, these elasticities are negative. E is negative when ξ1E > ξ2E , i.e. when the low ability worker’s productivity increases relatively more than the high ability type’s productivity as the level of pollution is decreased5. Based on the general conclusion of empirical
5 The reasoning is the same in the case where the effect of the externality on productivity is positive. E is positive, if a type 2 worker suffers more from the increased amount of the externality. The other possibilities are that (i) 1E < 0 and 2E > 0 E always negative, and (ii) 1E
> 0 and 2E < 0 E always positive.
findings in the literature6, we assume here that the low ability workers are more vulnerable to pollution than the high ability workers and E is negative. Assuming that E is negative means that the term LM is positive and it has an increasing effect on the shadow price.
The labour market term also involves an effect on redistribution. Negative E
means that when the government seeks to reduce the level of pollution, the wage ratio rises and wage differences decrease. Smaller wage differences mitigate the self-selection constraint and allow the low ability type to earn more. This in turn leads to less need for income transfers and the taxation of a high ability type can be decreased and both types can be better off. The income distribution target in this case is in accordance with environmental targets.
The last term in Eq. (11), Gi, refers to the indirect effect of the externality on government’s tax revenues. It tells how much government’s tax revenues from commodity taxation change due to the externality. The sign of the public sector term depends on the change in the demand for both goods due to the externality.
When an increased pollution level decreases the aggregate demand for both goods7, the tax revenue effect has a negative sign and the term Gi increases the shadow price. It is also possible that the externality affects the demands for dirty and clean good differently. The determination of the changes in demands would require specifying the exact forms of consumers’ utility functions. As in this model utilities are defined only on a very general level, the direction of the demand changes is left undefined.
If a decrease in the level of the externality increases the aggregate demand for goods there will appear a kind of double dividend. From government’s point of
6 See e.g. Hamilton and Viscusi (1999), and for a review OECD (2006).
7 Decreased level of externality means by definition a decreased demand for the dirty good. Thus the increasing aggregate demand implies that the demand for the clean good needs to grow sufficiently due to the effect of the externality. This is possible when dirty good and clean good are substitutes (or at least are not strongly complementary).
61 view it is advantageous to try to reduce the level of pollution because thus would mean not only better environmental quality but also higher tax revenues from commodity taxes. If the effect of the externality on aggregate demand is negative, emphasising the environmental objective has additional indirect costs through decreased commodity tax revenues.