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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