Assignment 5 - Problem Solving in Consumer Budget Lines | Microeconomics | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

Assignment 5 Problem solving Exercise.
1.1. 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 $1per unit", we
have the budget line equation for this customer: - 3X+Y=60 ⟺ Y=60-3X
1.2 . Identify MUx, MUy and MRSxy - TU=XY - MU = (TU)’ ➔ MUx = (XY)’=Y ➔ MUy = (XY)’=X - MRSxy = MUx= 𝑋 MUy 𝑌
1.3: What are optimal quantity of good X (X*) and optimal quantity of good Y
(Y*) that he should buy to maximize his utility?
- As prove above, budget line is 3X+Y= 60
Equilibrium: Marginal utility per one unit of money spent on each good is the same 𝑀𝑈𝑥 = 𝑀𝑈𝑦 𝑃𝑥 𝑃𝑦 ➔ Y=3X ( Due to MUx= 𝑋) MUy 𝑌
Instead of the equation 60 = 3X+Y ➔ X=10 Y=30
So, the optimal quantity of good X (X*) and the optimal quantity of good Y (Y*)
are 10 units and 30 units respectively to maximize his utility. Exercise 2:
a, Identify Lan’s budget line equation and draw that BL curve:
- We have: 20000X + 5000Y = 1000000 ➔ 20X + 5Y = 1000 ➔ 5Y = 1000 – 20X
➔ Y = 200 – 4X ( Budget Line Equation) 250 200 150 eat M 100 50 0 0 10 20 30 40 50 60 Potato b,
We have utility function for meat and potatoes is TU = (X - 2) Y.
The marginal utility of meat (X) is MUx = (TU)’x = Y
The marginal utility of potatoes (Y) is MUy = (TU)’y = X-2
To maximize her total utility, we based on the Budget Line and Indifference Line.
We need to calculate point E where: MRSxy = 𝑃𝑌 = 5000 = 1 𝑃𝑋 20000 4 ⇒ MRSxy = 𝑋−2 = 1 𝑌 4
That means Ms. Lan is willing to give up 1 unit of meat for 4 units of potatoes.
Now, we can find X function in terms of Y: X = 𝑌+ 2 4
Then, we substitute this into the budget line equation: Y = 200 – 4X X = 𝑌 +2 4
⇒ Y = 96. Then, we can find X = 26
So, to maximize her total utility, Ms. Lan should buy 26 kg of meat and 96 kg of potatoes.