A parent has two children living in cities with different costs of living. The c
ID: 1115221 • Letter: A
Question
A parent has two children living in cities with different costs of
living. The cost of living in city B is 3 times the cost of living in city A.
The child in city A has an income of 3,000 and the child in city B has an
income of $9,000. The parent wants to give a total of $4,000 to her two
children. Her utility function is U(CA; CB) = CA CB, where CA and CB
are the consumptions of the children living in cities A and B respectively.
She will choose to
(a) give each child $2,000, even though this will buy fewer goods for the
child in city B.
(b) give the child in city B 3 times as much money as the child in city A.
(c) give the child in city A 3 times as much money as the child in city B.
(d) give the child in city B 1.50 times as much money as the child in
city A.
(e) give the child in city A 1.50 times as much money as the child in
city B.
I believe the correct answer is (b). Please explain the method in detail
Explanation / Answer
We see that U = CA CB. Hence MUA = CB and MUB = CA. From equimarginal principle, we need to use the fact that MU/$ is same for all goods.
Hence we find that
MUA/PA = CB/PA and MUB/PB = CA/PB
CB/PA = CA/PB
CB/CA = PA/PB
Now it is given that the cost of living in city B is 3 times the cost of living in city A and the child in city B has an income which three times the income earned by child in city B. Price can be found by dividing income with cost of living.
Hence both face the following price ratio
PA/PB = income A/Cost of livining A / income B / Cost of living B
= 3000/Cost of livining A / 9000 / Cost of livining B
= 3000/Cost of livining A /9000/ 3 x Cost of livining A
= 1
Since PA/PB = 1, CB/CA = 1. Hence we have CA + CB = 4000 or 2CA = 4000. This gives CA = CB = 2000
Correct option is A
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