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Columns 1 through 3 in the table below show the marginal utility which a particular consumer would get by purchasing various quantities of products A, B, and C
Columns 1 through 3 in the table below show the marginal utility which a particular consumer would get by purchasing various quantities of products A, B, and C. (1) (2) (3) Unit of product Marginal utility, A Marginal utility B Marginal utility, First 18 39 12 Second 16 36 10 Third 14 33 Fourth 12 30 8 Fifth 10 27 7 Sixth 8 24 5 Seventh 6 21 3 If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these three products, what combination of the three products should be purchased in order to maximize utility?
Expert Solution
Q MUA MUA/2 MUB MUB/3 MUC MUC/1
1 18 18/2=9 39 39/3=13 12 12
2 16 16/2=8 36 36/3=12 10 10
3 14 14/2=7 33 33/3=11 9 9
4 12 12/2=6 30 30/3=10 8 8
5 10 10/5=2 27 27/3=9 7 7
6 8 8/2=4 24 24/3=8 6 6
7 6 6/2=3 21 21/3=7 5 5
At optimal combination
MUA/PA=MUB/PB=MUC/PC
given PA=2, PB=3, PC=1
MUA/2=MUB/3=MUC/1
Also at that point
Income= (PA×QA)+(PB×QB)+ (PC×QC)
26= (PA×QA)+(PB×QB)+ (PC×QC)
From the table we can see that MUA/2=MUB/3=MUC/1=8
at that point,
Units of A, QA=2
Units of B, QB=6
Units of C, QC=4
Verification
PA*QA= 2*2=4
PB*QB=3*6=18
PC*QC=4*1=4
(PA*QA)+(PB*QB)+(PC*QC)= 4+18+4=26
26=Income.
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