Figure 20 shows indifference curves for which a person will
work the same number of hours after the tax because the income effect (less leisure) equals the substitution effect (more leisure), so there is the same amount of leisure overall.
9.塞拉（Sarah）一周用于工作和闲暇的时间有 100 小时。在同一张图上分画出她每小时能挣 6 元、8 元和 10 元时的预算约束线。现在画出无差异曲线，这些无差异曲线要能使得工资为每小时 6 元和 8 元之间时，塞拉的劳动供给曲线是向上倾斜的，但当工资介于每小时8 元和 10 元之间时，她的劳动供给曲线是向后弯曲的。 Figure 21 shows Sarah's budget constraints and indifference curves if she earns $6 (BC1), $8 (BC2), and $10 (BC3) per hour. At a wage of $6 per hour, she works 100 – L6 hours; at a wage of $8 per hour, she works 100 – L8 hours; and at a wage of $10 per hour, she works 100 – L10 hours. Because the labor supply curve is upward sloping when the wage is between $6 and $8 per hour, L6>L8; because the labor supply curve is backward sloping when the wage is between $8 and $10 per hour, L10>L8.
10.某人面临在闲暇和工作时间分配的决策，画出他的无差异曲线。假设工资上升。他的消费有可能下降吗？这合理吗？请讨论。（提示：考虑收入效应和替代效应。）
An increase in the wage leads to both an income effect and a substitution effect. The higher wage makes the budget constraint steeper, so the substitution effect
increases consumption and reduces leisure. But the higher wage has an income effect that increases both consumption and leisure if both are normal goods. The only way that consumption could decrease when the wage increased would be if consumption is an inferior good and if the negative income effect outweighs the positive substitution effect. This could happen for a person who really placed an exceptionally high value on leisure 11.丹尼尔是个勤奋的学生，他喜欢得到 A 的成绩，但也喜欢看电影。他每周用于学习和看电影的时间为 100 小时。如果他想得到一个 A，他每周必须学习 20 小时。每部电影长 2个小时。
a.画出丹尼尔的预算约束线，它表示丹尼尔在成绩（A 的数量）和电影数量之间的权衡。假设他得到 3 个 A 时最开心。画出他的无差异曲线，标记出他的最优选择。他每周看几部电影？
新学期开始了，丹尼尔决定去除得 3 个 A 才最开心的困难要求。现在如果他想得到一个 A，他每周必须学习 25 小时。
b.在你的图上画出新的预算约束线。在图上画出一种可能的最优选择。收入效应和替代效应的相对大小如何决定了丹尼尔的成绩变好或变坏以及他看电影数量变多或变少？
a. Figure 23 shows Daniel’s budget constraint. If he maximizes his utility at earning 3 A’s, he will watch 20 movies. b. The budget constraint rotates in. One possible outcome will be that Daniel will earn fewer A’s and watch more movies as shown by point B in Figure 23. Daniel’s substitution and income effects for A’s will likely move in the same direction (i.e., A’s are “normal goods”). However, his choice of number of movies will depend on the
relative strengths of the income and substitution effects. The point chosen in Figure 23 assumes that the substitution effect outweighs the income effect.
12.一对妻正在考虑要生几个孩子。假设这对妻一生有 20 万小时的时间用于工作和抚养孩子。工资为每小时 10 元。抚养孩子需要 2 万小时。
a.画出这对妻的预算约束，它表示一生消费和抚养孩子数量之间的权衡（假设孩子数 量可以为非整数），画出无差异曲线和最优选择。
Figure 23 shows the budget constraint. The initial budget line is shown as BL1. If all hours are spent raising children, 10 children can be raised. If all hours are spent
working, $2,000,000 can be earned for consumption. The individual maximizes utility by choosing K1 children and a consumption level of C1.
b.假设工资上升为每小时 12 元，画出预算线的移动。使用收入效应和替代效应分析工资变动对孩子抚养数量和一生消费数量变化的影响。
c.我们看到，随着社会更富有和工资更高，人们通常少生孩子。这个事实与题目中的模型相符吗？请解释。
b. If the wage rises, the budget line rotates to BL2 in Figure 23. The budget line is now steeper indicating the higher opportunity cost of raising a child. The
substitution of this increase in the wage will mean a rise in consumption and a decline in the number of children. Assuming that both children and consumption are normal goods, the income effect of the increased wage will mean a rise in both children and consumption. The full effect on consumption is positive, but the end effect on children depends on the relative sizes of the income and substitution effects.
c. If the number of children declines as incomes rise, the substitution effect must outweigh the income effect.
13.经济学家乔治.斯蒂格勒（George Stigler）曾经写道，根据消费者理论，“如果消费者的收入上升时，他们不少买某种商品的话，那么当该商品价格上升时，他们肯定会少买。使用收入效应和替代效应的概念解释这段话。
12. If consumers do not buy less of a good when their incomes rise, the good in
question must be a normal good. For a normal good, the income and substitution effects both imply that the consumer will buy less if the price rises.
14.福利制度为穷人家庭提供资金。通常来说，无收入的家庭获得的资金补助最多，随着家庭开始挣取收入，它们得到的资金补助也逐渐下降，最终不再获得补助。下面我们考虑这种福利制度对某个家庭劳动供给的可能影响。
a.假设不存在福利制度，画出某个家庭的预算约束。在同一张图上，画出存在福利制度时的预算约束。
b.在你画出的图中添加无差异曲线，表明福利制度为何能减少家庭的工作之间。使用收入效应和替代效应进行解释。
c.使用你在（b）中的图，说明福利制度对家庭福利的影响。
a. Figure 25 shows the effects of the welfare program. Without the program, the budget constraint would begin on the horizontal axis at point Lmax when the family earns no labor income and would have a slope equal to the wage rate. The program
provides income of a certain amount if the family earns no labor income, shown as the point A on the figure. Then, if income is earned, the welfare payment is reduced, so the slope of the budget line is less than the slope of the budget line without welfare. At the point where the two budget lines meet, the welfare program provides no further support.
b. The figure shows how indifference curves could be shaped, indicating a reduction in the number of hours worked by the family because of the welfare program. Because the welfare budget constraint is flatter, there is a substitution effect away from consumption and toward leisure. Because the welfare budget constraint is farther from the origin, there is an income effect that increases both consumption and leisure, if both are normal goods. The overall effect is that the change in consumption is
ambiguous and the family will want to have more leisure; hence, it will reduce its labor supply.
c. There is no doubt that the family's well-being is increased, because the welfare program gives them consumption and leisure opportunities that were not available before and they end up on a higher indifference curve.
15.五个消费者都消费苹果和梨子，他们的边际效用分如下：
苹果的价格为每个 2 元，梨子的价格为每个 1 元。哪个消费者的效用达到了最大？对于
效用未达到最大的消费者，他们分应如何调整在两种水果上的支出？
Utility is maximized when the marginal utility per dollar spent is equal across goods. Claire and Alex are both purchasing the utility-maximizing combination of apples and pears. Phil and Haley each get greater utility per dollar spent on apples than on pears. Therefore, they should purchase more apples and fewer pears. On the other hand, Luke gets higher utility per dollar spent on pears than on apples. He should reallocate his budget as well, increasing his purchases of pears and reducing his purchases of apples.
Utility is maximized when the marginal utility per dollar spent is equal across
goods. Jerry and Elaine are both purchasing the utility-maximizing combination of apples and pears. George and Kramer each get greater utility per dollar spent on pears than on apples. Therefore, they should purchase more pears and fewer apples. On the other hand, Newman gets higher utility per dollar spent on apples than on pears. He should reallocate his budget as well, increasing his purchases of apples and reducing his purchases of pears.