# Suppose that x* = (x*1, x*2,..., x*n) is a Pareto-efficient allocation in an exchange economy (example 1.117)

## Question:

€¢ 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.

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