A curve that illustrates how the optimal mix of inputs varies with total output is:

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The question asks: A curve that illustrates how the optimal mix of inputs varies with total output is:

Since the provided answer is 'The firm’s expansion path', we can explain why this is the right concept in production theory.

First, think about the idea of input substitution as output changes. Firms choose the combination of inputs (like labor and capital) that minimizes cost for a given level of output. As output expands, the cost-minimizing combination can change because the relative productivity or prices of inputs shift with scale. The path traced by these cost-minimizing input bundles across all output levels is called the expansion path.

This concept is closely tied to the geometry of production: it can be drawn on an input space (e.g., units of capital vs. units of labor). Each point on the expansion path corresponds to the optimal input mix for a particular output level, given input prices.

Option-related reasoning if other choices were present (for contrast):
- If another option suggested a curve about total cost or marginal products alone, that would be incorrect because it would mix in total cost curves or marginal productivity patterns rather than the specific sequence of optimal input combinations as output changes.
- If an option claimed the curve represents technical efficiency or production frontiers only, that would miss the central idea of cost-minimization across output levels.

Limitations in this item: the provided data lacks the list of answer choices, so we cannot compare the stated correct option against alternatives. Nevertheless, the standard definition identifies the expansion path as the curve showing how the cost-minimizing input mix changes with output.

ECON3200001.1251 Quiz 10: Returns to Scale

A curve that illustrates how the optimal mix of inputs varies with total output is:

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