Assignment 5: Utility Maximization & Budget Constraints Analysis | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

ASSIGNMENT TOPIC 5 EXERCISE 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.
The budget line equation: 3X + Y = 60 Y = 60 – 3X 2. Identify MUx, Muy and MRSxy MUX = (TU)’X = (XY)’X = Y MUY = (TU)’Y = (XY)’Y = X MRSXY = = = 3. What are optimal quantity of good X (X*) and optimal quantity of good Y (Y*) that he should buy to maximize his utility. At point E
in the graph, his utility is maximized.
This is the equilibrium point, so we have: MRSXY = = = = 3 Y = 3X
So, we have a system of equations:
In conclusion, 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. EXERCISE 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.
1. Identify Lan’s budget line equation and draw that BL curve.
Lan’s budget equation: 20,000X + 5000Y = 1,000,000 Y = 200 – 4X
2. 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 = XY – 2Y MUX = (TU)’X = Y MUY = (TU)’Y = X – 2
At point E in the graph, the utility is maximized. This is the equilibrium point, so we have MRSXY = = = = = 4 Y = 4X
So, we have a system of equations:
In conclusion, optimal quantity of meat X (X*) and optimal quantity of potato Y (Y*) is
26 kg and 96 kg respectively in order to maximize Lan’s utility.