Economics of Welfare:
Illustrating Pareto Concepts:
• Consider the Edge worth Box of two individuals – Alice and Bob – trading two goods, x1 and x2.
• Starting at allocation A the shaded area to the upper right represents the allocations that Alice weakly prefers to A.
• The shaded area to the lower left corresponds to the allocations that Bob weakly prefers to A.
• The two sets overlap, and the lens-shaped area represents potential gains from trade – these are allocations that both Alice and Bob prefer to A.
• Since Alice and Bob individually favour allocation B to allocation A, allocation B “Pareto dominates” allocation A – that is switching from A to B would be a Pareto improvement neither is worse off and at least one is better off.
• Other allocations might Pareto dominate allocation B. Consider C, which Pareto dominates A and B, and is not Pareto dominated by any other alternative. From C, the only way to reach an allocation one or both prefer to C is to leave at least one worse off. For example, switching from allocation C to D would not be Pareto improving for the reason that Bob prefers C to D.
• Allocation C is Pareto optimal for the reasons that no further unambiguous gains remain – all the gains from trade have been exhausted.
• There is generally not a single Pareto most favourable allocation; Pareto optimal allocation form a set, the Pareto set – the upward-sloping curve in the Edgeworth box could be along one or two edges.
Defining Pareto Concepts:
• A possible allocation X Pareto dominates feasible allocation X ′ if and only if all individuals (weakly) prefer X to X ′ and at least one individual strictly prefers X to X ′ .
• A move from allocation X ′ to X is a Pareto development if X Pareto dominates X ′ .
• A possible allocation X is Pareto optimal if there doesn’t exists an allocation X ′ that wouldPareto dominate X - Pareto optimal allocation is “optimal” in the sense that all the gains from trade have been exploited.
• The Pareto set is the set of Pareto most favourable allocations.
- It is the locus of tangencies within the Edge worth box, if such tangencies exist.
- If Alice’s unresponsiveness curve crosses Bob’s indifference curve at some allocation X ′ , then X ′ would not be Pareto optimal: intersection of Alice’s and Bob’s preferred sets would not be empty (unless the allocation is along the edge of the box).
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