# 1994

94-01. Zapatero, F., *"Effects of Financial Innovations on Market Volatility when Beliefs are Heterogeneous"*

**Abstract:** We construct an intertemporal equilibrium with two agents with heterogeneous beliefs. Heterogeneity of beliefs induces volatility of the interest rate. We study the effect of financial innovation on interest rate volatility and conclude that, in a setting of asymmetric beliefs, introducing the asset that completes markets will (locally) increase the volatility of the endogenous interest rate process. We can design the "neutral" security so as to minimize the effects on volatility. Nevertheless, our model suggests that, overtime, introducing the new security will have a smoothing effect since beliefs will converge faster and uncertainty will be resolved quicker.

94-02. Martínez-Legaz, E. and Santos, M., *"On Expenditure Functions"*

**Abstract:** In this paper we present complete characterizations of the expenditure functions for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for expenditure functions and utility representations, and for expenditure functions and preference structures. These results apply indistinctly to finite- and infinite-dimensional spaces; moreover, in the case of preference structures they are valid for non-complete preorders.

94-03. Ladrón de Guevara, A., Ortigueira, S. and Santos, M., *"Equilibrium Dynamics in Two-Sector Models of Endogenous Growth"*

**Abstract: **Recent research has focused on the dynamics of the Lucas-Uzawa model of endogenous growth (e.g., Caballé-Santos (1993), Chamley (1993) and Faig (1993)). This model allows for permanent growth of both consumption and investment, propelled by a human capital technology. In contrast to the standard neoclassical growth model, the level of technological progress or education is determined by the decision process of economic agents, and thus the dynamics of growth is not driven by an exogenous force external to the economy. The model then yields certain specific predictions on the determinants of long-term growth, and on the interaction of physical and human capital in the transition off steady states. Also, this framework provides a useful setting to assess the effects of economic policies on the process of physical and human capital accumulation.

94-04. Goldstein, R. and Zapatero, F.,* "General Equilibrium with Constant Relative Risk Aversion and Vasicek Interest Rates"*

**Abstract: **We consider a pure exchange economy consisting of a single risky asset whose dividend drift rate is modelled by an Ornstein-Uhlenbeck process, and a representative agent with power-utility who, in equilibrium, consumes the dividend paid by the risky asset. Endogenously determined interest rates are found to be of the Vasicek (1977) type. The mean and variance of the equilibrium stock price are stochastic and have mean-reverting components. A closed form solution for a standard call option is determined for the case of log-utility.

94-05. Edlin, A., Epelbaum, M. y Heller, W., *"Surplus Maximization and Price Discrimination in General Equilibrium: Part I"*

**Abstract:** Regulators of natural monopolies advocate inducing monopolies to maximize the sum of consumer and producer surplus to the extent possible. Although such maximization is efficient in partial equilibrium, its general equilibrium properties have not yet been fully explored. We study the welfare properties of surplus maximization in a general equilibrium model that accounts for all interactions with other markets. We do so by embedding a single perfectly discriminating monopolist in an otherwise standard Arrow-Debreu economy. We find that although equilibria are efficient, not all Pareto optima can be decentralized. When the monopolist has increasing returns to scale, a tension arises between surplus maximization in a single market and fulfilling certain social objectives.

94-06. Edlin, A. and Epelbaum, M., *"Surplus Maximization and Price Discrimination in General Equilibrium: Part II"*

**Abstract: **Our companion paper introduced a new general equilibrium concept, called PDME, in which a natural monopoly maximizes its industry's surplus. While PDME's are always efficient, decentralization and existence sometimes fail under increasing returns to scale. This paper derives conditions under which PDME's exist and under which optima can be decentralized. We also link PDME to other equilibrium concepts with equilibrium conversion theorems. This allows us to provide new conditions when these earlier euilibrium concepts are efficient, and when the other equilibira exist. It also allows us to rank equilibrium concepts by the size of the set of decentralizable optimal allocations.

94-07. Hernández, A. and Santos, M., *"Competitive Equilibria for Infinite-Horizon Economies with Incomplete Markets"*

**Abstract: **In this paper we consider a sequential trading economy with incomplete financial markets and a finite number of infinitely lived agents. We propose a specification of agents' budget sets and show that such specification features several desirable properties. We then establish the existence of an equilibrium for a regular class of economies.

94-08. Cooley, T., Greenwood, J. and Yorukoglu, M., *"The Replacement Problem"*

**Abstract: **We construct a vintage capital model of economic growth in which the decision to replace old technologies with new ones is modeled explicitly. Depreciation in this environment is an economic, not a physical concept. We describe the balanced growth paths and the transitional dynamics of this economy. We illustrate the importance of vintage capital by analysing the response of the economy to fiscal policies designed to stimulate investment in new technologies.

94-09. Ortigueira, S. and Santos, M., *"On Convergence in Endogenous Growth Models"*

**Abstract: **In this paper we analyze the rate of convergence to a balanced path in a class of endogenous growth models with physical and human capital. We show that such rate depends locally on the technological parameters of the model, but does not depend on those parameters related to preferences. These results stand in sharp contrast with those of the one-sector neoclassical growth model where both preferences and technologies determine the speed of convergence toward a steady state.

94-10. Bona, J. and Santos, M., *"On the Role of Computation in Economic Theory"*

**Abstract:** The principal aim of this article is to provide commentary on the use of high-performance computers combined with numerical algorithms in the investigation of mathematical models of economic activity. The use of computer simulation to provide insight into mathematical models is distinguished from the better developed use of computers in recording and processing economic data, and it is intended here to concentrate only on the former.

94-11. Renero, J.M., **"Gresham's Law Type Equilibria in the Kiyotaki-Wright Models"**

**Abstract: **I establish new existence and welfare results for the Kiyotaki-Wright model (JPE, 1989). I show that good intrinsic properties are not necessary for an object to be universally accepted in equilibrium. Furthermore, bad objects may be socially desirable as media of exchange. One result is that for any number of goods larger than two and an open set of parameters, there exists a multiple equilibria in which the most costly to-store object is universally accepted. I also prove that there exists a contimuum of steady states of this kind. Moreover, there exist equilibria converging to each steady state of that continuum. For the case of three goods and no fiat object another result is that such equilibria may Pareto dominate other equilibria in which other less costly to-store objects are universally accepted. Moreover, steady states of this type may not exist while there exists a continuum of steady states in which the most costly to-store is universally accepted. In fact, these steady states may be the only ones which exist.