Problem 3
Use the following to answer the questions below:
z is the marginal utility per dollar, x is the amount spent on product A, and y is the amount spent
on product B.
Assume MUA = z = 10 – x and MUB = z = 21 – 2y.
Assume that the consumer has $10 to spend on A and B; that is, x + y = 10.
(a) What is best way to allocate the expenditure of the $10?
(b) What is the marginal utility per dollar in the optimal allocation?
Solution
(a) we know that at effecient allocation of resources to have purchases of different goods, the
marginal utility per dollar of each good should be equal.
We have, MUA = z = 10 – x and MUB = z = 21 – 2y
Equating the above two MUs as follows:
MUA = MUB
10 – x = 21 – 2y
-x = 11-2y
x = 2y - 11 ....................... equation (i)
and we have expenditure function as x+y = 10
putting value of x from equation (i) into the above function as follows:
2y - 11 + y = 10
3y = 21
y = 7
and x = 10 - 7 = 3
Thus, the consumer will spend $3 on good x and $7 on good y to get best allocation of the
expenditure.
(b) MU per dollar of good x = 10 - (3) = 7 utils.
MU per dollar of good y = 21 - 2(7) = 21 - 14 = 7 utils.
Hence the marginal utility per dollar in the optimal allocation is 7 utils.