If the inputs to a production process are perfect substitutes and the marginal rate of technical substitution is equal to the ratio of the prices of the two inputs,the firm can choose from a virtually infinite array of combinations of the two inputs to minimize the costs of producing a given level of output.

Question

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When the inputs are perfect substitutes, the firm can substitute one input for the other without any loss in output. Therefore, the firm can choose any combination of inputs that is the most cost-effective, i.e., the combination that minimizes the cost of producing a given level of output. This is possible because the marginal rate of technical substitution (MRTS) is equal to the ratio of the prices of the two inputs. Hence, the firm can substitute one input for the other until the two inputs are at the same price, and the MRTS equals the price ratio.

If the Inputs to a Production Process Are Perfect Substitutes