Could you provide the intuition behind the second welfare theorem, and prove in a few rows the theorem itself?


1 Answer 1


Here is a short argument due to Maskin and Roberts. I'll give it in the simpler context of a pure exchange economy.

Suppose you have a Pareto efficient allocation, and an equilibrium $(x,p)$ exists starting with this allocation as the endowment specification $e$. Then taking these equilibrium prices and everyone just consuming their endowment is an equilibrium; $(e,p)$ is an equilibrium. Indeed, since an agent's endowment is always in the budget set, and everyone chooses optimally, we must have $x_i\succeq_i e_i$ for every agent $i$. But we cannot have $x_i\succ_i e_i$ for some $i$, because then $x$ would be a Pareto improvement over $e$, which is impossible by assumption. So $x_i\sim_i e_i$ for every $i$, and just consuming the endowment is optimal given $p$. Since $e$ is also clearly feasible, we are done.

The argument is so simple because I have just assumed that the equilibrium $(x,p)$ exists. The standard proofs of the second welfare theorem include an existence proof, and that is also why the usual additional assumptions are needed.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.