Question

4) Consumer utility

Quantity	Total Utility from A	Total Utility from B
1	40	37
2	76	72
3	108	105
4	136	136
5	160	165
6	180	192
7	196	217
8	208	237
9	216	252
10	220	262
11	220	267
12	216	267
13	208	262
14	196	252
15	180	237

You are given the above total utilities for different consumption amounts of goods A and B. The consumer has a budget of 60, the price of A is 4, and the price of B is 5.

a) Calculate all the marginal utilities and marginal utility – price ratios and display them on a table. Show all your work.
b) Prepare a separate table that shows all the possible combinations of A and B, and their respective utilities. Add one to the total utility of each combination for each unspent unit from the budget (for combinations where not all the 60 can be spent).

2

c) Which combination maximizes utility? Explain in detail, using two pieces of evidence.
d) Graph your result using a budget line and an indifference map.

-The budget line should be precise with properly scaled x- and y- axes.
- Show a few indifference curves; at least one not optimal, at least one not attainable, and the optimal one, with correct point of tangency.

Answer 1

a) See the table below

		TUn - TUn-1				TUn - TUn-1
Q	Total utility from A	Marginal utility from A	PriceA	MU / Price	Total utility from B	Marginal utility from B	PriceB	MU / Price
1	40	40	4	10	37	37	5	7.4
2	76	36	4	9	72	35	5	7
3	108	32	4	8	105	33	5	6.6
4	136	28	4	7	136	31	5	6.2
5	160	24	4	6	165	29	5	5.8
6	180	20	4	5	192	27	5	5.4
7	196	16	4	4	217	25	5	5
8	208	12	4	3	237	20	5	4
9	216	8	4	2	252	15	5	3
10	220	4	4	1	262	10	5	2
11	220	0	4	0	267	5	5	1
12	216	-4	4	-1	267	0	5	0
13	208	-8	4	-2	262	-5	5	-1
14	196	-12	4	-3	252	-10	5	-2
15	180	-16	4	-4	237	-15	5	-3

b) & c) The table below shows the workings and budget line and utilitity from different combinations. Utility maximizing combination is 6 units of A, 7 units of B and 1 unit of unspent money, giving 398 units of utility

	Qa x 4	Integer(60 - Spend on A) / 5		60 - spend on A - spend on B
Qa	Spend on A	Qb	Spend on B	Money left	Total Utility from A	Total Utility from B	Utility from Money unspent	Total Utility
0	0	12	60	0	0	0	0	0
1	4	11	55	1	40	267	1	308
2	8	10	50	2	76	262	2	340
3	12	9	45	3	108	252	3	363
4	16	8	40	4	136	237	4	377
5	20	8	40	0	160	237	0	397
6	24	7	35	1	180	217	1	398
7	28	6	30	2	196	192	2	390
8	32	5	25	3	208	165	3	376
9	36	4	20	4	216	136	4	356
10	40	4	20	0	220	136	0	356
11	44	3	15	1	220	105	1	326
12	48	2	10	2	216	72	2	290
13	52	1	5	3	208	37	3	248
14	56	0	0	4	196	0	4	200
15	60	0	0	0	180	0	0	180

d) see the graph below with budget line and a few utility curves (the ones to the right of budget line are unattainable, and the ones to its left are sub-optimal, and the one which touches it is teh optimal one). Units of A are on horizontal axis and of B on vertical axis