Question

Units of A	MUa	Units of C	MUc	Units of B	MUb
1	56	1	32	1	21
2	48	2	28	2	18
3	32	3	24	3	9
4	24	4	20	4	7.5
5	20	5	12	5	6
6	16	6	10	6	4.5
7	12	7	8	7	3

You have $76 and must spend it all. The price of A is $8, the price of C is $4, and the price of B is $3.  

1. If you are a wise consumer how will you spend your money?
2. What will be your total satisfaction if you follow your own advice (answer a)

Answer 1

MUa	MUa/Pa	MUc	MUc/Pc	MUb	MUb/Pb
56	7	32	8	21	7
48	6	28	7	18	6
32	4	24	6	9	3
24	3	20	5	7.5	2.5
20	2.5	12	3	6	2
16	2	10	2.5	4.5	1.5
12	1.5	8	2	3	1

A)

At utility maximizing combination,

So MUa/Pa = MUb/Pb = MUc/Pc

& Total budget should be exhausted.

Thus the common values of MU/P are 7,6,3,2.5

At value of 2.5, Qa = 5, Qb = 4, Qc = 6

Then total cost = 5*8 + 6*4 + 4*3 = 76.

But at other values , entire budget is not used.

At common value = 3,

total cost = 32+20+9 = 61, total budget not exhausted.

thus answer = Q of A = 5, Q of B = 4, Q of C = 6

answer b) total satisfaction ( utility level)

from good A= summation of MU till Qa = 5,

So 56+48+32+24+20 = 180

From Good B, total utility = 21+18+9+7.5 = 55.5

From good C, total utility = 32+28+24+20+12+10 = 126

Thus total satisfaction = 180+55.5+126

= 361.5 answer

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