1. 消費者的選擇：
個人需求和市場需求的導出

2. 什麼是預算限制？
預算線的導出
價格、所得改變對預算線 的影響
什麼是效用？
無異曲線的導出
什麼是消費者的最適選擇？
價格、所得改變如何影響消費者的均衡？
範例:工作與休閒的選擇
個人需求和市場需求的導出

3. 預算的限制 預算線：有限所得最多可購買的各種產品的組合（消費的客觀限制）
graphical representation of all possible combinations of a household’s purchases of two goods, given their prices and a fixed amount of money to spend
the maximum amounts of the goods the consumer can afford

4. 預算線 Expenditure = Income 支出 = 所得
支出 = 所得
the price of soda PS, the quantity of soda QS, the price of a movie PM, the quantity of movies QM, and income Y.
budget equation is:
PSQS + PMQM = Y.

5. 預算線的截點 原所得 =$30，Pmovie=$6, Psoda=$3 可購買最多的電影票 (movie，soda)=(5 ，0)
可購買最多的可樂
(movie，soda)=(0 ，10)

6. Consumption Possibilities
PSQS + PMQM = Y
Divide both sides of this equation by PS, to give:
QS + (PM/PS)QM = Y/PS
Then subtract (PM/PS)QM from both sides of the equation to give:
QS = Y/PS – (PM/PS)QM
The term Y/PS is Lisa’s real income in terms of soda. 以可樂計算的實質所得
The term PM/PS is the relative price of a movie in terms of soda. 電影(以可樂價格計算)的相對價格

7. 價格改變使預算線 轉動 原所得 =$30，Pmovie=$6, Psoda=$3 P’soda=$1.5 可購買最多的電影票
(movie，soda)=(5 ，0)
可購買最多的可樂
(movie，soda)=(0 ，20)

8. A BUDGET LINE 20
soda 18 16 14 12 10 8 6 4 2 1 2 3 4 5 6 7
Copyright  2000 by Harcourt, Inc. All rights reserved.

9. Consumption Possibilities
A fall in the price of the good on the x-axis increases the affordable quantity of that good and decreases the slope of the budget line.
relative price相對價格的改變

10. 所得改變使預算線 平行移動 原所得 =$30，Pmovie=$6, Psoda=$3 價格不變而所得 增加至$36，預算線向外移出
價格不變而所得 減少至 $?，預算線向內移入

11. A BUDGET LINE 12 10 8 soda A G B C 6 4 D 2 E 1 2 3 4 5 6 71 2 3 4 5 6 7
Copyright  2000 by Harcourt, Inc. All rights reserved.

12. Consumption Possibilities
An change in the household’s income brings a parallel shift of the budget line.
The slope of the budget line doesn’t change because the relative price doesn’t change..

13. 預算線的斜率 ΔS/ΔM= income/Ps = Pm / Ps income/Pm
在所得不變的情況下，增加一單位M的消費，所必須放棄的S
(與Pm成正比，與Ps成反比)

14. 滿足感 satisfaction
快樂的程度
有朋自遠方來，不亦樂乎?
與其錦上添花，不如雪中送炭

15. 效用 Utility 消費的目的: 自身的滿足、快樂 選擇是為了帶給自己快樂
「沒有人每天釣魚、打高爾夫球。如果每天都做這些事，其實是很痛苦的。打高爾夫球、釣魚和旅行之所以快樂，是因為這些事情並非日常之事。」
～～大前研一
為自己而活 /為別人而活
不知為何而戰？

16. 消費者的選擇 有限所得 limited income 如何達到最大的快樂? Maximize utility
快樂的存量stock 和增加量increment

17. 快樂的程度有高低之分
有1朋自遠方來，有2朋自遠方來
有3朋自遠方來

18. 快樂的增加速度有高低之分
有1朋自遠方來，有2朋自遠方來
有3朋自遠方來

19. 快樂的衡量 效用線, 無異曲線 (indifference curve)： 所有能達到某一特定滿足水準的消費組合（主觀偏好）
a line connecting all combinations of goods that are equally desirable

20. 無異曲線
An indifference curve joins all those points that Lisa says are just as good as C
G is such a point. Lisa is indifferent between C and G..

21. Preferences and Indifference Curves
All the points above the indifference curve are preferred to the points on the curve.
And all the points on the indifference curve are preferred to the points below the curve.

22. Preferences and Indifference Curves
An indifference curve above I1 is I2 . All the points on I2 are preferred to those on I1 .
無異曲線愈高，滿足程度愈高
For example, point J is preferred to either point C or point G.

23. 總效用(Total utility) TU 消費者願意用以交換該物之最高金額
TOTAL UTILITY: the maximum amount of money that a consumer is willing to pay for a quantity of a good.
例：為1條牛仔褲願付最高價
TU1=800元

24. 邊際效用(marginal utility) MU
消費者願意用以交換一單位該物之最大金額
the maximum amount of money that a consumer she or he is willing to pay for one more unit of a good.
例: 為2條牛仔褲願付最高價=1500元
TU2牛仔褲=1500元
MU牛仔褲1=800元 ， MU牛仔褲2=700元

25. TOTAL AND MARGINAL UTILITY FOR PIZZA.
Quantity (Q)
Serving per month
(1) 1 2 3 4 5 6 7 8
$15.00
13.00
12.50
11.50
8.00
5.00
3.00
0.00
Marginal Utility
(MU = TU/Q)
(3)
Total Utility
(TU)
(2)
$ 0.00
15.00
28.00
40.50
52.00
60.00
65.00
68.00
Copyright  2000 by Harcourt, Inc. All rights reserved.

26. 邊際效用遞減法則(The law of diminishing marginal utility)
當一物的消費增加，它的邊際效用會愈來愈小
“LAW” OF DIMINISHING MARGINAL UTILITY: additional units of a commodity are worth less and less to a consumer in money terms.

28. Household Consumption Choices
Marginal Utility
Marginal utility is the change in total utility that results from a one-unit increase in the quantity of a good consumed.
As the quantity consumed of a good increases, the marginal utility from consuming it decreases.
We call this decrease in marginal utility as the quantity of the good consumed increases the principle of diminishing marginal utility.

29. Household Consumption Choices
Figure 7.2(b) illustrates diminishing marginal utility.
Utility is analogous to temperature.
Both are abstract concepts and both are measured in arbitrary units.

31. 水與鑽石的矛盾 paradox of value
水可以救命總效用高
鑽石的價格卻遠高於水:價格依邊際效用而定

32. Indifference curves do not cross

33. 無異曲線可能有不同的形狀 U=x*y, U=4 (x,y)可包括下列組合: (1,4)(2,2)(4,1) 如U=2x+y , U=4
(1,2) (2,0) (1.5,1)

34. 無異曲線不同的形狀代表不同的替代程度 Degree of Substitutability
The shape of the indifference curves reveals the degree of substitutability between two goods..
完全互補
完全替代

35. 無異曲線的斜率 效用 U = x*y MUx=y MUy=x ΔY/ΔX= ΔU/ΔX = MUx / MUy ΔU/ΔY

36. Figure 2 The Consumer’s Preferences
Quantity I2
Indifference
curve, I1
of Pepsi C B D 1
MRS A
Quantity
of Pizza

37. Marginal Rate of Substitution
邊際替代率
The marginal rate of substitution, (MRS), measures the rate at which a person is willing to give up good y, (the good measured on the y-axis) to get an additional unit of good x (the good measured on the x-axis) and at the same time remain indifferent (remain on the same indifference curve).
在效用不變的條件下，消費者願意用多少的y 換取額外一單位的x

38. Preferences and Indifference Curves
If the indifference curve is relatively steep, the MRS is high.(y的邊際效用高)
In this case, the person is willing to give up a large quantity of y to get a bit more x.
If the indifference curve is relatively flat, the MRS is low. .(y的邊際效用變低)
In this case, the person is willing to give up a small quantity of y to get more x.

39. Preferences and Indifference Curves
A diminishing marginal rate of substitution is the key assumption of consumer theory.
A diminishing marginal rate of substitution
邊際替代率遞減
is a general tendency for a person to be willing to give up less of good y to get one more unit of good x, and at the same time remain indifferent, as the quantity of good x increases.

40. Figure 4 Bowed Indifference Curves
Quantity
of Pepsi
Indifference
curve 14 2 1
MRS
= 6 8 3 A 4 6 3 7 B 1
MRS
= 1
Quantity
of Pizza

41. Preferences and Indifference Curves
At point C, Lisa is willing to give up 2 six-packs to see one more movie—her MRS is 2.
At point G, Lisa is willing to give up 1/2 a six-pack to see one more movie—her MRS is 1/2.

42. Maximizing Utility The Utility-Maximizing Choice
The key assumption of marginal utility theory is that the household chooses the consumption possibility that maximizes total utility.
The Utility-Maximizing Choice
We can find the utility-maximizing choice by looking at the total utility that arises from each affordable combination.
Table 7.2 (page 153) shows an example of the utility-maximizing combination, which is called a consumer equilibrium. 消費者的均衡

43. Maximizing Utility Equalizing Marginal Utility per Dollar Spent
Using marginal analysis, a consumer’s total utility is maximized by following the rule:
Spend all available income and equalize the marginal utility per dollar spent on all goods.
The marginal utility per dollar spent is the marginal utility from a good divided by its price.
Marginal decision making is the core of the economic way of thinking. Get your students to appreciate that, aside from the concept of opportunity cost, marginal reasoning is the most important tool for understanding the economic perspective. Remind them that we have been using marginal reasoning for many chapters now:
In Chapter 2 we derived the marginal cost of production from the PPF.
In Chapter 5 we discovered that competitive equilibrium is efficient because marginal benefit on the demand curve equals marginal cost on the supply curve.
In this chapter, we discover that equating the marginal utility per dollar spent across all goods and services maximizes a consumer’s utility.

44. Maximizing Utility Call the marginal utility of movies MUM
Call the marginal utility of soda MUS
Call the price of movies PM
Call the price of soda PS
The marginal utility per dollar spent on movies is MUM/PM
The marginal utility per dollar spent on soda is MUS/PS.
People don’t calculate and compare marginal utilities and prices. One of the challenges in teaching the marginal utility theory is getting the students to appreciate the fundamental role of a model of choice. The goal is to predict choices, not to describe the thought processes that make them. The physics model of the pool player’s choices (This Instructor’s Manual, Chapter 1, p. 6) is relevant here. Gary Becker told the story a bit differently and more pointedly for present purposes. Here’s what he said (Parkin, Economics, first edition, 1990, p. 154):
Orel Hershiser [substitute a current pitcher] is a top baseball player. He effectively knows all the laws of motion, of eye and hand coordination, about the speed of the bat and ball, and so on. He’s in fact solving a complicated physics problem when he steps up to pitch, but obviously he doesn’t have to know physics to do that. Likewise, when people solve economic problems rationally they’re really not thinking that well, I have this budget and I read this textbook and I look at my marginal utility. They don’t do that, but it doesn’t mean they’re not being rational any more than Orel Hershiser is Albert Einstein.

45. Maximizing Utility Total utility is maximized when: MUM/PM = MUS/PS
Table 7.3 (page 154) and Figure 7.3 on the next slide show why the utility maximizing rule works.
最後花的一塊錢，得到的邊際效用要相同
錢花在刀口上

46. 消費者的最適選擇(均衡) The Consumer’s Optimum
Quantity I3
The consumer would prefer to be on indifference curve I3, but does not have enough income to reach that indifference curve.
of Pepsi I2
Budget constraint I1
Optimum B A
The consumer can afford most of the bundles on I1, but why stay there when you can move out to a higher indifference curve, I2?
Quantity
of Pizza

47. Maximizing Utility
If MUM/PM > MUS/PS, then moving a dollar from soda to movies increases the total utility from movies by more than it decreases the total utility from soda, so total utility increases.
Only when MUM/PM = MUS/PS, is it not possible to reallocate the budget and increase total utility.

49. Maximizing Utility
Similarly, if MUS/PS > MUM/PM, then moving a dollar from movies to soda increases the total utility from soda by more than it decreases the total utility from movies, so total utility increases.
Again, only when MUM/PM = MUS/PS, is it not possible to reallocate the budget and increase total utility.
First work out what the consumer can afford. Some reviewers of this textbook have told us that we don’t need the budget line in a utility chapter and that it is only needed in an indifference curve chapter. We strongly disagree. The essence of the economic problem faced by the consumer is the economic problem of Chapter 2. The budget line is the constraint—analogous to the PPF. (Stress though that the PPF is based on technology while the budget line is based on market prices.) If you assign numerical problems on utility maximization, stress that the first step is to write down the feasible combinations. There is no point looking at combinations that the consumer can’t afford, and no point in looking at combinations that leave unspent income.
To compare marginal utility across goods requires knowledge of relative prices. Students have the most difficulty understanding why the utility maximizing rule equates the marginal utility per dollar spent rather than just plain marginal utility.
How does the consumer know how much additional utility from one good is made available when giving up some utility of the other good? Students usually grasp that the consumer must assess the marginal utility lost against the marginal utility gained as one good is substituted for another. Yet, students usually haven’t thought about how much of one good is available by forgoing some quantity of the other good. Point out that this is not known until the relative prices of the two goods are known, which is why the marginal utility is weighted by its price.

51. Predicting Consumer Behavior
The consumer’s best affordable point is:
On the budget line 在預算線上
On the highest attainable indifference curve 可達到最大效用(的無異曲線)
Has a marginal rate of substitution between the two goods equal to the relative price of the two goods

52. Predicting Consumer Behavior
Lisa can afford to consume more soda and fewer movies at point F.
And she can afford to consume more movies and less soda at point H.
But she is indifferent between F, I, and H and she clearly prefers C to I.
Waiter? We’re ready to order now. Have the students identify which combination of food and drink would equate the MRS to the relative price ratio for a given budget. Have the students show how a rise in the price of drinks would rotate the budget line and push the diner away from drink and toward food. Show how an increase in income shifts the budget line, allowing both dessert and the second glass of wine.
The meaning of tangency. Emphasize to the student the meaning behind the tangency point between the indifference curve and the budget line.
The marginal rate of substitution (MRS) shows the consumer’s willingness to give up one good to get more of the other good.
The relative price of the two goods shows what the consumer must give up one good to get more of the other good.
When a consumer equates the marginal rate of substitution (MRS) with the relative price ratio, he or she leaves no unrealized gains from substituting one good for another.
The consumer is just willing to give up what he or she must give up, and there are no unrealized gains from substituting one good for another.

53. 最適消費 MUx = Px MUy Py Max U=x*y s.t. 6x+3y=30
y/x =6/ x=30 (x*,y*)=(2.5, 5)
U*=12.5

54. 如果非最適消費 MUx > Px 或 MUx > MUy MUy Py Px Py
在所得相同的情況下，增加x的消費，減少y的消費，可以得到更高的效用
MUx/ Px: 每花一元買x可以得到的邊際效用

55. Jane is maximizing total utility while consuming food and clothing
Jane is maximizing total utility while consuming food and clothing. Her marginal utility from food and clothing are 50 utils and 25 utils, respectively. If clothing is priced at $5 per unit, the price of food must
A) be rising. B) be falling. C) equal $10. D) equal $20.
ANS: C

56. Predicting Consumer Behavior
At point F, Lisa’s MRS is greater than the relative price.
At point H, Lisa’s MRS is less than the relative price..
At point C, Lisa’s MRS is equal to the relative price.

57. 價格或所得的改變會影響最適消費組合
當A變貴，通常應降低A的消費量，增加B的消費量

58. 預算不變，價格改變 求出一條需求線 The budget line rotates outward.
The price of a movie then falls to $3. 價格下跌
The budget line rotates outward.
Lisa’s best affordable point is now J in part (a).
Explain that the fall in the price of a movie leads Lisa to substitute away from sodas and into movies. The change in the relative price changes the best affordable point. She can reach a higher indifference curve by substituting away from the relatively more expensive good and toward the relatively inexpensive good.
The new consumption bundle satisfies the three properties: it is on the new budget line, it is on the highest attainable indifference curve, and the MRS has changed, matching the slope of new budget line.
Also emphasize that tracking the change in the quantity of the good for which the price falls reveals the demand curve for that good.
In part (b), Lisa moves to point B, which is a movement along her demand curve for movies.
P=6, Q=6; P=3, Q=5

59. 個人需求線的導出 Deriving the Demand Curve
(a) The Consumer ’
s Optimum
(b) The Demand Curve for Pepsi
Quantity
Price of
of Pepsi
Pepsi
New budget constraint I2
Demand
750 B
250 $2 A I1
750 1 B
250 A
Initial budget
constraint
Quantity
Quantity
of Pizza
of Pepsi

60. 價格不變，預算改變 求出2條需求線上不同的點
A Change in Income
The effect of a change in income on the quantity of a good consumed is called the income effect 所得效果.
Figure 8.8 illustrates the effect of a decrease in Lisa’s income.
Initially, Lisa consumes at point J in part (a) and at point B on demand curve D0 in part (b).

61. 價格不變，預算改變 求出2條需求線上不同的點
Lisa’s income decreases and her budget line shifts leftward in part (a).
Her new best affordable point is K in part (a).
Her demand for movies decreases, shown by a leftward shift of her demand curve for movies in part (b).
Y= 30 Q=5; Y=21, Q=4

62. 價格的改變具2種效果
東西變便宜了
文大頭好像變有錢了
替代效果
所得效果

63. Predicting Consumer Behavior
Initially, Lisa has an income of $30, the price of a movie is $6, and she consumes at point C. The price of a movie falls from $6 to $3 and her budget line rotates outward. Lisa’s best affordable point is then J.

64. Predicting Consumer Behavior
We’re going to break the move from C to J into two parts.
The first part is the substitution effect and the second is the income effect.

65. 替代效果substitution effect
在維持同樣效用的條件下，文大頭因為電影變便宜，因而多看的電影:
(用較便宜的消費取代較貴的消費)
The substitution effect is the first reason why the demand curve slopes downward.

66. 所得效果 income effect 在維持同樣相對價格的條件下，文大頭因為實質所得增加，因而多看的電影:
The move from K to J is the income effect.
substitution effect =4 movie
income effect =1 movie

67. 價格下降的替代效果
只要價格下降，替代效果一定是增加消費

68. 價格下降的所得效果
價格下降，所得效果不一定是增加消費

69. 依據所得效果將產品分類
正常財normal good
劣等財inferior good

70. 正常財 normal good
所得增加，所得效果是增加消費
income effect is positive

71. 劣等財 inferior good
所得增加，所得效果是減少消費
income effect is negative

72. Predicting Consumer Behavior
If the negative income effect is stronger than the substitution effect, a lower price for inferior goods brings a decrease in the quantity demanded—the demand curve slopes upward!
This case has not been found in any real-world market.

73. Figure 10 Income and Substitution Effects
Quantity
of Pepsi I2 I1
New budget constraint C
New optimum
Income
effect
Income effect B A
Initial optimum
Initial
budget
constraint
Substitution
effect
Substitution effect
Quantity
of Pizza

74. 工作與休閒的選擇
勞動供給:
人如何決定工作時數？
工作可得到「所得」
不工作可得到「休閒」
U= (休閒,所得)
休閒的代價是損失的工資

75. Work-Leisure Choices 完全不工作，一週可休閒168小時 休閒下限100小時 完全工作，每小時工資5元
一週可賺$5*68=$340
工資提高，休閒變貴
(機會成本提高)
預算線向上轉出

76. Work-Leisure Choices 工資提高，休閒變貴，替代效果為負向，休閒應減少.
工資提高，如休閒是正常財，所得效果為正向，休閒應增加.

77. Work-Leisure Choices The Labor Supply Curve 工資是休閒的代價
工資提高，休閒變貴，替代效果為負向，休閒應減少.
工資提高，如休閒是正常財，所得效果為正向，休閒應增加.

78. Work-Leisure Choices 如果所得效果小於替代效果，則休閒減少 The move from A to B
如果所得效果大於替代效果，則休閒增加
The move from B to C

79. 後彎的勞動供給線 錢多事少離家近 The move from A to B所得效果小於替代效果 重賞之下有勇夫
The move from B to C所得效果大於替代效果
錢多事少離家近

80. 市場的需求
個人需求的水平加總 80 60 20 19 9 7 5 12 10 乙 市場 甲

81. Predictions of Marginal Utility Theory
A Fall in the Price of a Movie
When the price of a good falls the quantity demanded of that good increases—the demand curve slopes downward.
For example, if the price of a movie falls, we know that MUM/PM rises, so before the consumer changes the quantities consumed, MUM/PM > MUS/PS.
To restore consumer equilibrium (maximum total utility) the consumer increases the quantity of movies consumed to drive down the MUM and restore MUM/PM = MUS/PS.
The concept of utility is abstract and not comparable across people—and that can be a difficult idea to grasp. Students will initially be skeptical of measuring satisfaction with the concept of utility—not because the idea that consumer satisfaction increases with consumption is difficult to comprehend, but because there is no absolute standard by which different people’s satisfaction can be compared. Many students think that if one person’s utility can’t be converted into standardized units that are comparable across people, like converting spatial distance into miles or kilometers, then the concept simply isn’t worth understanding. (In mathematical terms, utility ordering is ordinal, not cardinal, making it impossible to directly compare separate utility functions.)

82. Predictions of Marginal Utility Theory
A change in the price of one good changes the demand for another good.
You’ve seen that if the price of a movie falls, MUM/PM rises, so before the consumer changes the quantities consumed, MUM/PM > MUS/PS.
To restore consumer equilibrium (maximum total utility) the consumer decreases the quantity of soda consumed to drive up the MUS and restore MUM/PM = MUS/PS.

83. Predictions … Table 7.4 and Figure 7.4 illustrate these predictions.
A fall in the price of a movie increases the quantity of movies demanded—a movement along the demand curve for movies,
and decreases the demand for soda—a shift of the demand curve for soda.

85. Predictions of Marginal Utility Theory
A Rise in the Price of Soda
Now suppose the price of soda rises.
We know that MUS/PS falls, so before the consumer changes the quantities consumed, MUS/PS < MUM/PM.
To restore consumer equilibrium (maximum total utility) the consumer decreases the quantity of soda consumed to drive up the MUS and increases the quantity of movies consumed to drive down MUM. These changes restore MUM/PM = MUS/PS.

86. Predictions … Table 7.5 and Figure 7.5 illustrate these predictions.
A rise in the price of soda decreases the quantity of soda demanded—a movement along the demand curve for soda,
and increases the demand for movies—a shift of the demand curve for movies.

88. Predictions of Marginal Utility Theory
A Rise in Income
When income increases, the demand for a normal good increases.
Table 7.6 illustrate this prediction
Table 7.7 summarizes the assumptions and predictions of marginal utility theory.

89. Predictions of Marginal Utility Theory
Individual Demand and Market Demand
The market demand for a good is the relationship between the price of the good and total quantity demanded of that good.
The individual demand for a good is the relationship between the price of the good and the quantity demanded by one person.
Figure 7.6 on the next slide shows how we sum the individual demand curves to obtain the market demand.

90. Predictions of Marginal Utility Theory

91. Predictions of Marginal Utility Theory
Marginal Utility and Elasticity
We can predict the price elasticity of demand for a good by knowing the characteristics of the marginal utility of the good.
If as the quantity consumed, marginal utility diminishes rapidly, then a given price change will bring a small quantity change to restore consumer equilibrium, and demand will be inelastic.
The concept of utility is abstract, but the implications of utility analysis are concrete. Help the students be less concerned about the abstract nature of measuring utility by emphasizing that it is enough to be able to carefully analyze one consumer’s consumption decisions and extrapolate generally what this behavior could imply for market behavior in general. Appeal to those concepts that students already understand from earlier chapters by linking the abstract concept of utility with concrete implications of consumer behavior.
Mention that if utility for one good increases quickly (slowly) with consumption, this implies that an increase in the price for that good will cause only a small (large) decrease in its consumption.
This implies that as the consumer substitutes away from that good to raise the marginal utility per dollar ratio and into other goods and services to lower other marginal utility per dollar ratios, the change in quantity consumed will be relatively small (large).
The student should quickly realize that a relatively small decrease in quantity demanded due to a given increase in price indicates a relatively inelastic (elastic) demand for that good. Make the link: consumers with steep (shallow) marginal utility functions for a good must have an inelastic (elastic) demand.

92. Efficiency, Price, and Value
Consumer Efficiency and Consumer Surplus
When consumers maximize their utility, they are using resources efficiently.
And the marginal benefit from a good or service is the maximum price the consumer is willing to pay for an extra unit of that good or service when his or her utility is maximized.
What’s the difference between marginal utility and marginal benefit?
Use your judgment on how deeply to pursue this question that good students sometimes ask. The simplest version of the answer is that on page 160 of the textbook: “Marginal utility is the maximum price that the consumer is willing to pay for an extra unit of a good or service when utility is maximized.” More formally, when utility is maximized, MUX/PX =  for all goods, so the marginal benefit of good X, MBX = PX = MUX/. In words for your students, the marginal benefit of each good is proportional to its marginal utility and the factor of proportionality is arbitrary. Back to the temperature analogy, marginal benefit is a dollar measure of value and marginal utility is a measure of value on an arbitrary scale.
What’s wrong with a dollar measure of value? Why do economists use utility?
When a student asks this question, the best way to answer it is to point out that  changes when income changes, so the dollar measure of value isn’t invariant to income while the utility measure is. The student can see that  changes when income changes by noting that at a higher income, the consumer has more of all goods, so MU is smaller for all goods. Smaller MU with given P means smaller .

93. Efficiency, Price, and Value
The Paradox of Value
鑽石與水的矛盾
The paradox of value “Why is water, which is essential to life, far cheaper than diamonds, which are not essential?” is resolved by distinguishing between total utility and marginal utility.
Figure 7.7 on the next slide illustrates the resolution of the paradox.

94. Efficiency, Price, and Value
The total utility and consumer surplus from water is large but the marginal utility and price of water is small.
In contrast, the total utility and consumer surplus from diamonds is small but the marginal utility and price of a diamond is large.