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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 ∈ ℜl+ 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* ∈ ℜl+ and
• A system of lump-sum taxes and transfers t ∈ ℜn with ∑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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