An application of duality theory: A portfolio composition of the West-German private non-bank sector, 1968–1975

The objective of this paper is to apply the duality approach in the theory of consumer behavior for deriving demand systems to analyse the allocation of assets and liabilities of the private non-bank sector. A commodity approach is chosen where service flows of assets, physical capital and liabilities enter the direct utility function and the corresponding interest rates and price of capital enter the indirect utility function. The approach results in a system of demand and supply functions for optimal stocks consistent with utility maximization. For econometric implementation an overall model in an asset aggregate, capital and a liability aggregate is fitted first. Next, two submodels are constructed for an optimal allocation of the asset aggregate and the liability aggregate to its various components that made up the aggregate. Empirical results for time series data of the German private non-bank sector are presented.