Question

Given the following marginal utility schedule for good X and good Y for an individual A, given that the price of X and the price of Y are both $10, and that the individual spends all his income of $70 on X and Y,

Qx	1	2	3	4	5	6	7
MUx	15	11	9	6	4	3	1
Qy	6	5	4	3	2	1	0
MUy	12	9	8	6	5	2	1

1. Provide the slope of the budget line

2. Estimate the MRS at the optimum

3. Indicate how much of X and Y the individual should purchase to maximize utility.

Answer 1

1.

Slope of the budget line = Price of Good X / Price of good Y

= 10/10

= 1

2.

At optimum, MRS = Px/Py

MUx/MUy = 1

MUx = MUy

Observing the table this occurs Qx = 4

So, MUx = 6 and MUy = 6

MRS = 1

3.

Budget Constraint: M = Px*X + Py*Y

70 = 10X + 10Y

MRS = Slope of budget line, when Qx = 4 and Qy =3. Entire budget is exhausted at this bundle.

So, optimal bundle (Qx*, Qy*) = (4, 3)

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