A short-run production function shows the relationship between a firm’s inputs and the output it produces when the firm

Question

BlackTom AI · Accepted Answer

A short-run production function is defined when at least one input is fixed.

1. Relevant knowledge points and concepts
- Production function: Q = f(inputs) gives maximum output Q from given inputs (labor L, capital K).
- Short run vs long run: Short run = at least one input is fixed (commonly capital); long run = all inputs are variable.
- Marginal product: short-run marginal products depend on fixed inputs, which can cause diminishing marginal returns when a variable input is increased while another stays fixed.

2. Complete reasoning process step by step
- Start with a general two-input production function Q = f(L, K).
- In the short run, K is fixed at K̄, so the short-run production function becomes Q = f(L, K̄). This explicitly shows Q as a function of the variable input(s) given the fixed input level.
- Thus the short-run production function expresses the relationship between output and variable inputs holding at least one input constant.

3. Calculation example (intermediate steps)
- Example: f(L, K) = L^0.5 K^0.5. Fix K = 4 (short run): Q(L) = L^0.5 * 4^0.5 = 2 * sqrt(L).
- Marginal product of labor: MP_L = dQ/dL = 2 * (1/(2 sqrt(L))) = 1 / sqrt(L).
- MP_L depends on the fixed K and decreases as L increases, illustrating short-run behavior.

4. Why the correct answer is correct
- The defining feature of the short run in microeconomics is that at least one input cannot be changed, so the production function in the short run must reflect output as a function of variable inputs while holding some inputs fixed.

5. Why other plausible options are incorrect
- “All inputs are variable” describes the long run, not the short run.
- Any option implying no fixed inputs, or that the short-run function assumes profit maximization or identical treatment as the long run, is incorrect because the short run specifically incorporates fixed input constraints.

6. Conclusion
Therefore the correct answer is: has at least one fixed input, which matches the provided answer.

A short-run production function shows the relationship between a firm’s inputs and the output it produces when the firm单项选择题

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