Question

For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case? a. A firm can hire only full-time employees to produce its output, or it can hire some combination of fulltime and part-time employees. For each full-time worker let go, the firm must hire an increasing number of temporary employees to maintain the same level of output. b. \(A\) firm finds that it can always trade two units of labor for one unit of capital and still keep output constant. c. \(A\) firm requires exactly two full-time workers to operate each piece of machinery in the factory.

Short answer

In Case a, the isoquant is convex with a diminishing MRTS. In Case b, the isoquant is a straight line with a constant MRTS of 2. In Case c, the isoquant is L-shaped with an undefined MRTS due to no substitution possibility.

Step-by-step solution

Draw Isoquant for Case a.

In this case, the more full-time workers replaced by part-time workers, the more part-time workers are needed to maintain the current output. So the isoquant should be convex to the origin meaning it has a diminishing MRTS. The further to the right, the steeper it gets, implying that it takes more and more part-time workers to replace each additional full-time worker while maintaining the same production level.

Draw Isoquant for Case b.

This case suggests a constant trade-off between labor and capital, so the isoquant is a straight line. The slope of the isoquant is -2, indicating that the firm can always trade two units of labor for one unit of capital to keep the output constant. So here, the MRTS is constant and equals 2.

Draw Isoquant for Case c.

This case implies a fixed ratio of inputs, as it takes exactly two full-time workers to operate each piece of machinery in the factory. This results in an isoquant which is L-shaped. Here, the MRTS is undefined as there is no possibility to substitute between labor and capital.