Question

Problem 1. For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case? 1. A firm requires exactly two full-time workers to operate each piece of machinery in the factory. 2. A firm can hire only full-time employees to produce its output, or it can hire some combination of full-time 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. 3. A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant

Answer 1

1. This firm operates under a fixed proportions technology, and the isoquants are L-shaped. The firm cannot substitute any labor for capital and still maintain output because it must maintain a fixed 2:1 ratio of labor to capital. The MRTS is infinite (or undefined) along the vertical part of the isoquant and zero on the horizontal part.

2. Place part-time workers on the vertical axis and full-time workers on the horizontal. The slope of the isoquant measures the number of part-time workers that can be exchanged for a full-time worker while still maintaining output. At the bottom end of the isoquant, at point A, the isoquant hits the full-time axis because it is possible to produce with full-time workers only and no parttimers. As we move up the isoquant and give up full-time workers, we must hire more and more part-time workers to replace each full-time worker. The slope increases (in absolute value) as we move up the isoquant. The isoquant is therefore convex and there is a diminishing marginal rate of technical substitution.

3. The marginal rate of technical substitution measures the number of units of capital that can be exchanged for a unit of labor while still maintaining output. If the firm can always trade two units of labor for one unit of capital then the MRTS of labor for capital is constant and equal to 1/2, and the isoquant is linear.