Question

- H u y | | | | - 2. Xin is a foodie and loves to spend all his money on food(x) and drinks(Y). As we know, the price of food and drinks are $8 and $3 per unit respectively. Please answer the following questions. A. Assume that Xin has 168 dollars, please write down his budget constraint and make a graph of it. Slope and intercepts have to be marked clearly. B. Xin's utility function is U = 2x+y?. Please calculate his MU and MRS. C. If Xin's MRS is 4, analyze the MRS and explain its meaning for Xin. D. Combine (A) and (B), calculate his optimal choice of two goods and draw the graph of it. (Hint: MRS=Px/Pv) 16:32

Answer 1

(A)

Budget constraint: 168 = 8X + 3Y

When X = 0, Y = 168/3 = 56 (vertical intercept) and when Y = 0, X = 168/8 = 21 (horizontal intercept).

Slope = - Px/Py = -8/3 = - 2.67

In following graph, AB is the budget line.

У |56 A АЧ Е 1Cо 12 Хо -х В о

(B)

MUx = $\dpi{80} \partial$ U/$\dpi{80} \partial$X = 8X³Y³

MUy = $\dpi{80} \partial$ U/$\dpi{80} \partial$Y = 6X⁴Y²

MRS = MUx/MUy = (8X³Y³) / (6X⁴Y²) = (4/3).(Y/X) = 4Y / 3X

(C)

If MRS = 4, it means that consumer is willing to give up 4 units of Y in order to consume 1 additional unit of X.

(D)

Utility is maximized when MRS = Px/Py

4Y / 3X = 8/3

12Y = 24X

Y = 2X

Substituting in budget line,

168 = 8X + 3Y

168 = 8X + (3 x 2X)

168 = 8X + 6X = 14X

X = 12

Y = 2 x 12 = 24

In above graph, utility is maximized at point E where indifference curve IC0 is tangent to AB with optimal bundle (X0, Y0) = (12, 24).