Manjira Datta

Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exist and are unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a monotone map approach to the problem. The class of economies for which we are able to obtain our existence result is apparently considerably larger than those considered in previous work. Additionally unlike previous work, we are able to also prove that this equilibrium is unique. We conclude by applying the new results to some important examples of monetary economies often used in applied work.

Monotone Methods for Markovian Equilibrium in Dynamic Economies

In this paper, we provide an overview of an emerging class of “monotone map methods” in analyzing distorted equilibrium in dynamic economies. In particular, we focus on proving the existence and characterization of competitive equilibrium in non-optimal versions of the optimal growth models. We suggest two alternative methods: an Euler equation method for a smooth, strongly concave environment, and a value function method for a non-smooth supermodular environment. We are able to extend this analysis to study models that allow for unbounded growth or a labor–leisure choice.

Dynamic Externalities and Policy Coordination

The paper introduces trade into dynamic models with externalities and capital accumulation, and evaluates the efficiency of the Cournot-Nash equilibrium. It considers mixed economies characterized by a blend of strategic and nonstrategic sectors. Also, there are two sources of interdependence: the existence of production externalities and the endogenous determination of market prices. It is shown that policy coordination is not needed when preferences are the same. In this case, the production externalities are internalized, so that an inefficient solution becomes the efficient integrated world equilibrium due to trade. Copyright 2000 by Blackwell Publishing Ltd.

Externalities and Price Dynamics

This paper analyzes dynamic movement of outputs and market-clearing when mutually interdependent economies trade. The equilibrium evolution of stocks admit the possibility of monotonic or cyclical behavior, even in the long run. However, the prices eventually reach a steady-state but may exhibit monotonic or oscillating behavior, in the short run. Also we show that higher consumption per unit of stock is associated with a lower productivity or with negative externalities. A stronger preference for the foreign good, increases or decreases consumption depending whether the externality is negative or positive.

Isotone Recursive Methods: The Case of Homogeneous Agents

Over the last decade, isotone recursive methods have provided unified catalog of results on existence, characterization, and computation of Markovian Equilibrium Decision Processes (MEDPs) in infinite horizon economies where the second welfare theorem fails. Such economies include models with production nonconvexities, taxes, valued fiat money, models with monopolistic competition, behavioral heterogeneity, and incomplete markets. In this paper, we survey this emerging class of methods. Our methods use a qualitative approach to economic equilibria first introduced in the work in operations research by Veinott and Topkis. As the methods emphasize the role of order, they are amenable for obtaining conditions for monotone comparison theorems on the space of economies. We are also able to describe monotone iterative procedures that provide the needed foundations for a theory of numerical solutions for MEDPs and stationary Markov equilibrium (SME). One interesting additional result of independent interest is we construct sufficient conditions for the existence of a new class of envelope theorems for nonconcave programming problems.

Isotone Recursive Methods

Over the last decade, isotone recursive methods have provided unified catalog of results on existence, characterization, and computation of Markovian Equilibrium Decision Processes (MEDPs) in infinite horizon economies where the second welfare theorem fails. Such economies include models with production nonconvexities, taxes, valued fiat money, models with monopolistic competition, behavioral heterogeneity, and incomplete markets. In this paper, we survey this emerging class of methods. Our methods use a qualitative approach to economic equilibria first introduced in the work in operations research by Veinott and Topkis. As the methods emphasize the role of order, they are amenable for obtaining conditions for monotone comparison theorems on the space of economies. We are also able to describe monotone iterative procedures that provide the needed foundations for a theory of numerical solutions for MEDPs and stationary Markov equilibrium (SME). One interesting additional result of independent interest is we construct sufficient conditions for the existence of a new class of envelope theorems for nonconcave programming problems.

Lattice Methods in Computation of Sequential Markov Equilibrium in Dynamic Games

This paper uses lattice programming methods along with the extension of Tarskis fixed point theorem due to Veinott (1992) and Zhou (1994) to establish sufficient conditions for existence of sequential symmetric Markov equilibrium in a large class of dynamic games. Our method is constructive and we provide specific algorithms for computing equilibrium. These results are applied to the classic fishwar game in the context of a finite horizon.

Nonclassical Brock-Mirman Economies

We show that monotone methods, especially, those based on lattice theory and lattice programming can produce results, e.g., on the monotonicity of the optimal programs, as well as on the existence of fixed points, consistent with the current macroeconomics literature, in the absence of continuity, differentiability and concavity. We illustrate the use and power of the lattice theory techniques in two simple and very useful models. First, the Brock-Mirman growth model is studied in a nonclassical setting. Here all the assumptions of the original model are made except that the production function is allowed to be non-concave. The second model is an extension of the Brock-Mirman model that goes beyond the planners solution and allows for decentralized decisions in equilibrium.

Intertemporal Cournot and Walras Equilibrium

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an ineffciency which does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., moving towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., moving away from the Walrasian amount).