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Economic Category: General Equilibrium

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General Equilibrium - Article

1. Arbitrage and Equilibrium

This articles concentrates on arbitrage and equilibrium through the discussion of the financial asset market equilibrium. [Details...]

2. Asset Structures and Spanning

One of the crucial requirements for the equivalence of Radner equilibrium and Arrow-Debreu equilibrium is that the asset structure of an economy spans the set of states. By "spanning" we mean that a combination of assets can be used to transfer any amount of purchasing power from one state to another. [Details...]

3. Atoms Revisited - The Oligopoly Equivalence Theorem

Is an economy with atoms perfectly competitive or, more accurately, does it yield the same result we obtain in a perfectly competitive economy? The answer, it turns out, is a resounding "Yes!" -- under certain conditions on the size and character of the "atoms". This surprising "oligopoly equivalence" result was first unearthed by Michael J. Farrell (1970) in the context of a Debreu-Scarf replica economy and by Jean-Jaskold Gabszewicz and Jean-Francois Mertens (1971) and Benyamin Shitovitz (1973) in the Aumann continuum economy. [Details...]

4. Aumann's Core Equivalence Theorem

Robert J. Aumann's (1964) core equivalence theorem states that the set of core allocations in his atomless economy is identical to the set of Walrasian equilibrium allocations, i.e. C(E) = W(E). The method of proof we follow here is not identical to Aumann's original. In particular, we make use of some rather simplifying procedures -- notably, we use Aumann's (1965) definition of "integration of correspondences" and Lyapunov's theorem (introduced into economics by Karl Vind (1964)). However, the essence of the proof is basically the same. [Details...]

5. Cantillon's "Land Theory of Value"

General equilibrium theory, indeed much of economics itself, owes its existence to an Irishman who lived obscurely in 18th Century France by the name of Richard Cantillon. In his remarkable Essai sur la Nature du Commerce en Generale (published only in 1755, but written c.1732-1734), Cantillon sets out, perhaps for the first time, the vision of an "economy" as a set of interacting markets connected by a price system with balanced circular flows of income between agents. Cantillon's setting was the first great breakthrough in economic theory - for it provided the fundamental structural idea behind the concept of an "economy" which was to possess all subsequent economics - Physiocratic, Classical and Neoclassical. [Details...]

6. Edgeworth's "Indeterminacy of Contract"

This article covers Barter Exchange, Recontracting and the Core, and The Core: mathematical restatement. [Details...]

7. Edgeworth's Conjecture

This article covers Competition and the Core, Replication, The Shrinking Core, and The Limit Theorem. [Details...]

8. Incomplete and Intransitive Preferences

This article covers Incomplete and Intransitive Preferences. [Details...]

9. Radner Equilibrium

The Radner equilibrium considers a situation where there are multiple assets, multiple goods, multiple time periods and multiple states (thus uncertainty). [Details...]

10. Restricted Cores - The Epsilon Equivalence Theorem

Anthropologists tell us that 150 is about the maximum number of people any given individual can know intimately enough to bond with. We know that in Edgeworthian exchange, agents who are in the process of forming coalitions must know the preferences and endowments of others. If we decide to call this "intimacy" and call coalitions "bonding", then what are the consequences of the anthropologists' observation for the theory of the core? It is clear that the process of coalition-formation is going to be restricted, but exactly in what manner? [Details...]

11. The Consumer: Choice and Equillibrium

Discussion including competitive equilibrium, the consumer, choice and indifference curves, working towards the optimal bundle, indicators, the invisible hand, income and substitution effect, demand curves, and applications to the housing market and subsidies, and utility and utility functions. There are also practice problems. [Details...]

12. The Continuum Economy

This article covers The Continuum Economy: Beginner's guide, The Continuum Economy: Formal Statement, Aumann's Core Equivalence Theorem, Existence of Equilibrium, Restricted Cores: the Epsilon equivalence theorem, and Atoms Revisited: the Oligopoly equivalence theorem. [Details...]

13. The Equivalence Theorem - Arrow-Debreu and Radner

This article proves that the allocations in a Radner equilibrium would be equivalent to the allocations in an Arrow-Debreu equilibrium. [Details...]

14. The General Glut Controversy and Say's Law

In a simple shoe-hat world, at any one time, three possible situations may arise: (1) there may be a sufficient amount of shoes and hats to satisfy all demand; (2) there may be too many shoes offered on the market - implying too great a demand for hats; and (3) there may be too many hats and not enough shoes. Situations (2) and (3) are situations when markets have not made precise the allocations. However, the essence of Say's Law is that there can never be too much of both shoes and hats. A shoemaker would not make more shoes if he did not desire more hats. Therefore, Say's Law concludes, general gluts cannot exist. [Details...]

15. The Hart Existence Problem

For Radner equilibrium, we need to assume complete asset markets. This does not require that we have a full set of "state-contingent" markets as in Arrow-Debreu, but rather only that the set of assets can "span" the entire state returns space. However, assuming this does not end all difficulties. Recall that the return of asset f in state s is equal to the payoff of asset f in state s evaluated at the spot prices in state s. The fact that returns in different states depend on different state prices can lead to some rather unpleasant consequences, as pointed out by Oliver D. Hart (1975). [Details...]

16. The Opportunity Cost Doctrine

This article covers Opportunity Cost and The Austrian-Marshallian Debate. [Details...]

17. The Paretian System - Efficiency

This article covers Pareto-Optimality and The Fundamental Welfare Theorems. [Details...]

18. The Paretian System - Equilibrium

This article covers general equilibrium in the Paretian System first with a graphical illustration of a two-sector model, and then a more general multi-sector model. [Details...]

19. The Paretian System - Social Welfare

This article covers The Social Optimum, The New Welfare Economics, Welfare Comparisons, and Bergson-Samuelson Social Welfare Functions. [Details...]

20. Walrasian Pure Exchange

This article covers The Walrasian Exchange Economy, Demand-and-Supply Representation, Edgeworth-Bowley Box Representation, and Production as Indirect Exchange. [Details...]

General Equilibrium - Interactive Tutorial

21. Completing Markets: Options and Long-Lived Securities

Options are one of the more interesting securities to which arbitrage reasoning can be applied. (European) options, recall, are assets who derive their value from an underlying security, thus they have a return structure ro = [max(0, r1 - c), max(0, r2 - c), .., max(0, rS-c)] where r1, r2, .., rS are the returns on the underlying security and c is the "strike" price. The strike price is the asset price at which the owner of the option is entitled to buy (if a call option) or sell (if a put option) a unit of an underlying security if he decides to "exercise" it. One of the more interesting results, as stressed by Stephen Ross (1976), is that we can use options to "complete" incomplete markets: specifically, we can construct options to span a space when there are an insufficient number of fundamental assets. [Details...]

22. Edgeworth Box application

An interactive application that allows the user to enter and change the parameters used in an Edgeworth box display. Note that this application requires Java to be installed on your computer. [Details...]

23. IS-LM Model

The IS-LM model depicts the causes and consequences of simultaneous equilibria within the product market and the money market. A graphical system visually demonstrates how an equilibrium level of income established in the product market interacts with the equilibrium rate of interest determined in the money market. [Details...]

24. Money Market

The equilibrium in the money market reflects the simultaneous interaction of the supply of and, the demand for, money. In this model, the supply of money is set by the FED and, the demand for money comprises both the speculative and transactions demand for money. [Details...]

25. Trade Equilibrium

The one-country international trade equilibrium model includes community indifference curves (denoted CIC, suggested to show demand) to reveal preferences in consumption and production possibilities frontiers (PPF) with increasing opportunity costs in production. [Details...]

General Equilibrium - Online Book

26. Edgeworthian Exchange

A collection of articles providing a comprehensive coverage of the Edgeworthian Exchange. The following topics are covered: Edgeworth's Indeterminacy of Contract, Determinacy Restored, Edgeworth's Conjecture, Monopoly Pricing and Contracts, The Continuum Economy, Imperfect Curiosa, The Non-Standard Economy, Core Convergence, Adjustment Processes, and Coalitional Exchange. [Details...]

27. The Paretian System

A collection of articles providing a comprehensive coverage of the Paretian System. The follwoing topics are covered: Equilibrium, Efficiency, Market Failure, and Social Welfare. [Details...]

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