Question

what is the second fundamental theorem of welfare economics ?

please provide detail explanation and an example for it

Answer 1

The second theorem of welfare economics says that when all agents have convex preferences then there always must be available a set prices so that each pareto efficient allocation is a market equilibrium, given an appropriate endownment.

In other words it can be said that this theorem implies that given an appropriate endownment, any pareto efficient outcome can be get.

This means that for any given endownment, any individual can redistribute the endownment for getting an efficient outcome which he wants.

For example when preferences are convex, then at pareto efficient allocation the bundle preferred by person A and preferred by person B must be efficient. Therefore when the two persons have convex preferences, we can draw a line between the 2 sets of preferred bundles which separate one from another. The slope of this line is relative prices and any endownments on this line will lead to final market equilibrium and it will be the original pareto efficient allocation.

All this has been shown in the below diagram.