Suppose there are two inputs in the production function, labor and capital, and

Question

Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitues. The existing technology permits one machine to do the work of three workers. The firm wants to produce 100 units of output. Suppose the firm price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225?

Explanation / Answer

Because labor and capital are perfect substitutes, the isoquants (in bold) are linear and the firm will use

only labor or only capital, depending on which is cheaper in producing 100 units of output.

The (absolute value of the) slope of the isoquant (MPE / MPK) is 1/3 because 1 machine does the work of

3 men. When the wage is $900 (left panel), the slope of the isocost is 300/750. The isocost curve,

therefore, is steeper than the isoquant, and the firm only hires capital (at point A). When the weekly wage

is $225 (right panel), the isoquant is steeper than the isocost and the firm hires only labor (at point B).

Weekly Salary = $300 Weekly Salary = $225

The elasticity of labor demand is defined as the percentage change in labor divided by the percentage

change in the wage. Because the demand for labor goes from 0 to a positive quantity when the wage

dropped to $225, the (absolute value of the) elasticity of labor demand is infinity.

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