General Equilibrium with Financial Markets: Existence, Uniqueness, and Implications for Corporate Finance

Abstract

THE OBJECT OF THIS PAPER is to examine some critical issues in corporate finance in the context of a general equilibrium framework. Rather then take Arrow-type [1] state prices as a starting point, we shall start with share and bond prices and show how, in a general equilibrium framework, these prices relate to the state prices.1 In particular we establish an equivalence theorem for a general equilibrium with financial markets and Arrow markets with state-dependent prices. We then discuss the two famous results of Modigliani and Miller [7, 8] in the context of our markets. While the MM dividend irrelevance theorem is true-though only in a specific sense-we show that there is a meaningful sense in which capital structure is fixed in the presence of firm bankruptcy, no matter what the probability of such a bankruptcy, and without any attendant non-perfect market phenomena such as bankruptcy costs or secured debt.2 Starting with a two-period, one-commodity model (this latter assumption is merely simplifying and is not necessary to the results of the paper), we outline the nature of production: Firms purchase inputs today in order to produce from them tomorrow, but production tomorrow from today's inputs is uncertain, as it depends on the state of nature at the time of production. This state of nature affects the production function. To finance today's purchases of inputs, each firm may sell either new equity or bonds. The former merely dilutes the earnings of equity holders in the second period. Bonds, on the other hand, have a prior claim on firm income in the second period: If the income from production suffices to