Modeling economic system with the use of matrix algebra (Leontief input-output model)

Abstract

The purpose of the study was to determine the external industrial demand output, given a 3 x 3 matrix input values with prescribed demand values. The Leontief input-output model leads to a better understanding of modeling economic systems. The identity matrix and a 3 x 3 matrix was used to produce industry’s output unit for external demand. Of the 8619 external demand output unit turned out by a farmer, 0.4 unit of farmer’s product were used up by farmers, 0.5 unit of baker’s product and 0.5 unit of Grocer’s product were utilized by the farmers. Of the 4684 external demand output unit turned out by a Baker, 0.00 unit of Baker’s product were used up by the Bakers, 0.30 unit of Farmer’s product and 0.30 unit of Grocer’s product were utilized by the Bakers. Of the 3661 external demand output unit turned out by a Grocer, 0.00 unit of Grocer’s product were used up by Grocers, 0.20 unit of baker’s product and 0.20 unit of Farmer’s product were utilized by the Grocer. Leontief input-output model is an effective tool in modeling economic system in the industries. Key words: Input-output model, matrix algebra.