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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.

Respuesta :

olasunkanmilesanmi

Answer:

a. x= $6, y= $8

b. z= $2

Step-by-step explanation:

at equilibrium, the marginal utility per dollar spent will be equal i.e

zA=zB

20-3x=18-2y

upon simplification, we arrive at

[tex]x=\frac{2}{3} (1+y)\\[/tex]......equation 1

since the total amount to spend is $14, then

x+y=14

x=14-y..............equation 2

if we solve equation 1 and equation 2 simultaneously

[tex]14-y=\frac{2}{3} (1+y)\\42-3y=2+2y\\5y=40\\y=8[/tex]

Hence for y=8

x=14-y=14-8

x=6

Hence the amount spent on Product A is $6 and the amount spent on product B is $8

b. to determine the amount of utility the marginal dollar will yield, we substitute the values of y and x into the the given equation,

zA=20-3x=20-3(6)

zA=20-18=2

zB=18-2y=18-2(8)

zB=18-16=2

hence the amount spent on the marginal utility is $2

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