Which of the following statements is (are) TRUE, assuming the firm is choosing the optimal bundle of inputs that minimizes the cost of producing a given quantity of output?
A) I and II
B) I, II, III, and IV
C) IV
D) I and III

Question

Which of the following statements is (are) TRUE, assuming the firm is choosing the optimal bundle of inputs that minimizes the cost of producing a given quantity of output? 
A) I and II 
B) I, II, III, and IV 
C) IV 
D) I and III

Quizplus · Accepted Answer

Statement I is true: If the firm is using the optimal bundle of inputs, then the marginal product of labor divided by the wage rate should be equal to the marginal product of capital divided by the rental rate, known as the marginal rate of technical substitution (MRTS). This ensures that the firm is using the inputs in the most efficient way possible.

Statement III is true: If the price of one input increases, then the firm will adjust its usage of that input relative to the other inputs in order to minimize cost. This is reflected in the MRTS - as the price ratio of inputs changes, the MRTS should change to compensate.

Statement II is false: The marginal cost of production is not necessarily equal to the wage rate (or any input price for that matter). Marginal cost depends on the entire cost function, which includes fixed costs as well as variable costs. The optimal input bundle will minimize the total cost of production for a given level of output, not just the variable cost of labor and capital.

Statement IV is false: The MRTS tells us how the firm will substitute between labor and capital as input prices change, but it does not necessarily tell us how much output the firm will produce. The level of output is determined by the production function, which reflects the technological possibilities for combining inputs to produce output.

Which of the Following Statements Is (Are) TRUE, Assuming the Firm