Explanation Given Information: The sectors are Primary, Secondary and Tertiary, the payoff matrix is A = [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] and Mexico produced 860 billion pesos of raw materials, 23 , 000 billion pesos of manufactured goods and 8 , 500 billion pesos of services. Formula used: In an input output model, X = A X + D where A is the technology matrix, X is the production vector and D is the external demand vector. For matrices A with dimension m × n and B with dimension k × l , the product AB is defined if the number of columns in A equal number of columns in B , n = k . For two matrices A and B with equal dimension, A + B and A − B is the sum and difference of the corresponding entries of the matrices respectively. Calculation: Consider sectors are Primary, Secondary and Tertiary, the payoff matrix is A = [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] and Mexico produced 860 billion pesos of raw materials, 23 , 000 billion pesos of manufactured goods and 8 , 500 billion pesos of services. Since, in an input output model, X = A X + D where A is the technology matrix, X is the production vector and D is the external demand vector. Subtract AX from both sides of the equation X = A X + D . X − A X = A X + D − A X X − A X = D Since, Mexico produced 860 billion pesos of raw materials, 23 , 000 billion pesos of manufactured goods and 8 , 500 billion pesos of services. Write the goods and services produced as a column vector. Thus, X = [ 860 23 , 000 8 , 500 ] Substitute [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] for A and [ 860 23 , 000 8 , 500 ] for X in X − A X = D . D = [ 860 23 , 000 8 , 500 ] − [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] [ 860 23 , 000 8 , 500 ] Recall that for matrices A with dimension m × n and B with dimension n × k , the product AB is the matrix of dimension m × k and ij th entry of AB is the sum of product of corresponding entries of row i of A and column j of B . Since, number of rows in [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] is 3 and number of columns is 3 , Substitute 3 for m and 3 for n in m × n . Thus, dimension of [ 0.09 0.03 0.00 0.14 0.23 0.08 0.07 0.12 0.15 ] is 3 × 3 . Since, number of rows in [ 860 23 , 000 8 , 500 ] is 3 and number of columns is 1 , Substitute 3 for m and 1 for n in m × n . Thus, dimension of [ 860 23 , 000 8 , 500 ] is 3 × 1

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Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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Chapter 4.5, Problem 28E

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To calculate: The amount of raw materials exported where the sectors are Primary, Secondary and Tertiary, the payoff matrix is A=[0.090.030.000.140.230.080.070.120.15] and Mexico produced 860 billion pesos of raw materials, 23,000 billion pesos of manufactured goods and 8,500 billion pesos of services.

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Chapter 4.5, Problem 27E

Chapter 4.5, Problem 29E

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Solution Summary: The author calculates the payoff matrix for raw materials, manufactured goods, and services exported to Mexico.

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