No Such Thing as a Free Lunch: Principles of Economics (Part 47)

"There is much of economic theory which is pursued for no better reason than its intellectual attraction; it is a good game. We have no reason to be ashamed of that, since the same would hold for many branches of mathematics."

John Hicks

Input Demand: The Labor and Land Markets

(Part C)

by

Charles Lamson

A Firm Employing Two Variable Factors of Production in the Short and Long Run

You have seen that inputs can be complementary or substitutable. Land, labor, and capital are used together to produce outputs. The worker who uses a shovel digs a bigger hole than one with no shovel. Add a steam shovel and that worker becomes even more productive. When an expanding firm adds to its stock of capital, it raises the productivity of its labor, and vice versa. Thus, each factor complements the other. At the same time, though, land, labor, and capital can also be substituted for one another. If labor becomes expensive, some labor-saving technology---robotics, for example---may take its place.

In firms employing just one variable factor of production, a change in the price of that factor affects only the demand for the factor itself. When more than one factor can vary, however, we must consider the impact of a change in one factor price on the demand for other factors as well.

Substitution and Output Effect of a Change in Factor Price Table 2 presents data on a hypothetical firm that employs variable capital and labor. Suppose that the firm faces a choice between two available technologies of production---technique A, which is capital-intensive, and technique B, which is labor intensive. When the market price of labor is $1 per unit and the market price of capital is $1 per unit, the labor-intensive method of producing output is less costly. Each unit cost only $13 to produce using technique B, while the unit cost of production using technique A is $15. If the price of labor rises to $2, however, technique B is no longer less costly. Labor has become more expensive relative to capital. The unit cost rises to $23 for labor-intensive technique B, but to only $20 for capital-intensive technique A.

Table 3 shows the impact of such an increase in the price of labor on both capital and labor demand when a firm produces 100 units of output. When each input factor costs $1 per unit, the firm chooses technique B and demands 300 units of capital and 1000 units of labor. Total variable cost is $1,300. An increase in the price of labor to $2 causes the firms to switch from technique B to technique A. In doing so, it substitutes capital for labor. The amount of labor demanded drops from 1,000 to 500 units. The amount of capital demanded increases from 300 to 1,000 units, while total variable cost increases to $2,000.

TABLE 3

The tendency of firms to substitute away from a factor whose relative price has risen and toward a factor whose relative price has fallen is called the factor substitution effect. The factor substitution effect is part of the reason that input demand curves slope downward. When an input, or factor of production, becomes less expensive, firms tend to substitute it for other factors and thus buy more of it. When a particular input becomes more expensive, firms tend to substitute other factors and buy less of it.

The firm described in Tables 2 and 3 continued to produce 100 units of output after the wage rate doubled. An increase in the price of a production factor, however, also means an increase in the costs of production. Notice that total variable cost increased from $1,300 to $2,000. When a firm faces higher costs, it is likely to produce less in the short run. When a firm decides to decrease output, its demand for all factors declines---including, of course, the factor whose price increased in the first place. This is called the output effect of a factor price increase.

A decrease in the price of a factor of production, in contrast, means lower costs of production. If their output price remains unchanged, firms will increase output. This, in turn, means that demand for all factors of production will increase. This is the output effect of a factor price decrease.

The output effect helps explain why input demand curves slope downward. Output effects and other substitution effects work in the same direction. Consider, for example, a decline in the wage rate. Lower wages mean that a firm will substitute labor for capital and other inputs. Stated somewhat differently, the factor substitution effect leads to an increase in the quantity of labor demanded. Lower wages mean lower costs, and lower costs lead to more output. This increase in output means that the firm will hire more of all factors of production, including labor itself. This is the output effect of a factor price decrease. Notice that both effects lead to an increase in the demand for labor when the wage rate falls.

Many Labor Markets

Many labor markets exist. There is a market for baseball players, for carpenters, for chemists, for college professors, and for unskilled workers. Still other markets exist for taxi drivers, assembly line workers, secretaries, and corporate executives. Each market has a set of skills associated with it and a supply of people with requisite skills.

If labor markets are competitive the wages in those markets are determined by the interaction of supply and demand. As we have seen, firms will hire workers only as long as the value of their product exceeds the relevant market wage. This is true in all competitive labor markets. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 205-207*

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