Suppose that x (x 1, x 2, , x n) is a Pareto efficient allocation in an exchange economy (example 1 117) in which each of the n consumers has an endowment wi l of the l commodities Assume that cent Individual preferences iquest i are convex, continuous and strongly monotonic cent x is a feasible al...

By the previous exercise there exists a price system p such that x i ...

Suppose that x* = (x1, x2,..., x*n) is a Pareto-efficient allocation in an exchange economy (example 1.117)

Question:

Suppose that x* = (x*1, x*2,..., x*n) is a Pareto-efficient allocation in an exchange economy (example 1.117) in which each of the n consumers has an endowment wi ˆˆ „œl+ of the l commodities. Assume that
€¢ Individual preferences ‰¿i are convex, continuous and strongly monotonic
€¢ x* is a feasible allocation, that is

Show that there exists
€¢ A list of prices p* ˆˆ „œl+ and
€¢ A system of lump-sum taxes and transfers t ˆˆ „œn with ˆ‘i ti = 0
such that (p*, x*) is a competitive equilibrium in which each consumer's after-tax wealth is mi = (p*)Twi + ti.