The Theory of General Economic Equilibrium

Mas-Colell, Andreu

doi:10.1017/ccol0521265142

Cited by 655 publications

(397 citation statements)

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“…All these issues are worth exploring for SPLC equilibria and our algorithm as well. We note that the notion of index has already been studied for regular markets [35,42]; however, it uses the Hessian of the demand functions and hence is not applicable to our case.…”

Section: Combinatorial Interpretation For Linear Casementioning

confidence: 99%

A Complementary Pivot Algorithm for Market Equilibrium under Separable, Piecewise-Linear Concave Utilities

Garg¹,

Mehta²,

Sohoni³

et al. 2015

SIAM J. Comput.

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Abstract. Using Lemke's scheme, we give a complementary pivot algorithm for computing an equilibrium for Arrow-Debreu markets under separable, piecewise-linear concave (SPLC) utilities. Despite the polynomial parity argument on directed graphs (PPAD) completeness of this case, experiments indicate that our algorithm is practical-on randomly generated instances, the number of iterations it needs is linear in the total number of segments (i.e., pieces) in all the utility functions specified in the input. Our paper settles a number of open problems: (1) Eaves (1976) gave an LCP formulation and a Lemke-type algorithm for the linear Arrow-Debreu model. We generalize both to the SPLC case, hence settling the relevant part of his open problem. (2) Our path following algorithm for SPLC markets, together with a result of Todd (1976), gives a direct proof of membership of such markets in PPAD and settles a question of Vazirani and Yannakakis (2011). (3) We settle a question of Devanur and Kannan (2008) of obtaining a "systematic way of finding equilibrium instead of the brute-force way" for the separable case and we obtain a strongly polynomial algorithm if the number of goods or agents is constant. (4) We give a combinatorial way of interpreting Eaves' algorithm for the linear case, hence answering Eaves' question (1976), "That the algorithm can be interpreted as a 'global market adjustment mechanism' might be interesting to explore."

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Section: Combinatorial Interpretation For Linear Casementioning

confidence: 99%

A Complementary Pivot Algorithm for Market Equilibrium under Separable, Piecewise-Linear Concave Utilities

Garg¹,

Mehta²,

Sohoni³

et al. 2015

SIAM J. Comput.

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“…To see the smoothness of H, we notice, in view of Proposition 2.7.2 of Mas-Colell (1989), that Z u (p) is smooth on E, so there remains to prove the smoothness of Z h (p, R(p,t)) for h = 1, . .…”

Section: Lemma 1 the Homotopy H(pt W)mentioning

confidence: 99%

A simple method for computing equilibria when asset markets are incomplete

2015

Journal of Economic Dynamics and Control

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The problem of computing equilibria for general equilibrium models with incomplete real asset markets, or GEI models for the sake of brevity, is reconsidered. It is shown here that the rank-dropping behavior of the asset return matrix could be dealt with in rather a simple fashion: We first compute its singular value decomposition, and then, through this decomposition, construct, by the introduction of a homotopy parameter, a new matrix such that it has constant rank before a desired equilibrium is reached. By adjunction of this idea to the homotopy method, a simpler constructive proof is obtained for the generic existence of GEI equilibria. For the purpose of computing these equilibria, from this constructive proof is then derived a path-following algorithm whose performance is finally demonstrated by means of two numerical examples.

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“…It is, in fact, possible even without such separability if preferences over 4 Throughout the paper we say that a property holds generically if the closure of the set of couples' preferences, incomes and prices at which it fails to hold has empty interior. To make such a statement we require a topology on smooth preferences such as the compact-open topology discussed in, say, Kannai (1970) or Mas-Colell (1985) those individually contributed goods from which there is not separability are also identical between the partners since there exist equilibria with quantities of these goods also identical in equilibrium 5 . Lechene and Preston (2005) demonstrate the possibility of such cases.…”

Section: Jointly Contributed Public Goodsmentioning

confidence: 99%

Noncooperative household demand

Lechêne

Preston

2011

Journal of Economic Theory

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We study noncooperative household models with two agents and several voluntarily contributed public goods, deriving the counterpart to the Slutsky matrix and demonstrating the nature of the deviation of its properties from those of a true Slutsky matrix in the unitary model. We provide results characterising both cases in which there are and are not jointly contributed public goods. Demand properties are contrasted with those for collective models and conclusions drawn regarding the possibility of empirically testing the collective model against noncooperative alternatives and the noncooperative model against a general alternative. JEL: D11, C72

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The Theory of General Economic Equilibrium

Cited by 655 publications

References 0 publications

A Complementary Pivot Algorithm for Market Equilibrium under Separable, Piecewise-Linear Concave Utilities

A Complementary Pivot Algorithm for Market Equilibrium under Separable, Piecewise-Linear Concave Utilities

A simple method for computing equilibria when asset markets are incomplete

Noncooperative household demand

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