Eric's link to this article about taxes on unhealthy food, has started me thinking again about how to do welfare economics when using a paternalistic value judgement. As I noted in my original Offsetting post, it is perfectly legitimate to invoke paternalism, but you have to then be careful to apply that value judgement consistently and not just carelessly carry over analysis that implicitly rests on welfare analysis that eschews paternalism.
In the case of taxes on unhealthy food, if we don't make a paternalistic value judgement, data on how responsive consumers are to changes in the price of unhealthy food is largely irrelevant, but if we do want to intervene to save some people from the consequences of their eating habits, responsiveness is to price matters hugely for whether fat taxes and the like will be effective.
The study cited in the article linked to above found that low-income people are more sensitive to price changes for unhealthy food than are those with higher incomes. Now there are two reasons why an increase in the price of a good might lead to a reduction in the amount someone consumes of that good. It could be that the price increase induces them to substitute away from that good to a-now-relatively-cheaper-alternative (the "substitution effect" in economic jargon), or it could be that the price increase represents a loss of real spending power, forcing the consumer to reduce consumption in general due to the loss of real income (the "income effect").
Now let's say that we found that the responsiveness of demand for unhealthy food to price increases was mostly due to the income effect, not the substitution effect. This is certainly consistent with the observation that the responsiveness of higher-income consumers is less than that of lower-income consumers, although it is not the only explanation of that observation. If this were true, we would be able to achieve our paternalistic objectives by increasing income taxes on the poor and reducing them on the rich. So my question then is: What would your paternalistic welfare judgment have to be to justify excise taxes on unhealthy food but not a rejigging of the income-tax system to make it less progressive if the only reason the excise tax would have the desired effect is by reducing income? And if your welfare judgement can't separate those two policies in that case, doesn't any empirical work showing responsiveness of demand to price have to address the question of whether that responsiveness is primarily due to the substitution or the income effect?