Question

omy where preferences and endowments 2. /20) Consider an Edgeworth box econ are given by d(z, zl) = (zl): (x), ei = (6,6) (a) 4 Carefully state the theorem regarding thé 'existence of a Walrasian equilibrium that was given in the lectures. (b) [6) Using the normalization p2 - 1, find the Walrasian equilibrium. (c) 4] Carefully state the Walras' Law and verify that it holds. (d) [6] Can the allocation ((5,23.4), (5, 2.6)) be supported as an equi- librium with transfers? If yes, find the supporting prices (normalize the price of the second good to one) and transfers. If no, explain.

Answer 1

a) The theorem which states the existence of a Walrasian equilibirum if the First Welfare Theorem. It says that a market equilibrium attained through exchange will always be pareto optimal.

b)

x_1¹ = 2 , x₁² = 8

x₂¹ = 18, x₂² = 8

p₁ = 3, p₂ = 1

c) Walras' law asserts that existence of equilibrium in all other market will prove the existence of equilibrium in the examined market.

In the above example , when good x₁ is in equilibrium it causes the market for good x₂ to be in equilibrium as well.

d) Yes such an equilibrium can be achieved through transfers as at such distribution MRS of both agents are equal.

Now finding prices