Final answer:
The correct answer is option b: In the long run, a firm makes optimal input choices when the marginal rate of technical substitution equals the input price ratio. This ensures efficient substitution of inputs and cost minimization.
Step-by-step explanation:
The student's question pertains to production decisions that firms make in the long run. Specifically, the question addresses the nature of input variability and the strategic choices firms make regarding production technology and input costs. In the long run, unlike the short run where some inputs are fixed, all inputs are variable. Firms have the flexibility to change production methods, the mix of inputs, and the scale of operations to achieve the least costly way of producing their desired output.
Answering the multiple-choice question: Option b is correct. In the long run, a firm is making the optimal input choice when the marginal rate of technical substitution is equal to the input price ratio. This condition ensures that the firm is substituting between inputs in the most cost-efficient manner, adhering to the principle of cost minimization.
The concept of an expansion path is associated with a firm's increase in production, but it represents the combination of inputs chosen at different levels of output to minimize cost, rather than how the marginal products of inputs change.