Profit-maximizing managers can alter their resource mix in the long run to achieve productive efficiency so that production costs for any given amount of output are minimized. Equivalently, they try to maximize the output produced for a given total cost. Efficiency requires conformity with the law of equal marginal advantage, which, applied to consumer behavior, yields the principle of equal marginal utilities per dollar. This law applies in a parallel way to production.
The principle of equal marginal productivities per dollar: Marginal physical products of resources must be proportional to their prices.
This application of the law of equal advantage to production means that
where MPPK equals the marginal physical product of capital, MPPN equals the marginal physical product of land, iequals the interest rate, and nequals the rental rate for land. To see why this equation works, suppose that the last $1 paid in wages generated 1 ton of sand while the last $1 you spent on capital yielded 2 tons of sand. You would gain an extra ton of sand to sell if you shifted $1 away from labor towards capital.
Similar gains of output (or reductions in cost) are possible any time the marginal productivities of resources are not proportional to resource prices.
Least cost production in the long run entails adjustments until this principle of equal marginal productivities per dollar is met.
This principle suggests that relatively higher wages will induce a firm to substitute capital for labor. This has occurred in the auto industry in recent years as high labor costs have caused an army of industrial robots to invade the assembly line. Symmetrically, higher capital costs induce substitution toward labor. When interest rates are high, investment in new capital falls, and labor is substituted for capital.
You should not get the impression, however, that resources are only substitutes for one another. Resources may also be complements in production. Labor productivity, for example, tends to be positively related to the capital and land with which labor has to work. Increases in non-labor resources tend to raise labor's total, average, and marginal physical products. The close short run relationships between production and costs (total, average, and marginal products and costs) suggest that in the long run, average and marginal costs will be influenced by all the resources used.