第二章 主題一
計數效用分析法 2 − 7
滿足消費者均衡境界，表示消費者不再改變商品組合。
Bianca consumes apples and bananas and is in consumer equilibrium.
The marginal utility of the last apple is 10 and the marginal utility of the
last banana is 20. If the price of an apple is $0.50, then what is the price
of a banana?
$0.10. $0.50.
$1.00.
¯；
MU a MU b
10 20
=
→
=
Pa
Pb
0.5 Pb
$0.25.
【97嘉義管理】
∴ Pb = 1
If bread costs $1 per pound and meat costs $2 per pound, a consumer
whose marginal utility of meat equals 40 utility per pound is maximizing
utility only if the marginal utility per pound of bread equals
10. 5. 40. 20.
【98中央企管】
¯；
MU b MU m
MU b 40
=
→
=
Pb
Pm
1
2
∴ MU b = 20
Sarah consumes only strawberries and cream, and she is spending all
of her income. Her marginal utility of her last dish of strawberries is 200
and her marginal utility of her last pint of cream is 200. The price of
strawberries is $1.00 per dish and the price of cream is $2.00 per pint.
To maximize her utility, Sarah should
buy more strawberries and less cream. buy more cream and less
strawberries.
not change her purchases of strawberries and cream.
not enough information for the question.
【100暨南國企】
¯ ；
MU s 200 MU c 200
∵
=
>
=
Ps
Pc
1
2
âSarah應增加strawberries（s），減少cream（c）的消費。
Kumiko is not at her consumer equilibrium. She sees too many movies
and buys too few books. As she moves toward her consumer
2 − 8 個體經濟學經典題型解析
equilibrium, her marginal utility from movies will
decrease. So will her marginal utility from books. increase, but her
marginal utility from books will decrease.
utility from books will increase.
decrease, but her marginal
increase. So will her marginal utility
from books.
【99暨南國企】
¯ ；
MU m MU b
下，消費者應該減少movies（m）且增加book（b）的消
在
<
Pm
Pb
費，來提高總效用。在此過程中，隨著movies↓會負 MU m↑，且books↑
MU m MU b
時重獲消費者均衡。
會負 MU b↓，直到
=
Pm
Pb
題型1-4 消費者均衡之計算分析
【重點指引】
公式：
⎧ MU X MU Y
=
= MU M
⎪
PY
⎨ PX
⎪P X + P Y = M
Y
⎩ X
Questions  through  refer to the Catt family whose utility is described in Table 1
Table 1
Gallons of Milk Utility from Milk Number of Fish Utility from Fish
1
10
1
25
2
16
2
40
3
20
3
46
4
22
4
48
5
23
5
49
The marginal utility of the second gallon of milk to the Catt family in Table
第二章 主題一
計數效用分析法 2 − 9
is
10. 6. 16. 26. Impossible to determine from Table 1.
If fish costs $3 each and milk costs $2 per gallon, and if the Catt family in
Table 1 has an income of $8 to spend on milk and fish, then it maximizes
its utility by consuming
2 gallons of milk and 1 fish. 2 fish and 1 gallon of milk. 1 fish
and 1 gallon of milk. no fish and 4 gallons of milk. an amount that
cannot determined from Table 1.
If fish and milk cost $3 and $2 respectively and the income of the Catt
family in Table 1 increases to $15. then it should consume
1 fish and 6 gallons of milk. 5 fish and no milk. 2 fish and 4
gallons of milk.
3 fish and 3 gallons of milk.
an amount that
cannot be determined from Table 1.
【99台大國發】
¯；
MU X =
∆TU X 16 − 10
=
=6
2 −1
∆X
；
X
（milk）
TU X MU X
MU X
PX
（fish）
TU Y
MU Y
MU Y
PY
Y
1
10
10
5
1
25
25
25
3
2
16
6
3
2
40
15
5
3
20
4
2
3
46
6
2
4
22
2
1
4
48
2
2
3
5
23
1
0.5
5
49
1
1
3
⎧ MU X MUY
⎪ P = P →( X , Y ) = (1, 2),(3,3)
Y
⎨ X
⎪ 2 X + 3Y = 8→( X ∗ , Y ∗ ) = (1, 2)
⎩
2 − 10 個體經濟學經典題型解析
亦即同時滿足消費者均衡與預算限制式的最適組合為 ( X ∗ , Y ∗ ) = (1, 2) 。
；
⎧ MU X MUY
=
→( X , Y ) = (1, 2),(3,3)
⎪
PY
⎨ PX
⎪ 2 X + 3Y = 15
⎩
故同時滿足消費者均衡與預算限制式的最適組合為 ( X * , Y * ) = (3,3) 。

Quantity
Total utility of apple
Quantity
Total utility of cake
0
0
0
0
1
126
1
54.0
2
243
2
103.5
3
342
3
145.5
4
414
4
177.0
5
441
5
196.5
The table gives the total utility Jamal derives from the consumption of
apples and cakes. Jamal has $12 to spend on these two confectionery
goods. The price of an apple is $3 and the price of cake is $1.50.
Suppose Jamal’s budget is $12. In order for Jamal to maximize his utility,
of apples.
he will buy
Suppose the price of an apple increase to $6. Jamal’s income does not
change and neither does the price of cake. What combination Jamal will
of apples and cakes now?
buy
Jamal’s demand curve for apples is
¯
Qa
MU a
1
2
3
4
5
126
117
99
72
27
 Qa = 3
MU a
3
42
39
33
24
9
MU a
6
21
19.5
16.5
12
4.5
.
【97元智國企、企管】
Qc
MU c
1
2
3
4
5
54
49.5
42
31.5
19.5
MU c
1.5
36
33
28
21
13