1 Welfare Theorems

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Oct 8, 2013 (3 years and 8 months ago)

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1 Welfare Theorems
1.1 The …rst welfare theorem
If every relevant good is traded in a market at publicly known prices (i.e.if there is a complete set of
markets),and if households and …rms act perfectly competitive (i.e.as prices takers),then the market
outcome is Pareto optimal.That is,when markets are complete,any competitive equilibriumis necessarily
Pareto optimal.
Assumptions:
² The de…nition of market equilibrium and the de…nition of Pareto e¢ciency.
Implicit assumptions:
² no externalities (utility and production)
² Agents are price takers and adjust quantities.No monopolists.
² No asymmetric information.
Interpretation:
² The market mechanism does always achieve an e¢cient allocation.
² The market mechanism is not necessarily the only mechanism that achieves an e¢cient allocation.
But it is a very simple one:Every individual simply maximizes its own utility while only knowing
its own preferences and the market prices.(Smith:Invisible Hand).
² Other allocation mechanisms require much more information (especially in a big economy with lots
of markets and agents).
1.2 The second welfare theorem
If household preferences and …rm production sets are convex,there is a complete set of markets with
publicly known prices,and every agent acts as a price taker,then any Pareto optimal outcome can be
achieved as a competitive equilibrium if appropriate lump-sum transfers of wealth are arranged.
Additional Assumptions:
² Technical:Preferences are monotonous,convex,and continuous.
² Information:If a social planner wants to have a certain Pareto e¢cient allocation by using the
market mechanism he needs to know the preferences of all agents and the production sets of all
…rms.
Interpretation:
² A certain allocation is achieved by assigning a certain level of initial wealth to all agents.
² The market mechanism ensures e¢ciency.
² It is not necessary to have price interventions.Prices play a distributive and a allocative role.
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