ADVANCED ANALYSIS Given the following zA 20 3x zB 18 2y

ADVANCED ANALYSIS Given the following: zA = 20 - 3x zB = 18 - 2y, where z is marginal utility per dollar spent, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $14 to spend on A and B—that is: x + y = $14. Instructions: Enter your answers as whole numbers. a. How is the $14 best allocated between A and B? $ on A. $ on B. b. How much utility will the marginal dollar yield? utils.

Solution

MU/$ for A = zA = 20 - 3x

MU/$ for B = zB = 18 - 2y.

Income is $14 so that x + y = $14.

a. For optimum allocation, equimarginal principle suggests that

MU/$ for A = MU/$ for B

zA = zB

20 - 3x = 18 - 2y

2 = 3x - 2y as well as x + y = 14

2 = 3(14 - y) - 2y

2 = 42 - 3y - 2y

5y = 40

y = 8 and x = 6

Hence on A, one should spend $6 and on B one should spend $8

b. The utility provided by the marginal dollar = 18 - 2*8 = 2 utils.