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week 2 general equilibrium, Resúmenes de Microeconomía

Una explicación sobre el equilibrio de mercado con precios fijos y cómo se llega a un equilibrio walrasiano. También se discuten las propiedades del equilibrio, como la optimalidad de Pareto y los teoremas de bienestar. útil para estudiantes de economía que deseen comprender los conceptos básicos del equilibrio general y su relación con la optimalidad de Pareto.

Tipo: Resúmenes

2020/2021

A la venta desde 02/03/2023

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Week 2: General Equilibrium II
GENERAL EQUILIBRIUM II
EQUILIBRIUM ANALYSIS
We study a very simple equilibrium mechanis
Market with fixed prices:
- there is an entity that fixes prices. (Government/auctioneer/invisible hand)
- Agents take prices as GIVEN and they solve their consumer problem (each of them
separately).
- The excess demand / supply are exchanged in the market.
- Instead of 2 agents you can think of many agents that can be divided in 2 groups with
same preferences.
WALRASIAN EQUILIBRIUM
HOW DO WE GET TO THE EQUILIBRIUM?
- A market is in equilibrium if the demand is equal to the supply.
- There is no guarantee that the market reaches an equilibrium. It depends on prices.
- The idea of equilibrium implies that prices change until an equilibrium is reached. →
Excess demand: prices go up. Excess supply: prices go down.
- If demand is equal to supply we are at a Walrasian Equilibrium.
EXAMPLE: A DISEQUILIBRIUM SITUATION
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Week 2: General Equilibrium II

GENERAL EQUILIBRIUM II

EQUILIBRIUM ANALYSIS

We study a very simple equilibrium mechanis Market with fixed prices:

  • there is an entity that fixes prices. (Government/auctioneer/invisible hand)
  • Agents take prices as GIVEN and they solve their consumer problem (each of them separately).
  • The excess demand / supply are exchanged in the market.
  • Instead of 2 agents you can think of many agents that can be divided in 2 groups with same preferences. WALRASIAN EQUILIBRIUM HOW DO WE GET TO THE EQUILIBRIUM?
  • A market is in equilibrium if the demand is equal to the supply.
  • There is no guarantee that the market reaches an equilibrium. It depends on prices.
  • The idea of equilibrium implies that prices change until an equilibrium is reached. → Excess demand: prices go up. Excess supply: prices go down.
  • If demand is equal to supply we are at a Walrasian Equilibrium. EXAMPLE: A DISEQUILIBRIUM SITUATION

EQUILIBRIUM: PROPERTIES

  1. The equilibrium allocation must lie in the core. Intuition: no agent can be worse off in equilibrium than she was with her initial endowment.

Intuition: From consumer theory, we know that, if preferences are convex, a consumer will demand an allocation for which her indifference curves are tangent to the budget line ⇔ Marginal Rate of Substitution (MRS) = Relative Price. Here, given prices are the same for all consumers, in equilibrium all agents have the same MRS.

WALRAS’S LAW: IMPLICATIONS

  1. If k − 1 markets are in equilibrium, the remaining one is also in equilibrium.
  2. Existence of a numéraire. EXISTANCE AND UNIQUENESS How do we know whether the equilibrium exists and is unique? We do not prove it in this course, but it can be shown that if the aggregate excess demand function (zj^ ) is continuous, an equilibrium exists and it is unique. This happens if:
  • Every agent has a continuous demand function and a concave utility function
  • Consumers are small with respect to the market. Example: Cobb-Douglas Summary

Until now we have seen:

_- Graphical representation of an exchange economy (Edgeworth’s Box

  • The set of Pareto optimal allocation (Contracts Curve)
  • How to find an equilibrium
  • Intuition of why the equilibrium should be Pareto optimal._

The first welfare theorem is completely silent over the distribution of welfare and wealth in the population. For example, an equilibrium could be one in which one agent has everything. Nevertheless, it is important to know that in this simplified world the market always reaches an outcome that is P.O. Laissez faire Limitations: We needed some assumptions Important: perfectly competitive market (agents are price-takers). With market imperfections, e.g. externalities, market power, public goods, etc., the first welfare theorem does not hold. SECOND WELFARE THEOREM The first welfare theorem states that each equilibrium is P.O. Now we want to know whether any P.O. allocation (contracts curve) can be an equilibrium Let’s suppose that the government can redistribute the initial endowment and then let the market reach its equilibrium. Statement: If the intial endowment can be modified, then any allocation on the contract curve can be reached as a market equilibrium. Assumptions: We need convex indifference curves (concave utility functions). PROOF

VIOLATION OF THE SECOND WELFARE THEOREM