Linear Algebra and Economics

Steve Levandusky

Input Coefficient Matrix Example

             Suppose that there are three goods manufacturing, transportation, and labor. The inputs for manufacturing consist of 0.2 units of manufacturing, 0.2 units of transportation, and 0.4 units of labor. The inputs for transportation consist of 0.6 units of manufacturing, 0.1 units of transportation, and 0.1 units of labor. The inputs for labor consist of 0.3 units of manufacturing, 0.6 units of transportation, and 0.0 units of labor. Also the final demand for manufacturing is $250, for transportation is $140, and for labor is $100.

             So, consider the input coefficient matrix and the final demand:










Thus, the economy needs to produce $1228.57 of manufacturing, $881.63 of transportation, and $679.59 of labor in order to meet the final demands of the three goods. [1]

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