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Consumer Choice & Utility Theory | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Problem 1: 1. 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. 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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Topic 5: Consumer Choice using Utility Theory
Name: Ta Quyet Tien
Class: E-BBA 14.3
E-mail: Tienpbe12345@gmail.com
Student code: 11226262
Problem 1:
1. 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
3X + Y = 60
Y = 60 - 3X
2. The utility function of this consumer is TU=XY.
=> MU = (TU) ’ = Y.
X X
=> MU
Y
= (TU)
Y
’= X .
=> MRS = MU / MU = Y / X .
XY X Y
3.
- In order to maximize his utility: I = P X+ P Y and MU = MU
X Y X
/P
X Y
/P
Y
(=>
MU
X
/MU = P /P Y/X = 3/1= 3)
Y X Y
3X + Y =60 and Y = 3X.
=> X=10 ( units) and Y=30 ( units).
- So, optimal quantity of good X (X*) and optimal quantity of good Y (Y*) is 10
units and 30 units respectively in order to maximize his utility.
Problem 2:
1, Identify Lan’s budget line equation and draw that BL curve.
Lan’ s budget line equation:
20000x + 5000y = 1000000
Or:
y = 200 – 4x
1, We have Lan’ s budget line equation: 20,000X + 5,000Y = 1,000,000.
Or: Y = 200 – 4X.
2.
- We have the utility function for patato and meat is: TU= (X-2)Y.
So the marginal utility for meat is: MU = (TU)’ = Y.
X X
and MU = (TU)’ = X-2.
Y Y
- To calculate the amount of goods to maximize Ms.Lan’s total utility, we based on
budget line and indifference curve.
=> In order to maximize her utility: I = P X+ P Y and MU = MU
X Y X
/P
X Y
/P
Y
(=>
MU
X
/MU = P /P Y/(X-2) = 20,000/5,000 = 4).
Y X Y
20,000X + 5,000Y = 1,000,000 and 4X – Y = 8.
=> X= 26 ( kg) and Y=96 (kg).
- So, optimal quantity of good X (X*) and optimal quantity of good Y (Y*) is 26
kilograms and 96 kilograms respectively in order to maximize her utility.

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Topic 5: Consumer Choice using Utility Theory Name: Ta Quyet Tien Class: E-BBA 14.3 E-mail: Tienpbe12345@gmail.com Student code: 11226262 Problem 1:
1. 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 - 3X
2. The utility function of this consumer is TU=XY. => MUX = (TU)X’ = Y. => MUY = (TU)Y’= X .
=> MRSXY = MUX / MUY = Y / X . 3.
- In order to maximize his utility: I = PXX+ PYY and MUX/PX = MUY/PY (=>
MUX /MUY = PX /PY Y/X = 3/1= 3) 3X + Y =60 and Y = 3X.
=> X=10 ( units) and Y=30 ( units).
- So, optimal quantity of good X (X*) and optimal quantity of good Y (Y*) is 10
units and 30 units respectively in order to maximize his utility. Problem 2:
1, Identify Lan’s budget line equation and draw that BL curve.
Lan’ s budget line equation: 20000x + 5000y = 1000000 Or: y = 200 – 4x
1, We have Lan’ s budget line equation: 20,000X + 5,000Y = 1,000,000. Or: Y = 200 – 4X. 2.
- We have the utility function for patato and meat is: TU= (X-2)Y.
So the marginal utility for meat is: MUX = (TU)’X = Y. and MUY = (TU)’Y = X-2.
- To calculate the amount of goods to maximize Ms.Lan’s total utility, we based on
budget line and indifference curve.
=> In order to maximize her utility: I = PXX+ PYY and MUX/PX = MUY/PY (=>
MUX /MUY = PX /PY Y/(X-2) = 20,000/5,000 = 4).
20,000X + 5,000Y = 1,000,000 and 4X – Y = 8.
=> X= 26 ( kg) and Y=96 (kg).
- So, optimal quantity of good X (X*) and optimal quantity of good Y (Y*) is 26
kilograms and 96 kilograms respectively in order to maximize her utility.

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