Answer to Question #213426 in Microeconomics for Tanya

Question

"As long as preferences are Convex, every Pareto efficient allocation can be supported as competitive equilibrium" Explain using edge worth box.

Answer 1

This is the second welfare theorem that says if preferences are convex, we can attain any competitive equilibrium using transfers. So we can attain any Pareto optimal outcome as competitive equilibrium in such a setup.

Since convex preference is there, there is an interior solution, and at competitive equilibrium, we have MRS1=MRS2 and demand =supply; hence we can attain equilibrium in such a sense. We just transfer endowments by tax and subsidy and change the initial endowments in the Edgeworth box and attain equilibrium.