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What you will learn
        in this Module:



        • How firms determine the      Module 72
           optimal input mix
        • The cost-minimizing rule for
           hiring inputs               The Cost-Minimizing

                                       Input Combination







                                       In the past three modules we discussed the markets for factors of production—land,
                                       capital, and labor—and how firms determine the optimal quantity of each factor to
                                       hire. But firms don’t determine how much of each input to hire separately. Production
                                       requires multiple inputs, and firms must decide what combination of inputs to use to
                                       produce their output. In this module, we will look at how firms decide the optimal
                                       combination of factors for producing the desired level of output.


                                       Alternative Input Combinations

                                       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 rela-
                                       tively little labor. Alternatively, they could have a more labor-intensive operation by hir-
                                       ing 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 maxi-
                                       mize their profits.
                                          To begin our study of the optimal combination of inputs, we’ll look at the relation-
                                       ship between the inputs used for production. Depending on the situation, inputs can
                                       be either substitutes or complements.

                                       Substitutes and Complements in Factor Markets
                                       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


        706   section 13      Factor Markets
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