Isoquants

Producing any given amount of output can be accomplished with numerous combinations of inputs. For example, suppose you own a firm that packages and sells "Birdhouse" gourd seeds to home gardeners who grow houses for their feathered friends. You estimate that you can wholesale 10,000 cases of packaged seeds at \$2 per case over the course of a season. Five of the many different possible combinations of capital (machines) and labor (workers) that will accomplish the job are listed in Table 9.

These combinations run the gamut from a few machines with many workers hand-counting and stuffing the packages to production processes using numerous automated machines and very few workers to load seeds and watch the machines work. As you might expect, the process you would eventually gravitate to will be the one with the lowest cost. The last column of Table 5 depicts the total costs of packaging 10,000 cases of seeds if labor and capital each cost \$1,000 per unit. To minimize the costs of producing 10,000 packages, you would employ three machines and three workers. The information in Table 5 is graphed in Figure 10; a smoothly curved line connects the five combinations from Table 5. This curve represents all possible mixtures of labor and capital that can produce 10,000 cases, and is referred to as an isoquant.

Table 5 The Various Combinations of Labor and Capital that Will Package 10,000 Cases of "Birdhouse" Gourd Seeds

 Point Units of Capital K Units of Labor L Output:  Cases of Gourd Seeds q Total Cost if w = \$1,000, r = \$1,000 TC (\$) a 1 9 10,000 10,000 b 2 5 10,000 7,000 c 3 3 10,000 6,000 d 5 2 10,000 7,000 e 9 1 10,000 10,000

Isoquants are similar to the consumer indifference curves discussed in the optional material at the end of an earlier chapter, but with one major difference. Isoquants show constant levels of output, which is measurable; indifference curves show constant levels of satisfaction, which cannot be measured with precision. Just as the slope of an indifference curve reflects the relative subjective desirability of the two goods considered (-MUa/MUb), isoquants reflect the relative marginal productivities of the two resources (-MPPL/MPPK).

Let us take a moment to examine what happens to the marginal products of labor and capital relative to each other when we substitute labor for capital or vice versa. When we change from production process c to production process b (move from point c to point b in Figure 10), we "give up" one unit of capital; to keep production constant, we must hire two units of labor, which suggests that the third machine does the work of two workers. When we move from point b to point a (giving up another machine), how many workers must be hired to keep production constant? The answer is four, suggesting that the productivity of four workers is required to replace that lost from the second machine. As we substitute more and more labor for capital (move down and to the right on the isoquant in Figure 10), ever-increasing amounts of labor are necessary to keep production constant. Alternatively, the marginal product of labor declines relative to that of capital. The opposite is true when capital is substituted for labor (movements to the left on the isoquant). Thus, the law of diminishing marginal productivity is reflected in the shapes of isoquants, which are convex (bowed in) from the origin.

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