Many citizens, economists, and policy makers share the view that it is legitimate to intervene in the distribution of well-being in society to decrease poverty. There is much less agreement, of course, on how to intervene. One of the many dilemmas that one faces is whether the government should intervene on prices, through commodity taxation — typically the rates of v.a.t., or whether it should restrict its intervention to income transfers. For instance, when an increase in the price of energy decreases the welfare of poor people, should the government subsidize the price of energy for the poor, that is, decrease the v.a.t. rate on energy (maybe up to a negative rate)? Or should it compensate the increase in energy price by an appropriate increase in welfare benefits.
The debates among economists around that question have been illuminated in the early 1950’s by a major theorem of economic theory, called the second fundamental theorem of welfare economics. It says that all distributions of well-being that can be reached by a system of tax and transfers can also be reached by a system of appropriate lump-sum cash transfers, but the converse is not true. To put it differently, if the government succeeds in helping a particular group of people in society by taxing and subsidizing the consumption or production of some commodities, then it can obtain the same outcome and maybe a better one by organizing an appropriate system of lump-sum transfers towards that group of people.
The intuition of that fundamental theorem can be easily illustrated in the case of the energy price. Let us assume that, before the change in price, the consumption of an household is 1000 l of fuel and the price per litre is 1€. Let us assume, then, that the price of fuel increases by 20 cents. If the government decreases the tax on fuel or subsidizes it, it can obtain a decrease in the price facing the household from 1,20 € to 1 €. Let us note that the cost of that policy is equal to 0,20 €/l * 1000 l= 200 €. After the government has implemented that policy, the household we are looking at faces the same prices and the same income as before, and it is able to consume the same basket of goods as well: its well-being has not decreased.
Let us now consider the policy that consists in increasing the income of that household by 200 €, without changing the price of fuel. With this additional money, the household can afford the same bundle of goods as before, so that, again, its well-being is not affected. The difference is that, with the latter policy, the household faces a fuel price of 1,20 €. Consequently, in spite of the increase in income, the household is likely to change its consumption, trying to save on the fuel bill. This change in behavior is clearly one that can benefit the entire society. That illustrates the intuition of the theorem: it is better for society that our behaviors be driven by prices, that reflect the real cost of their consumption to society, whereas the distribution of well-being be driven by a redistribution of means of living that should affect our behaviors as little as possible.
The reasoning above is a powerful one that continues to influence the way economists design policy proposals. It is no more than a theorem, though, with the consequence that it depends on a list of assumptions, and the validity of the theorem can be debated as soon as one assumption of the theorem does not hold.
In a recent paper, Bargain and Donni draw our attention on one assumption that does not hold when one tries to apply the theorem to child poverty. The theorem, indeed, assumes that each person in society has an income and chooses to spend it the way she wishes. Children do not have an income to spend. Their material well-being is determined by the consumption choices of their parents, who may decide to spend more or less on goods that are consumed by children. Bargain and Donni prove an alternative theorem to the second fundamental theorem by raising the following question: assume the government wishes to increase the material well-being of children living in poor household; should it increase the income of those households or play with taxation/subsidy rates, and, therefore, prices, of consumption goods? If households are a little bit richer, then they are likely to consume more of many goods, some of which are not consumed by children. If the v.a.t. rate on goods that are only consumed by children decreases, then the authors show that the change in consumption will be more favorable to the children.
There is another major difference, though, between increasing the incomes of poor people and subsidizing the price of goods that are only consumed by children. It comes from the fact that a decrease in the price of goods will benefit all households, as retailers will not be able (nor allowed) to discriminate among their customers on the basis of their incomes. The authors then show that it remains more efficient to subsidize prices as long as the targeted goods are primarily consumed by children of poorer families, such as non-luxurious food, clothes or school equipment.
The conclusion of the paper is not that the government should blindly decide to subsidize the price of goods that are consumed by children of poor families. Still, it is worth comparing the likely effects of increasing low incomes versus subsidizing some prices. An important progress has been made by the authors, though, first because they have drawn our attention on the possible benefits of a policy that used to be criticized by economists, and second because they succeed in deriving the precise formula that needs to be applied to measure the potential effects of both policies. The remaining work is for governments to estimate this formula.
 We say that a cash transfer is lump-sum when it does not depend on the current choices of the person who receives it. It may depend on age, gender, school degree, housing location, and, under some circumstances, on past choices.
 O. Bargain and O. Donni (2012) ‘Targeting and child poverty,’ Social Choice and Welfare 39: 783-808.
 There are two reasons why a government may wish to increase the well-being of children. First, the government may believe that parents do not care enough for the well-being of their children. Second, even if the government believes that parents do care enough, it may put such a larger weight on the well-being of children than on that of parents that any means to increase the former is viewed as a social improvement.