Existence Results in General Equilibrium Theory

Abstract

This dissertation seeks to answer three existing questions in general equilbrium theory and introduce a framework permitting for the extension of equilibrium analysis to a new class of models.

Models with uncertainty at the aggregate and idiosyncratic level have become standard within macroeconomics due to their greater explanatory power. In 1998, Per Krusell and

Anthony Smith laid the foundation that permitted much of this work to take place by introducing a theoretical framework featuring such shocks but which was also amenable to study via practical numerical

methods. Existence of equilibrium in their model was not formally analyzed until Jianjun Miao studied the problem in 2006; unfortunately, arguments presented

therein have important complications. First, we provide a correct, and novel, proof for the existence of sequential equilibrium in the

Krusell-Smith model. An extension of the model to include economies with endogenous labor choices and non-zero borrowing will then be developed.

Within the literature, an important working assumption is the existence of stochastic processes featuring conditional-no-aggregate-uncertainty (CNAU). This requirement that the empirical distribution of the idiosyncratic and

aggregate shock processes depend only on realizations of the aggregate shock process can be easily met when there are countably many agents by the law of large numbers, but for a continuum of agents arguments

of the type will not work. As such, we will provide two methods for constructing processes featuring CNAU in a general setting.

Practicality and behavioral demands also make it important for sequential equilibria to be reproducible via the recursively optimal behavior of agents who have a sufficiently simple set of state variables.

In this vein, we will propose an intuitive and sufficient state variable that allows for the replication at least some sequential equilibria, while making savings in the

informational demands placed on actors; thereby, giving an affirmative answer to a weakened formulation of the existence of recursive equilibria question.

Finally, we present an equilibrium framework for economies featuring rational inattention. In particular, we will study the behavior of agents who face

information constraints regarding the observation of shocks and prices in a production economy and present an existence result.