Suppose that a society believed that the distribution of income generated by competitive markets was too unequal. What kind of intervention would be needed to bring about greater economic equality?

The second theorem addresses precisely this issue. Its answer is that only very limited intervention is needed. The government does not need to worry about the quantities of cabbage and cheese that each person gets, or with any other details of the individual commodity bundles. It does not even have to ensure that sufficient resources are devoted to cabbage farming or cheese production or any other activity. A policy that simply redistributes purchasing power, and then allows people to trade in competitive markets, is as good as any policy can be.

The claim of the second theorem, like that of the first theorem, is valid only for economies that satisfy certain well-specified – and very restrictive – conditions. One of these conditions is that the government's redistribution of purchasing power be lump sum. Transfer recipients must not be able to increase their transfers by changing their behaviour, and taxpayers must not be able to reduce their tax payments or become transfer recipients by changing their behaviour. This requirement is very strong. It means that the redistribution cannot be from the rich to the poor: a person's income is determined in part by market behaviour (for example, by the quantity of labour offered for sale), and market behaviour can be changed.