Question

1. A consumer is considering to buy only two products, X, and Y. The amount of total utility yielded by their consumption is shown in the table below. Assume that the prices of X, and Y are $8, and $2 respectively, and that the consumer has an income of $24 to spend. a) Complete the following table by computing the marginal utility and the marginal utility per dollar for successive units of product X and Y. (4 marks) b) How many units of product X and Y will the consumer buy when maximizing total utility and spending all income? SHOW ALL WORKS. (6 marks) c) What total utility will you realize? (2 marks) d) Assume that, other things remaining unchanged, the price of X falls to $4. What quantities of X and Y will you now purchase? SHOW ALL WORKS. (4 marks) Product-X No of Total MUX unit Utility (TU) MUX/Px Product-Y of Total Utility (TU) No unit MUY MUY/PY 0 22 36 48 80 104 120 128 132 46 54 OWN 60 64

Answer 1

a) Find the marginal utility using the difference in total utility for every additional unit purchased. Then divide the marginal utility with the price of the product. Do this for both X and Y. This gives the following table

Product X				Product Y
Units	TU	MU	MU/$	Units	TU	MU	MU/$
0	0			0	0
1	48	48	6	1	22	22	11
2	80	32	4	2	36	14	7
3	104	24	3	3	46	10	5
4	120	16	2	4	54	8	4
5	128	8	1	5	60	6	3
6	132	4	0.5	6	64	4	2

b) Optimum bundle must has MU/$ for X = MU/$ for Y as well as XPx + YPy = M

Here when X is 2 and Y is 4, we have MU/$ for X = MU/$ for Y = 4.

Also, we have 2*8 + 4*2 = $24 which satisfies both conditions.

Hence, the optimum utility maximizing bundle is X = 2 and Y = 4

c) Total utility realized = 80 + 54 = 134 utils

d) Optimum bundle must has MU/$ for X = MU/$ for Y as well as XPx + YPy = M

Here when X is 4 and Y is 4, we have MU/$ for X = MU/$ for Y = 4.

Also, we have 4*4 + 4*2 = $24 which satisfies both conditions.

Hence, the optimum utility maximizing bundle when price of X is reduced to $4 is X = 4 and Y = 4

Product X				Product Y
Units	TU	MU	MU/$	Units	TU	MU	MU/$
0	0			0	0
1	48	48	12	1	22	22	11
2	80	32	8	2	36	14	7
3	104	24	6	3	46	10	5
4	120	16	4	4	54	8	4
5	128	8	2	5	60	6	3
6	132	4	1	6	64	4	2