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General equilibrium

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Optional. Walras, Cassel . �The equations of general equilibrium (I)

Léon Walras (1834-1910)

Gustav Cassel (1866-1945)

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Dispensable. Cassel 's equations

The Theory of Social Economy , https://archive.org/details/theoryofsocialec0000cass/page/137/

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Optional. Arrow, Debreu . �The equations of general equilibrium (II)

Prices as coordinators of the actions of the agents economic .

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Kenneth J. Arrow (1921-2017)

Gérard Debreu (1921-2004)

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Optional. General balance, Debreu version

  • Goods are items or services, fully specified physically, temporally and spatially.
    • It is supposed to be assigned from here to a future time, in a series of time steps and geographical regions.
    • Each item has a price, which depends on the time and the region in which it is located.
    • There are certain quantities of resources available.
  • There are two types of economic agents:
    • Producers who maximize their profit.
    • Consumers who maximize their utility, under their wealth constraint.
  • Given certain prices, each producer maximizes their profits, which are distributed among the consumer-shareholders.
  • The allocation is supposed to be established in the present, but with a "telescopic" forecast of the entire future.
  • Can prices be found that make the actions of consumers and producers compatible with total resources (at all time steps and in all geographical regions)?

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  • Equilibrium is a state in which no consumer can improve their preferences without increasing their spending and no producer can increase their profits.
  • The optimum is a state where it is not possible to satisfy the preferences of any consumer without satisfying the preferences of another.
  • It is shown that, under certain assumptions:
    • If a feasible state for certain prices is an equilibrium, that state is an optimum.
    • If a feasible state is an optimum, there are prices at which the economy is in equilibrium.
  • The equilibrium existence theorem demonstrates that (under certain conditions) there exist prices that make the actions of consumers and producers compatible with total resources. A feasible state is an optimum if and only if there are prices to which all agents adapt.
  • These two essential theorems of the theory of value thus explain the role of prices in an economy. The theory of value explains the prices of all goods and the actions of consumers and producers in a privately owned economy.

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Optional. General balance, Debreu version

Theory of Value : https://archive.org/details/theoryofvalueaxi0000debr

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Optional.

ABC, 7-4-1984, page 65,

https://www.abc.es/archivo/periodicos/abc-madrid-19840407-65.html

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Review of the overall balance

  • General equilibrium, despite its widespread acceptance as a fundamental theory in education, cannot be compared to a conventional scientific model. Models in science are tested against facts, allowing for their continuous improvement. But general equilibrium has not undergone any empirical testing . The very fact that it involves an allocation in the present, while completely predicting the future, makes any kind of testing virtually impossible.
  • Furthermore, internal difficulties and inconsistencies have been demonstrated.
  • Furthermore, the model only postulates a state of equilibrium, but does not explain the mechanism by which that state could be reached.
  • The very fact that in reality there are cycles of economic crises, unemployment, imbalances, etc. shows that the model is very far removed from reality.
  • General equilibrium, by focusing on exchanges and limiting price to being an exchange rate, disregards other fundamental aspects of price, which are emphasized by other schools, such as optimization .
  • In any case, the model emphasizes the role of economic agents in coordinating prices, an aspect that should be taken advantage of.