## Production Choices and Costs: The Long Run

Read this section to learn about the behavior of the producer in the long run. Take a moment to read through the stated learning outcomes for this chapter of the text, which you can find at the beginning of each section. These outcomes should be your goals as you read through the chapter. Attempt the "Try It" problems at the end of the section before checking your answers.

### Choosing the Factor Mix

How shall a firm decide what mix of capital, labor, and other factors to use? We can apply the marginal decision rule to answer this question.

Suppose a firm uses capital and labor to produce a particular good. It must determine how to produce the good and the quantity it should produce. We address the question of how much the firm should produce in subsequent chapters, but certainly the firm will want to produce whatever quantity it chooses at as low a cost as possible. Another way of putting that goal is to say that the firm seeks the maximum output possible at every level of total cost.

At any level of total cost, the firm can vary its factor mix. It could, for example, substitute labor for capital in a way that leaves its total cost unchanged. In terms of the marginal decision rule, we can think of the firm as considering whether to spend an additional $1 on one factor, hence$1 less on another. The marginal decision rule says that a firm will shift spending among factors as long as the marginal benefit of such a shift exceeds the marginal cost.

What is the marginal benefit, say, of an additional $1 spent on capital? An additional unit of capital produces the marginal product of capital. To determine the marginal benefit of$1 spent on capital, we divide capital's marginal product by its price: MPK/PK. The price of capital is the "rent" paid for the use of a unit of capital for a given period. If the firm already owns the capital, then this rent is an opportunity cost; it represents the return the firm could get by renting the capital to another user or by selling it and earning interest on the money thus gained.

If capital and labor are the only factors, then spending an additional $1 on capital while holding total cost constant means taking$1 out of labor. The cost of that action will be the output lost from cutting back $1 worth of labor. That cost equals the ratio of the marginal product of labor to the price of labor, MPL/PL, where the price of labor is the wage. Suppose that a firm's marginal product of labor is 15 and the price of labor is$5 per unit; the firm gains 3 units of output by spending an additional $1 on labor. Suppose further that the marginal product of capital is 50 and the price of capital is$50 per unit, so the firm would lose 1 unit of output by spending $1 less on capital. $\frac{MP_L}{P_L} > \frac{MP_K}{P_K}$ $\frac{15}{5} >\frac{50}{50}$ The firm achieves a net gain of 2 units of output, without any change in cost, by transferring$1 from capital to labor. It will continue to transfer funds from capital to labor as long as it gains more output from the additional labor than it loses in output by reducing capital. As the firm shifts spending in this fashion, however, the marginal product of labor will fall and the marginal product of capital will rise. At some point, the ratios of marginal product to price will be equal for the two factors. At this point, the firm will obtain the maximum output possible for a given total cost:

Equation 8.9

$\frac{MP_L}{P_L} = \frac {MP_K}{P_K}$

Suppose that a firm that uses capital and labor is satisfying Equation 8.9 when suddenly the price of labor rises. At the current usage levels of the factors, a higher price of labor (PL′) lowers the ratio of the marginal product of labor to the price of labor:

$\frac{MP_L}{P_L'} < \frac{MP_K}{P_K}$

The firm will shift funds out of labor and into capital. It will continue to shift from labor to capital until the ratios of marginal product to price are equal for the two factors. In general, a profit-maximizing firm will seek a combination of factors such that

Equation 8.10

$\frac{MP_1}{P_1} =\frac {MP_2}{P_2} =...=\frac{MP_n}{P_n}$

When a firm satisfies the condition given in Equation 8.10 for efficient use, it produces the greatest possible output for a given cost. To put it another way, the firm achieves the lowest possible cost for a given level of output.

As the price of labor rises, the firm will shift to a factor mix that uses relatively more capital and relatively less labor. As a firm increases its ratio of capital to labor, we say it is becoming more capital intensive. A lower price for labor will lead the firm to use relatively more labor and less capital, reducing its ratio of capital to labor. As a firm reduces its ratio of capital to labor, we say it is becoming more labor intensive. The notions of labor-intensive and capital-intensive production are purely relative; they imply only that a firm has a higher or lower ratio of capital to labor.

Sometimes economists speak of labor-intensive versus capital-intensive countries in the same manner. One implication of the marginal decision rule for factor use is that firms in countries where labor is relatively expensive, such as the United States, will use capital-intensive production methods. Less developed countries, where labor is relatively cheap, will use labor-intensive methods.

Now that we understand how to apply the marginal decision rule to the problem of choosing the mix of factors, we can answer the question that began this chapter: Why does the United States employ a capital-intensive production process to clean streets while China chooses a labor-intensive process? Given that the same technology – know-how – is available, both countries could, after all, use the same production process. Suppose for a moment that the relative prices of labor and capital are the same in China and the United States. In that case, China and the United States can be expected to use the same method to clean streets. But the price of labor relative to the price of capital is, in fact, far lower in China than in the United States. A lower relative price for labor increases the ratio of the marginal product of labor to its price, making it efficient to substitute labor for capital. China thus finds it cheaper to clean streets with lots of people using brooms, while the United States finds it efficient to clean streets with large machines and relatively less labor.

Maquiladoras, plants in Mexico where processing is done using low-cost workers and labor-intensive methods, allow some U.S. firms to have it both ways. They complete part of the production process in the United States, using capital-intensive methods. They then ship the unfinished goods to maquiladoras. For example, many U.S. clothing manufacturers produce cloth at U.S. plants on large high-speed looms. They then ship the cloth to Mexico, where it is fashioned into clothing by workers using sewing machines. Another example is plastic injection molding, which requires highly skilled labor and is made in the U.S. The parts are molded in Texas border towns and are then shipped to maquiladoras and used in cars and computers. The resulting items are shipped back to the United States, labeled "Assembled in Mexico from U.S. materials". Overall maquiladoras import 97% of the components they use, of which 80 to 85% come from the U.S.

The maquiladoras have been a boon to workers in Mexico, who enjoy a higher demand for their services and receive higher wages as a result. The system also benefits the U.S. firms that participate and U.S. consumers who obtain less expensive goods than they would otherwise. It works because different factor prices imply different mixes of labor and capital. Companies are able to carry out the capital-intensive side of the production process in the United States and the labor-intensive side in Mexico.