FINANCE AS AN INDUSTRY: A SIMPLE MODEL OF GROWTH*

Abstract

THE PURPOSE of the dissertation is to integrate financial intermediation into a theoretical model of real economic output and growth. The methodology involves construction of a model in which capital accumulation is based upon an interest-elastic demand for the capital stock. This model is shown to be capable of adjusting to an equilibrium capital intensity and saving share. To this growth model is added a financial intermediary sector to form a two-sector model of an economy. The production sector uses real inputs of capital and labor to produce a homogeneous good which is then allocated to consumption and real capital accumulation. The financial intermediary sector uses real inputs of capital and labor to produce financial intermediary services. Financial intermediary output is described by a production function for the financial intermediary in which real capital and labor inputs are related to the units of real capital placed by the financial intermediary with production sector firms. That is, for each unit of real capital used to produce the homogeneous good, the financial intermediary expends real resources of capital and labor to gather capital from surplus households in order to place this capital with deficit production units. It is assumed that at the firm level the financial production functions exhibit the usual decreasing average product after some point, which leads to increasing average unit costs. At the aggregate sector level the financial production function exhibits constant returns to scale and constant unit costs, as expansion is carried out by the introduction of new and similarly efficient financial intermediaries. The financial intermediary thus employs real capital and labor in profit-maximizing quantities and pays these factors the competitive factor returns. The intermediary pays deposit rates to attract deposit capital which it then lends to production sector units and earns a loan rate equal to the marginal product of capital. The financial intermediary earns unit revenues equal to the difference between the loan rate and deposit rate. This quantity, called the unit cost of finance, is a per period rate per unit of capital. Total revenues of the intermediary are then composed of these per unit charges. When competition prevails in the financial intermediary market for deposit capital the intermediary is forced to pay a high enough deposit rate so that the intermediary merely covers its real factor input costs. The intermediary thus is capable of adjustments in deposit rates and factor inputs; and in a competitive equilibrium situation it produces financial services at minimum average costs. The deposit rate in a competitive equilibrium is then equal to the production sector marginal product of capital (loan rate) less the minimum average unit cost of financial services. The solution for the variables of the system are determined by a simultaneous solution of the sectoral production functions, the capital demand function (saving function), and capital and labor allocation equations (perfect substitutability). The model is solved for the sectoral capital intensities, the distribution of labor and capital between sectors, the real rates in the system (deposit rate and marginal product of capital), as well as aggregate and per capita income, investment and consumption.