[4] The second theorem states that with further restrictions, any Pareto efficient outcome can be achieved through a competitive market equilibrium,[3] provided that a social planner uses a social welfare function to choose the most equitable efficient outcome and then uses lump sum transfers followed by competitive trade to achieve it.
Economists viewed welfare economics as the branch of the discipline concerned with delineating the actions a governing body should undertake.
It was commonly accepted that the term "maximizing welfare" held a specific meaning rooted in the philosophical framework of utilitarianism.
This debate seemed to have been addressed by Abram Bergson's seminal paper in 1938, "A Reformulation of Certain Aspects of Welfare Economics."
Bergson demonstrated that economic efficiency conditions could be precisely formulated without fully specifying the underlying social welfare function.
He argued that rational law satisfies four conditions: partial universality, the Pareto principle, totalitarianism, and free will Arrow concluded that there is no rational way to articulate individual preferences forms together resulting in a harmonious social status of the various social societies.
Sen said collective action often arises in social decision-making, because Arrow's theory is delivered through the aggregate of individual preferences rather than the formation of government or income, especially those that exist because of neutrality, presented a challenge to reconcile conflicting interests in revenue sharing.
This restriction did not exclude important information about an individual’s social status or position needed to make an income allocation decision.
The ordinal-behaviorist approach, originally called the new welfare economics, is based on the work of Pareto, Kaldor, Hicks, and Scitovsky.
Using the Kaldor criterion, the change is desirable if the maximum amount the winners would be willing to pay is greater than the minimum the losers would accept.
No economic activity will increase social welfare unless it improves the position of the society member that is the worst off.
The Max-Min social indifference curve takes the shape of two straight lines joined so as they form a 90-degree angle.
A crude social welfare function can be constructed by measuring the subjective dollar value of goods and services distributed to participants in the economy.
[9] More specifically, the existence of competitive equilibrium implies both price-taking behaviour and complete markets, but the only additional assumption is the local non-satiation of agents' preferences – that consumers would like, at the margin, to have slightly more of any given good.
[4] The second fundamental theorem states that given further restrictions, any Pareto efficient outcome can be supported as a competitive market equilibrium.
[3] These restrictions are stronger than for the first fundamental theorem, with convexity of preferences and production functions a sufficient but not necessary condition.
[5][10] A direct consequence of the second theorem is that a benevolent social planner could use a system of lump sum transfers to ensure that the "best" Pareto efficient allocation was supported as a competitive equilibrium for some set of prices.
[3][5] More generally, it suggests that redistribution should, if possible, be achieved without affecting prices (which should continue to reflect relative scarcity), thus ensuring that the final (post-trade) result is efficient.
Numerous utility functions can be derived, one for each point on the production possibility frontier (PQ in the diagram above).