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

a. The firm faces a convex-shaped isoquant with decreasing marginal rate of technical substitution (MRTS), as illustrated in the following figure.

b. The firm faces a linear isoquant with constant MRTS, as illustrated in the following figure.

c. The firm faces an L-shaped isoquant with undefined MRTS, as illustrated in the following figure.

Step-by-step solution

The isoquant for part a

An isoquant is a locus that shows various combinations of inputs that produce a specific level of output. The marginal rate of technical substitution defines the slope of an isoquant.

The following figure illustrates the relevant isoquant

In the figure above, part-time and full-time workers are placed on the vertical and horizontal axes, respectively. A point on the curve shows the firm can produce its output by employing full-time workers only. However, as one moves up the curve from point A to B, the firm sacrifices some units of full-time workers and hires more part-time employees to produce the level of output.

Therefore, as the firm moves up the isoquant, the employment of full-time workers falls, and the employment of part-time workers rises. So, the absolute value of the slope rises as the firm moves up the isoquant. So, the isoquant is convex with decreasing marginal rate of technical substitution.

The isoquant for part b

The marginal rate of technical substitution is the rate at which one input can be exchanged for another input to produce the same output level.

The following figure illustrates the relevant isoquant.

The firm always exchanges two units of labor for one unit of capital to produce the same output level. So the value of slope or MRTS of labor for capital is equal to 1/2 and is constant. Thus part-time and full-time workers are perfect substitutes in this case. Hence, the isoquant is linear with a constant marginal rate of technical substitution, as shown in the above figure.

The isoquant for part c

The following figure illustrates the relevant isoquant.

The firm needs two full-time workers to operate one unit of machinery, i.e., the ratio of input requirement is 2:1. So the firm uses a fixed proportion technology, and the isoquant is L-shaped. The value of MRTS or the slope of the isoquant is undefined along the vertical part and zero along the horizontal part.