Question

You are choosing between two goods, X and Y, and your marginal utility from each is as shown below. Units of X Units of Y MUY MUX 20 16 14 12 6 Instructions: Enter your answers as whole numbers. a. If your income is $18.00 and the prices of X and Y are $4.00 and $2.00, respectively, what quantities of each will you purchase to maximize utility? units X = units b. What total utility will you realize? < Prey 2 of 2 !!! Next >

Answer 1

Utility is maximized when MUx/Px = MUy/Py

(a) Px = 4, Py = 2, so budget line: 18 = 4X + 2Y

Qx	MUx	Px	MUx/Px	Qy	MUy	Py	MUy/Py
1	20	4	5	1	16	2	8
2	16	4	4	2	14	2	7
3	12	4	3	3	12	2	6
4	8	4	2	4	10	2	5
5	6	4	1.5	5	8	2	4
6	4	4	1	6	6	2	3

Possible Utility-maximizing bundles are: A(X = 1, Y = 4), B(X = 2, Y = 5) and C(X = 3, Y = 6).

Total cost, bundle A = 4 x 1 + 2 x 4 = 4 + 8 = 12 (budget is not exhausted)

Total cost, bundle B = 4 x 2 + 2 x 5 = 8 + 10 = 18 (budget is exhausted)

Total cost, bundle C = 4 x 3 + 2 x 6 = 12 + 12 = 24 (budget is exceeded)

So, bundle B exhausts budget with X = 2 and Y = 5.

(b)

Total utility = Utility from 2X + Utility from 5Y = (20 + 16) + (16 + 14 + 12 + 10 + 8) = 96

(c) Px = 2, Py = 2, so budget line: 18 = 2X + 2Y [i.e. 9 = X + Y]

Qx	MUx	Px	MUx/Px	Qy	MUy	Py	MUy/Py
1	20	2	10	1	16	2	8
2	16	2	8	2	14	2	7
3	12	2	6	3	12	2	6
4	8	2	4	4	10	2	5
5	6	2	3	5	8	2	4
6	4	2	2	6	6	2	3

Possible Utility-maximizing bundles are: A(X = 2, Y = 1), B(X = 3, Y = 3), C(X = 4, Y = 5) and D(X = 5, Y = 6).

Total cost, bundle A = 2 x 2 + 2 x 1 = 4 + 2 = 6 (budget is not exhausted)

Total cost, bundle B = 2 x 3 + 2 x 3 = 6 + 6 = 12 (budget is not exhausted)

Total cost, bundle C = 2 x 4 + 2 x 5 = 8 + 10 = 18 (budget is exhausted)

Total cost, bundle D = 2 x 5 + 2 x 6 = 10 + 12 = 22 (budget is exceeded)

So, bundle C exhausts budget with X = 4 and Y = 5.

(d)

Price	Quantity demanded
$4	2
$2	4