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Lizenzierung Namensnennung - Nicht-kommerziell - Keine Bearbeitung (CC BY-NC-ND)     (Unversité de Genève, cours de Pr. Monika Mrazova)
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STWE: Can a Pareto efficient allocation be achieved as a competitive equilibrium?

Yes, if preferences are convex
 

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FTWE does not hold in 

the presence of externalities

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FTWE focuses on efficiency, not fairness

Allocation where one person owns everything is Pareto efficient

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The FTWE tells us that

the resulting equilibrium from these independent, self-interested and decentralised actions is efficient

This is the nature of the “Invisible Hand” of Adam Smith

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Implicit assumptions of the FTWE: Each consumer knows only

his own tastes, endowment and the market prices

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FTWE

any competitive equilibrium is Pareto efficient

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Using Walras’ Law we can show that 

if demand equals supply in one market, the same must be true in the other market.

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Walras’ law states that

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the value of aggregate excess demands is always 0 (at any prices), i.e

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In equilibrium the aggregate excess demand for each good

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Aggregate excess demand for good 1

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Net/Excess demand of consumer A for good 1

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The Algebra of Equilibrium

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Equilibrium is a set of prices (p1*;p2*) such that

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total demand for each good equals total supply

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Competitive Equilibrium: we must have

 

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A competitive equilibrium is

an allocation E* and a set of prices, p1* and p2*, such that, given these prices (and given the initial endowments), each consumer is maximising his/her utility at that allocation

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Edgeworth Box: adjustment to equilibrium

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Edgeworth Box: Disequilibrium

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Economic Problem
Given initial endowments, what is the allocation that ensures that

consumers maximise their utility
demand equals supply in all markets

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Trade and Pareto Efficiency: The Core

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Contract curve (Pareto set)

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Edgeworth-Bowley Box: Pareto Efficiency

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Pareto Efficiency

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A Pareto efficient allocation is such that

there is no way to make all the people involved better off

there is no way to make some individual better off without making someone else worse off

all the gains from trade have been exhausted

there are no mutually advantageous trades to be made

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Pareto improvement and trade

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Pareto-improving allocation

An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another

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Edgeworth-Bowley Box: Trade

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All points in the box, including the boundary, represent

feasible allocations of the combined endowment

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Edgeworth-Bowley Box: Endowment

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Feasible allocation

xA1 + xB1 < wA1 + wB1 and xA2 + xB2 < wA2 + wB2