2.3  Regulation and Tax

Where institutional and trade solutions are not appropriate policy makers should consider whether specific interventions, regulation or specific taxes are appropriate to address externalities. These measures are preferable to the market solution when the net efficiency gains from the intervention are larger than the associated administrative and compliance costs. This suggests they are only likely to be desirable when externalities are reasonably large. The intervention most suited to address the externality should be used.

Regulatory and specific interventions are likely to be appropriate when they can be targeted at particular individuals/activities that are known to be more likely to generate externalities. Examples of this are law enforcement measures and restricting the purchase of a certain good to those over a certain age. Regulatory measures are also likely to be appropriate to ensure consumers are adequately informed.

Specific (Pigouvian) taxes are used to encourage the efficient use of resources. An optimal per unit Pigouvian tax is defined as a tax that would provide an incentive for each consumer to consume that consumer’s socially optimal quantity of a good.[8] For a given consumer this is the quantity at which the social marginal benefit (given by the income-compensated demand curve, Dc in figure 1) of that consumer’s consumption equals the social marginal cost (represented by the social costs line below) of that consumer’s consumption. This is given by point A. For a given consumer, the optimal per unit tax/subsidy is equal to the net marginal external cost of that consumer’s consumption at that consumer’s optimal consumption level. The length AB gives the optimal tax.[9]

Figure 1: The Optimal Pigouvian Tax

If all consumers were identical each consumer would have the same optimal tax. However, where consumers have different demand or cost functions each consumer will have a different optimal tax. If individuals can be distinguished at low cost it will be efficient to levy different taxes on different individuals of groups of individuals. However in most cases information costs imply this will not be cost effective and the government will be constrained to applying the tax uniformly to a range of units of the good, rather than the consumer. Where a tax is imposed on units of a good there must be a clear causal relationship between consumption of the good and the externality.

Where consumers differ and cannot be distinguished at low cost one can define an optimal uniform tax.[10] An optimal uniform tax, based on the Pigouvian principle, would be a weighted average of each consumer’s non-uniform optimal tax. A uniform tax will result in some consumers reducing consumption too much and some consumers reducing consumption too little, relative to the case where a different tax is levied on each consumer. An optimal uniform tax must balance the efficiency gain from the reduction in the externality against the loss of consumption benefits from reduced consumption that are not regained as tax revenue.[11]

Setting the tax rate as an average of consumers’ optimal tax rates means that the tax rate depends on the magnitude of each consumer’s non-uniform optimal tax and the number of consumers that produce large externalities relative to those who produce low (or no) externalities. In determining the weight to be applied to each consumer two further factors need to be considered.

First, taxation is only effective in addressing externalities if those who generate large externalities are responsive to price. However, the more price-responsive are consumers who generate low levels of externality, the larger the loss of consumption benefits. Thus the tax rate should increase as the price-responsiveness of large externality generating consumers increases relative to those who generate low levels of externality. Second, holding all other factors constant, the higher is the initial consumption of externality generating consumers, the larger is the change in their absolute consumption from a tax and the larger the proportion of the tax they pay. The lower is the initial consumption of those who do not generate externalities the less their absolute consumption will change in response to price changes, thus the less the reduction in consumer surplus due to the tax, and the less the proportion of tax they will pay. Thus the tax rate should be higher the higher the initial consumption of those who generate large externalities relative to those who generate small externalities. This suggests that tax would not be an effective tool where those who generate large externalities have lower consumption than those who generate small externalities. This may be the case in relation to activities that require skill or preparation for which a low level of participation in the activity may be more risky than a high level of participation in the activity.

These considerations suggest that the weight should measure the extent to which the consumer will change his/her absolute level of alcohol consumption in response to the tax. A measure of this is the consumer’s price derivative of demand at the consumers optimal tax rate, where the weights add to one.[12] The price derivative of demand takes into account both the price responsiveness (uncompensated elasticity) of each consumer and the consumption level of the consumer. Standardising the price derivative of demand ensures the tax rate depends on the relative price responsiveness and relative initial consumption of consumers.

Thus the optimal uniform tax rate would weight each consumer’s optimal tax by the consumer’s standardised price derivative and sum these weighted externalities.[13]

The ability of the government to set an optimal uniform tax is limited by information constraints. In the first instance valuation of externalities is problematic. The value of an externality is subjective, being the value that the affected party places on it. Where there is no market transaction there will be no observable value of the externality and proxies will need to be used.

Further, in order to calculate the uniform Pigouvian tax as discussed one would need information on the optimal non-uniform tax and price-responsiveness of each individual. In most cases this information will not be available. However, an appropriate level of the tax rate may still be inferred if there is information on the total level of the externality, the incidence of the externality, the responsiveness of consumers and on patterns of consumption in the population. This is because this information would allow a conclusion to be drawn as to the relationship between the total externality and the amount of revenue that would be raised under an optimal uniform tax.

The relationship between the total externality and revenue is clear in the case of a single individual or where the marginal damage is constant.[14] The relationship is complicated in the case of many consumers and where marginal damage increases with consumption. Consider figure 2 and assume that the optimal uniform tax has been imposed (dotted line). The demand curve, marginal externality curve and price line of consumers is illustrated. The consumers have the same marginal externality function but different demand curves. The revenue raised from the tax is illustrated by the black boxes. The total value of the externality is represented by the area between the marginal social cost function and the price line, up to the consumer’s consumption level. For the first consumer the revenue raised exceeds the externality of this consumer. For the second consumer the relationship is unclear. The revenue raised may or may not exceed the externality that this consumer generates. Where there are many consumers the relationship between the amount of revenue that would be raised under an optimal uniform tax and the total externality will depend on the relative number of heavy and light consumers and on the shape of the damage function from consumption. There must be sufficient information on these variables to be able to set a Pigouvian tax.

Figure 2: Revenue and Externality

The following section considers the appropriate role of government in the case of alcohol consumption.