Knowledge that Transforms

The primary purpose of this study is to develop a model based on linear programming and input-output techniques which will assist in the formulation of development programs for underdeveloped areas. I. The elements of the development problem and the data available are considered from the point of view of selecting the most significant structural relationships for a formal model. II. A nonlinear programming model is presented which is designed particularly to analyze the choice between self-sufficiency and international specialization and the resulting investment patterns under various types of restrictions. III. A method of solving the programming problem by a simple iterative procedure is suggested. It takes advantage of the structure of the matrix of activities and the limited number of primary factors involved. Convergence of the solution is demonstrated. IV. A development model for Southern Italy is constructed for purposes of illustration, based on studies of consumption, investment, and input structure and assumptions as to the remaining parameters. A solution for a hypothetical development program is given, showing the method of solution and the effect of variation in several of the parameters. V. The implications of the results for the solution of a more general model are considered. The relationship of the interindustry model to sector analyses and the

possess negative real parts. The answer to this question given by James and Belz in [4] is not very useful from a practical point of view for it amounts essentially to the determination of the roots of the characteristic equation themselves. A stability criterion using only the given coefficients and not the roots of the characteristic equation was given by Hayes in [3]. But here, too, the transcendental auxiliary equation x* cot x = c must be solved first. In this paper we present another proof of the stability criterion using the so-called graphical methods of control engineering, i.e., Cauchy's theorem of residues. We thereby arrive at an expression for the criterion which seems to be better adapted to practical purposes (because with given coefficients only the auxiliary equation cos x = c has to be solved). The connection with the other forms of the stability criterion will be clarified and the criterion will be illustrated by an example from economics. For general discussion of these problems and further economics examples, compare Tustin [6].