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,

Q x 1 2 3      4      5      6 7
MUX 15 11 9 6 4 3 1
Q y 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

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

1) Given: Px= Py = $10

Income = $70

Slope of the Budget Line = -Px/Py = -10/10 = -1

2) MRS = -MUx/MUy

At optimum indifference curve should be tangent to the budget line

=> Slope of indifference curve (MRS) = Slope of budget line (Px/Py)

=> MRS = -1

3) To maximize utility, an indivdual should consume X and Y such that it is at optimum level, i.e. where MRS = Mux/MUy is equal to 1

=> As marked in the table above, MUX/MUy = 1 when, Qx=4 and Qy = 3 because at that point, MUx/MUy = 6/6 =1

Hence, an individual should consume 4 units of good X and 3 units of good Y to maximize utility.