Question 1.58 Choose the correct answerThe figure shows a student’s production function with the final grade (the output) related to the number of hours spent studying (the input). Read the following statements regarding the average product of labour (APL) and select the correct one.

Question

BlackTom AI · Accepted Answer

Average product of labour (APL) = output per unit of input, here Grade / Study Hours.

1) Relevant knowledge points and concepts
- APL is defined as total output divided by total units of labour: APL = Grade / Hours.
- Marginal product (MPL) is the slope of the tangent (change in output per additional hour). APL corresponds to the slope of the straight line from the origin to a point on the production function, not the tangent slope (MPL).

2) Step-by-step reasoning
- Inspect the production curve: grade rises with hours but flattens out as hours increase. That implies output grows, but at a decreasing rate.
- APL is the ratio Grade/Hours at each point. If Grade increases less than proportionally to Hours, the ratio falls.

3) Intermediate calculations (approximate values read from the graph)
- At about 1 hour: Grade ≈ 30 → APL ≈ 30/1 = 30.
- At about 5 hours: Grade ≈ 60 → APL ≈ 60/5 = 12.
- At about 10 hours: Grade ≈ 80 → APL ≈ 80/10 = 8.
- At about 20 hours: Grade ≈ 82 → APL ≈ 82/20 = 4.1.
These approximate calculations show APL falling as hours increase.

4) Why the correct answer is correct
- The computed APL values decline as study hours grow because the marginal gain in grade per additional hour is small while the denominator (hours) grows. Thus average output per hour is decreasing across the range shown.

5) Why the other options are incorrect
- (a) “After 13 hours the APL remains constant.” Incorrect — even if the grade curve flattens, APL = grade/hours continues to fall because hours keep increasing while grade barely rises.
- (c) “The APL at 10 hours is 100.” Incorrect — APL at 10 hours ≈ Grade/10 ≈ 80/10 = 8, not 100.
- (d) “The APL is the slope of the tangent line.” Incorrect — that slope is the marginal product (MPL). APL is the slope of the line from the origin to the point on the curve.

6) Conclusion
The APL is decreasing with hours of study, so the correct answer is (b). This matches the provided answer.

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