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Econ 101 Assignment 5: Utility Maximization and Budget Lines | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Identify the budget line equation for this consumer From the hypothesis: "A consumer who uses $60 to buy 2 goods: X and Y. Given that price of the good X is $3 per unit and price of the good Y is $1 per unit", we have the budget line equation for this customer: 3X+Y=6. Tài liệu được sưu tầm và soạn thảo dưới dạng file PDF để gửi tới các bạn cùng tham khảo, ôn tập đầy đủ kiến thức, chuẩn bị cho các buổi học thật tốt. Mời bạn đọc đón xem!

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Problem 1:
Suppose that a consumer who uses $60 to buy 2 goods: X and Y. Given
that price of the good X is $3 per unit and price of the good Y is $1 per
unit. Suppose that the utility function of this consumer is TU=XY
1, Identify the budget line equation for this consumer
From the hypothesis: "A consumer who uses $60 to buy 2 goods: X and Y.
Given that price of the good X is $3 per unit and price of the good Y is $1
per unit", we have the budget line equation for this customer:
⟺ Y =60 −3 X
2. Identify MUx, MUy and MRSxy
The utility function of this consumer is TU=XY
⟹
MUx =
∆ Mx
∆ Qx
=(TUx) ' = (XY) ' =Y =60
−¿
3X
⟹
MUy=
∆ My
∆ Qy
=¿
(TUy) ' = (XY) ' =X =
60−Y
3
⟹
MRSxy
¿
MUx
MUy
=
Y
X
=
180−9 X
60−Y
3. What are optimal quantity of good X (X*) and optimal quantity of good
Y (Y*) that he should buy to maximize his utility
To maximize his utility : MRSxy =
Px
Py
=
MUx
MUy
We have :
{
MUx
Px
=
MUx
Py
3 X +Y =6
{
Y
3
=
X
1
3 X +Y =6
{
3 X =Y
3 X +Y =6
⟺
{
X=10
Y =30
Problem 2:
a. Identify Lan’s budget line equation and draw that BL curve
* Identify Lan’s budget line:
X.
P
X
+ Y.
P
Y
= I
X. 20000 + Y. 5000 = 1000000
4X + Y = 200
* BL curve:
b. Assume that Lan’s utility function for meat and potato is TU= (X-
2).Y, what is Lan’s optimal choice between meat and potato to
maximize her total utility?
TU max MU = P
{
MU
x
P
x
=
MU
y
P
y
X . P
x
+Y . P I
y
=
MU
X
=
(
TU
)
'
X
=
(
XY Y−2
)
'
=Y
MU
Y
=
(
TU
)
'
Y
=
(
XY Y−2
)
'
=X−2
{
Y
20000
=
X−2
5000
X .20000+Y . 5000 1000000=
{
X=26
Y =96

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Problem 1:
Suppose that a consumer who uses $60 to buy 2 goods: X and Y. Given
that price of the good X is $3 per unit and price of the good Y is $1 per
unit. Suppose that the utility function of this consumer is TU=XY
1, Identify the budget line equation for this consumer
From the hypothesis: "A consumer who uses $60 to buy 2 goods: X and Y.
Given that price of the good X is $3 per unit and price of the good Y is $1
per unit", we have the budget line equation for this customer: 3X+Y=60 ⟺ Y =60−3 X
2. Identify MUx, MUy and MRSxy
The utility function of this consumer is TU=XY ∆ Mx ⟹MUx =
=(TUx) ' = (XY) ' =Y =60−¿3X ∆ Qx 60−Y
⟹ MUy= ∆ My =¿(TUy) ' = (XY) ' =X = ∆ Qy 3 180−9 X
⟹MRSxy ¿ MUx = Y = MUy X 60−Y
3. What are optimal quantity of good X (X*) and optimal quantity of good
Y (Y*) that he should buy to maximize his utility Px
To maximize his utility : MRSxy = = MUx Py MUy We have : = MUx {MUx Px Py 3 X +Y =6 = X { Y3 1 3 X +Y =6
{ 3 X=Y ⟺{X=10 3 X +Y =6 Y =30 Problem 2:
a. Identify Lan’s budget line equation and draw that BL curve
* Identify Lan’s budget line:
X. P + Y. P = I X Y
 X. 20000 + Y. 5000 = 1000000  4X + Y = 200 * BL curve:
b. Assume that Lan’s utility function for meat and potato is TU= (X-
2).Y, what is Lan’s optimal choice between meat and potato to maximize her total utility? TU max MU = P  { MU MU x = y P P x y X . P + Y . P = y I x
MU = (TU )' =(XY −2Y )'=Y X X
MU = (TU )' =( XY −2 Y )'=X−2 Y Y = X−2  { Y 20000 5000  {X=26 Y =96
X .20000+ Y . 5000 1000000 =

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