In many instances a firm can choose among a number of alternative combinations of inputs that will produce a given level of output. For example, on George and Martha’s wheat farm, the decision might involve labor and capital. To produce their optimal quantity of wheat, they could choose to have a relatively capital-intensive operation by investing in several tractors and other mechanized farm equipment and hiring relatively little labor. Alternatively, they could have a more labor-intensive operation by hiring a lot of workers to do much of the planting and harvesting by hand. The same amount of wheat can be produced using many different combinations of capital and labor. George and Martha must determine which combination of inputs will maximize their profits.

To begin our study of the optimal combination of inputs, we’ll look at the relationship between two inputs used for production. Depending on the situation, inputs can be either substitutes or complements.

In Section 2 we discussed substitutes and complements in the context of the supply and demand model. Two goods are substitutes if a rise in the price of one good makes consumers more willing to buy the other good. For example, an increase in the price of oranges will cause some buyers to switch from purchasing oranges to purchasing tangerines. When buyers tend to consume two goods together, the goods are known as complements. For example, cereal and milk are considered complements because many people consume them together. If the price of cereal increases, people will buy less cereal and therefore need less milk. The decision about how much of a good to buy is influenced by the prices of related goods.

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The concepts of substitutes and complements also apply to a firm’s purchase of inputs. And just as the price of related goods affects consumers’ purchasing decisions, the price of other inputs can affect a firm’s decision about how much of an input it will use. In some situations, capital and labor are substitutes. For example, George and Martha can produce the same amount of wheat by substituting more tractors for fewer farm workers. Likewise, ATM machines can substitute for bank tellers.

Capital and labor can also be complements when more of one increases the marginal product of the other. For example, a farm worker is more productive when George and Martha buy a tractor, and each tractor requires a worker to drive it. Office workers are more productive when they can use faster computers, and doctors are more productive with modern X-ray machines. In these cases the quantity and quality of capital available affect the marginal product of labor, and thus the demand for labor. Given the relationship between inputs, how does a firm determine which of the possible combinations to use?