The following diagram depicts a production function for grain. Read the following statements and select the correct one(s).

Question

BlackTom AI · Accepted Answer

The production function reaches a maximum output value (a horizontal plateau), indicating an upper limit to output.

1. Relevant knowledge points and concepts
- Production function Q = f(L) maps labour L to total output Q.
- Average product (AP) = Q / L. AP is constant only if Q is directly proportional to L (Q = kL).
- Marginal product (MP) = ΔQ / ΔL. A plateau in Q means MP = 0 for additional workers.
- If Q is constant while L increases, AP falls because denominator increases while numerator stays fixed.

2. Complete reasoning process step by step
- The graph shows Q increasing with L up to a point and then flattening (a horizontal line). A horizontal section means additional workers add zero to total output: MP = 0.
- Because Q becomes constant (say Qmax) beyond that point, AP = Qmax / L will change as L changes (it will decline as L increases), so AP is not constant in that region.
- For the first 100 workers to exhibit constant AP, the graph would have to be a straight line through the origin (Q proportional to L) over that interval. The depicted curve is not linear in that interval (it rises at a changing rate), so AP is not constant there either.

3. Calculations with intermediate steps (illustrative numeric example)
- Assume plateau value Qmax = 200 units for illustration. If L = 150, AP = 200 / 150 = 1.333.
- If L increases to 200 while Q stays 200, AP = 200 / 200 = 1.000.
- AP changes from 1.333 to 1.000 as L increases → not constant.

4. Why the correct answer is correct
- The flattening of the production function is exactly the visual indication of an upper limit: beyond some labour input, output does not increase. That means there is a maximal achievable grain output given current technology/other inputs.

5. Why the other options are incorrect
- Option 1 (constant AP for first 100 workers): Constant AP would require Q = kL (linear). The curve for the first 100 workers is not a straight line proportional to L, so AP is not constant.
- Option 2 (constant AP when L > 150): With Q constant beyond 150, AP = Q / L decreases as L increases, so AP cannot be constant in that region.

6. Conclusion
The only correct choice is "There is an upper limit to how much grain can be produced." This matches the provided answer.

The following diagram depicts a production function for grain. Read the following statements and select the correct one(s). 多项选择题

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