Question

ADVANCED ANALYSIS Given the following: zA = 35 - 4x zB = 25 - 5y, 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 $7 to spend on A and B—that is: x + y = $7. Instructions: Enter your answers as whole numbers. a. How is the $7 best allocated between A and B? $ on A. $ on B. b. How much utility will the marginal dollar yield? utils.

Answer 1

We have the following equations

• zA = 35 - 4x, zA = (MU/$)A,  x is the amount spent on product A,
• zB = 25 - 5y, zB = (MU/$)B, y is the amount spent on product B.  

Income is $7 to spend on A and B so that x + y = $7.

a. How is the $7 best allocated between A and B?

This will be done in a way so that equimarginal principle is satisfied. This implies  (MU/$)A =  (MU/$)B

35 - 4x = 25 - 5y

10 = 4x + 5y

Use now x + y = 7 and solve for x and y

10 = 4*(7 - y) + 5y

10 = 28 - 9y

y* = 2 and x* = 5.

Amount spent on x is $5 and on y is $2.

b. How much utility will the marginal dollar yield?

Marginal uility is given by zA = zB

35 - 4*5 or 25 - 5*2 = 15 utils.

Thus the marginal dollar yields 15 utils.