Utility Maximization Exercises | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

Problem solving exercise
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.
According to the given topic, we have this consumer’s budget line equation: XPX + YPY = I  3X + Y = 60  Y = 60 - 3X
So, we have the budget line curve: Budget Line 70 60 50 40 $1) = Y 30 Y(P 20 10 0 0 5 10 15 20 25 X(P =$3) X
2. Identify MUx, MUy and MRSxy.
The utility function of this consumer is TU=XY MUX = TUX’= Y MUY = TUY’ = X  MRSXY = MUX = Y MUY 𝑋
3. What is optimal quantity of good X (X*) and optimal
quantity of good Y (Y*) that he should buy to maximize his utility? We have 2 equations: XPX + YPY = I MUX = MUY 𝑃𝑋 𝑃𝑌 3X + Y = 60 Y = X 3 1 X = 10 Y = 30
To maximize his utility, he should buy 10X* & 30Y*.
Problem 2: Monthly, Ms. Lan spends 1 million VND for buying
meat (X) and potato (Y). Price of meat is 20,000 dong/kg and
price of potato is 5000 dong/kg.
a. Identify Lan’s budget line equation and draw that BL curve.
From given information, we know Lan’s budget line equation: XPX + YPY = I
 20,000X + 5000Y = 1,000,000  Y = 200 4X –  Budget line curve: Lan's budget line 250 200 ) ND 150 V 0 0 0 5 = 100 (P Y Y 50 0 0 10 20 30 40 50 60 X(P =20,000VND) X
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?
Lan’s utility function is TU = (X - 2)Y = XY – 2Y MUX = TUX’ = Y MUY = TUY’ = X – 2 We have 2 equations: XPX + YPY = I MUX = MUY PX PY 20,000X + 5000Y = 1,000,000 Y = X−2 20,000 5000 X = 26 Y = 96
So, Lan should choose 26kg of meat & 96kg of potato to maximize her total utility.