Question 3.22 Choose the correct answerIn the period before 1870, in Britain both wages and hours worked rose, while in the 20th century, working hours fell even though wages continued to rise. Based on this information, read the following statements and select the correct one.

Question

BlackTom AI · Accepted Answer

In the labor–leisure choice, a higher wage makes leisure relatively more expensive (substitution effect) and increases real income (income effect). The substitution effect tends to raise hours worked (reduce free time); the income effect can either raise free time (if leisure is a normal good) or raise hours worked (if leisure is inferior).

1) Relevant knowledge points and concepts
- Labor–leisure tradeoff: individuals allocate time between work (earns consumption) and leisure (free time).
- Substitution effect of a wage increase: leisure becomes costlier, so people work more (substitution effect → more hours).
- Income effect of a wage increase: higher real income can lead to more leisure if leisure is a normal good, or to less leisure if leisure is an inferior good.
- Observed facts: pre-1870 both wages and hours worked rose; in the 20th century wages rose while hours worked fell.

2) Step-by-step reasoning
- Pre-1870: wages ↑ and hours worked ↑. That means the net effect of the wage increase was to raise hours worked. The substitution effect always pushes toward more hours; for hours to also rise as a result of the income effect, the income effect must have been in the same direction (i.e., income effect also increased hours). Therefore both substitution and income effects were positive for hours (equivalently, both reduced free time).
- 20th century: wages ↑ but hours worked ↓. That implies the income effect dominated and raised free time (leisure behaved as a normal good then), offsetting the substitution effect.

3) Calculations/intermediate steps
- No numeric calculations are required; logical sign inference:
  Pre-1870: Δwage > 0 → Δhours > 0 ⇒ substitution effect (↑hours) + income effect (↑hours) net positive.
  20th c.: Δwage > 0 → Δhours < 0 ⇒ income effect (↑leisure) > substitution effect (↑hours).

4) Why the correct answer is correct
- Option c states that before 1870 both substitution and income effects of rising wages led to workers taking less free time. Interpreting those “effects” as their influence on hours worked, both effects being positive explains why wages and hours rose together — exactly the observed pattern. So c correctly matches the implications of the labor–leisure model.

5) Why the other options are incorrect
- a: If the substitution effect dominated, free time would fall (people would work more); it would not rise. So a is wrong.
- b: The marginal rate of transformation (the wage) rising is not implied by the pattern in hours across periods in the way stated; more importantly, the observed change in hours reflects changing effect dominance, not necessarily a simple increase in the MRT in the stated direction.
- d: The substitution effect of a wage rise on free time is inherently negative (higher wage makes leisure more costly). It does not change sign from negative to positive across periods; what changed was the relative strength of the income effect.

6) Conclusion
All evidence and logical steps support answer c. The correct answer is: c. In the period before 1870, the positive substitution and income effects of rising wages led to workers taking less free time.

Question 3.22 Choose the correct answerIn the period before 1870, in Britain both wages and hours worked rose, while in the 20th century, working hours fell even though wages continued to rise. Based on this information, read the following statements and select the correct one.单项选择题

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