The purpose of this paper is to consider some problems arising in several applications of the theory of portfolio analysis pioneered by Markowitz [8] and Tobin [13]. This theory of asset choice under uncertainty has been applied to a large and growing set of problems beyond the original application to the selection of the investor's optimal portfolio, e.g., the capital budgeting decision of the firm (Lintner [7]), international capital flows (Grubel [5]), the choice of an export mix for a country (Brainard and Cooper [1] and the flow of direct investment (Stevens [12] and Prachowny [10]). In all applications a common element is the set of efficient portfolios which, in turn, is determined. by the set of moments—means, variances, and covariances—of the returns from the different assets that are. Considered for inclusion in the portfolio.

Recently, Cohen and Gujarati [2] have suggested that when multicollinearity is present there is “ …danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero…” The problem they discuss is not a new one and has been extensively treated in the existing literature. However, their approach is straightforward and will certainly aid the practitioner in his understanding of the problems associated with multicollinearity.

As has been demonstrated, the process of deciding whether or not to produce beyond the split-off point is not as simple as set forth in most managerial accounting books. Linear programming can be used in these situations as long as the production relationships remain relatively constant. However, in applying linear programming it is necessary to allow for inventories of unused intermediate outputs or optimality may not be truly found. It is not possible to construct a general model, but a wide variety of assumptions have been discussed in this paper with the goal of establishing a methodology of formulating decision models when joint products are involved.

[Using a general definition of a generalized inverse of a singular matrix we generalized the k class and three stage least squares procedures so that they can be applied when the sample size, say T, is smaller than the number of exogenous variables, say K, in a system of equations. These generalized k class and three stage least squares estimators, in usual cases, coincide with ordinary least squares and Zellner's [7] efficient estimators respectively as long as T @ extless K and coincide with the usual k class and three stage least squares estimators respectively as T exceeds K.]