Leontief model

This model considers an open sector, where labor, profits, etc. are considered in the following way. Let xi be the total output of industry i to satisfy the Demand from the open sector and all industries (in dollars). So xi = ai1x1 + ai2 x2 +... + ain xn + di where di denotes the demand of the sector opened by industry i. Here aijxij represents the input requirements of industry j by industry i. This can be written in matrix form as X = AX + d Consider the following input coefficient matrix A and the demand vector of the open sector d, for 10 interdependent industries in the United States

Industry Type 1 Agriculture and Food 2 energetic 3 Construction 4 Chemistry 5 Textile 6 paper 7 Steel 8 Engineering 9 Precious metals 10 Services Calculate the output levels of the ten industries.

1. Use the given matrices A and d to numerically compute the output levels xi for each type of industry. 2. Interprets in economic language the numerical value of the element xi in the output matrix.