Yves Balasko
Professor of Economics
Department of Economics and Related Studies
Heslington, York YO10 5DD
contact: yves.balasko@york.ac.uk
Selected Publications:
"General Equilibrium Theory of Value," Princeton University Press, NJ., 2011; "On the number of critical equilibria separating two equilibria," forthcoming in Theoretical Economics; "On the stability of
nonsunspot equilibria," forthcoming in Journal of Economic Theory; "General equilibrium
without utility functions: How far to go?" (with Mich Tvede, Economic Theory, 45, 2010;
"The Equilibrium Manifold," MIT Press, Cambridge, MA., 2009; "Out-of-equilibrium price dynamics," Economic Theory, 33, 2007; "Economies with price-dependent preferences," Journal of Economic
Theory, 109, 2003; "Temporary financial equilibria,'' Economic Theory, 21, 2003; "The natural projection approach to the infinite horizon model," Journal of Mathematical
Economics, 27, 1997; "Market participation and sunspot equilibria," with David Cass and Karl Shell, Review
of Economic Studies, 62, 1995; "The set of regular equilibria," Journal
of Economic Theory, 58, 1992; "The structure of financial equilibrium with exogenous
yields: The case of incomplete markets," with David Cass, Econometrica,
57, 1989 "Foundations of the Theory of General Equilibrium," Academic
Press, Boston, 1988; "The overlapping-generations model I and II, " with Karl Shell,
Journal of Economic Theory, 23-24, 1980-1981; "Number and definiteness
of economic equilibria," Journal of Mathematical Economics, 7, 1980; "Some
results on uniqueness and on stability of equilibrium in general equilibrium
theory," Journal of Mathematical Economics, 2, 1975.
Just Published :
This
book develops the equilibrium manifold approach to the general
equilibrium model. No prior knowledge of economic theory is
strictly necessary. The main mathematical concepts are defined in a way
that make them directly applicable to the models considered in the
book.
The
first part of the book is devoted to a thorough study of
the properties of the exchange model and of its equilibria. These
properties include: the diffeomorphism of the equilibrium manifold with
a Euclidean space; the negative definiteness of the Jacobian matrix of
aggregate demand at no-trade equilibria; the closedness and measure
zero of the set of critical equilibria; the smoothness and
properness of the natural projection; the identification of the
preimage by the natural projection of the set of equilibrium
allocations with the set of no-trade equilibria; the inclusion of the
set of equilibrium allocations into one pathconnected component of the
set of regular economies; the uniqueness of equilibrium for
endowments belonging to that pathconnected component. The second
part of the book is devoted to showing that those properties of the
exchange model extend remarkably well to models with private ownership
of decreasing and constant returns to scale production.
This
book offers a comprehensive foundation for the general equilibrium
exchange and production models that lie at the heart of economic
theory. The approach developed in the book is directly applicable to
the more complex models that deal with assets and incomplete markets
through the explicit introduction of time and uncertainty.
This up-to-date presentation of economic theory will be most
useful to graduate students in economics and researchers in the field.
This book can also be used by mathematics students that are looking for
an introduction to economic theory.
Recent papers:
On the number of critical equilibria separating two equilibria
Abstract: It is shown that two arbitrary equilibria in the general equilibrium model without sign restrictions on endowments can be joined by a continuous equilibrium path that contains at most two critical equilibria. This property is strengthened by showing that regular equilibria having an index equal to one, a necessary condition for stability, can be joined by a path containing no critical equilibrium. These properties follow from the real-algebraic nature of the set ofcritical equilibria in any fiber of the equilibrium manifold. (Theoretical Economics, forthcoming.)
On the stability of nonsunspot equilibria
Abstract: This paper analyzes the stability of the (Pareto efficient) nonsunspot equilibria as a function of the constraints faced by consumers in their ability to transfer wealth between states of nature. The nonsunspot equilibria are independent of the constraints since they can be identified to the equilibria of the associated certainty economy. It is shown that the equilibria that are stable for the certainty economy define nonsunspot equilibria that are stable in the following two polar cases: 1)~All consumers are unconstrained; 2)~All consumers are fully constrained. Furthermore, the stable certainty equilibria with small trade vectors define nonsunspot equilibria that are stable independently of the constraint levels. Instability can develop for intermediate constraint levels only at nonsunspot equilibria that feature sufficiently large trade vectors. A small change in the constraint levels may then trigger a jump from a Pareto efficient nonsunspot equilibrium to a Pareto inefficient sunspot equilibrium. (Journal of Economic Theory, forthcoming.)
General equilibrium without utility functions: How far to go? (Joint with Mich Tvede)
Abstract: How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers' preferences. We show in this paper that if consumers' non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: 1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; 2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; 3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; 4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; 5) the pathconnectedness of the sets of stable equilibria. (Economic Theory, 2010.)
Out-of-equilibrium price dynamics
Abstract: A trading-post organization of exchange is shown to determine an out-of-equilibrium price dynamics. The unique equilibrium of quasi-linear economies (defined by log-linear utility functions) is stable for the discrete time version of the dynamics. Equilibria that are stable for the continuous time version include those that satisfy the gross-substitutability property, the no-trade equilibria and, more generally, those for which trade intensity is relatively small. In addition, the set of stable equilibria is path-connected when endowments are allowed to vary without sign restrictions. (Economic Theory, 2007.)
On the satisfaction of peak demand in the certainty case
Abstract: The concept of full-capacity flat-rate equilibrium is explored for a version of the Arrow-Debreu model with time-differentiated goods and production subject to a capacity constraint. The corresponding equilibrium allocations are shown to be inefficient in general. It is also shown that rationing peak-demand is Pareto superior to non-rationing. ( Journal of Mathematical Economics, 2008.)
Economies with price-dependent preferences
Abstract: Except existence, not much is known of economies where individual preferences are affected by prices. We show that the main properties of competitive equilibria that fall under the general heading of qualitative comparative statics remain true when preferences are price dependent, provided that the total resources are allowed to vary in the parameter space. The equilibrium set is a smooth manifold diffeomorphic to a Euclidean space; the natural projection is a smooth proper map, with topological degree one; equilibria always exist, and are locally unique for an open and dense set of economies. (Journal of Economic Theory, 2003.)
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