An economy consists of three sectors: agriculture, manufacturing, and energy. The prices of outputs of these...
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An economy consists of three sectors: agriculture, manufacturing, and energy. The prices of outputs of these three industries are $5, $4, and $2 respectively. Production of a unit of agricultural product requires 0.25 units from agriculture, 0.4 units from manufacturing, and 0.3 units from energy. Production of a unit of manufacturing product requires 0.2 units from agriculture, 0.5 units from manufacturing, and 0.4 units from energy. Production of a unit of energy requires 0.l units from agriculture, 0.2 units from manufacturing, and 0.2 units from energy. The agriculture, manufacturing, and energy face the following external, or final, demands: 500, 800, and 400 respectively. (a) Write down the equations of the Leontief model for this economy. (b) Write the system of equations from part (a) above in the matrix notation. If you introduce a matrix or vector, show explicitely the elements of that matrix or vector. (c) Find the unit value added in industry 3. Explain. (d) The solution to the Leontief model is x, =2676.69, x, =5428.57, x,=4218.04. Find the value added in industry 3. Explain. An economy consists of three sectors: agriculture, manufacturing, and energy. The prices of outputs of these three industries are $5, $4, and $2 respectively. Production of a unit of agricultural product requires 0.25 units from agriculture, 0.4 units from manufacturing, and 0.3 units from energy. Production of a unit of manufacturing product requires 0.2 units from agriculture, 0.5 units from manufacturing, and 0.4 units from energy. Production of a unit of energy requires 0.l units from agriculture, 0.2 units from manufacturing, and 0.2 units from energy. The agriculture, manufacturing, and energy face the following external, or final, demands: 500, 800, and 400 respectively. (a) Write down the equations of the Leontief model for this economy. (b) Write the system of equations from part (a) above in the matrix notation. If you introduce a matrix or vector, show explicitely the elements of that matrix or vector. (c) Find the unit value added in industry 3. Explain. (d) The solution to the Leontief model is x, =2676.69, x, =5428.57, x,=4218.04. Find the value added in industry 3. Explain.
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Finite Mathematics and Its Applications
ISBN: 978-0134768632
12th edition
Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
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