Use the following to answer the questions below z is the mar

Use the following to answer the questions below:

z is the marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B.

Assume MUA = z = 40 – x and MUB = z = 84 – 4y.

Assume that the consumer has $40 to spend on A and B; that is, x + y = 40.

What is the marginal utility per dollar? What is best way to allocate the expenditure of the $40?

Please show your work? (can this also be done in excel?)

As per the question,

MUA = z = 40 – x

MUB = z = 84 – 4y

As per law of equi-marginal utility,

MUA = MUB =z

=> 40 –x = 84-4y

=> x-4y=-84+40

=> x-4y = -44 …….eq(1)

Also the budget constraint is given,

x+y = 40 …… eq(2)

We need to solve equation (1) and (2) to find the value of x and y

Putting x = 4y-44, in equation (2) and solving for x,

4y-44 + y = 40

=>5y = 84

=> y = 84 / 5

=> y = 16.8

Putting y= 16.8 in equation (2),

x + 16.8 = 40

=> x = 40 -16.8

=> x = 23.2

As per question, MUA = z = 40 –x

=> z = 40 – 23.2

=> z = 16.8

Hence, marginal utility per dollar = z = 16.8

The best way to allocate $40 is,

x = $23.2 amount can be spent on product A

y = $18.8 amount can be spent on product B