Question

Let Marginal utility of A (MUA)=2z-20-2x and Marginal utility of B (MUB)=2z=42-y. where z is marginal utility per Naira measured in utils, x is the amount spent on product A. and y is the amount spent on product B. Assume that the consumer has N10 to spend on A and B-that is, x+y= 10. i. How is the benefit of N10 maximized between A and B? ii. How much utility will the marginal Naira yield?

Answer 1

Solution:

i.). The benefit of N10 between A and B is maximized where:$\frac{MU_{A} }{P_{A}} = \frac{MU_{B} }{P_{B}}$

= $\frac{2z - 20 - 2x}{x} = \frac{2z - 42 + y}{y}$

X = $\frac{2y(z-10)}{2z - 42+y}$

10 = x + y

$10 = \frac{2y(z-10)}{2z - 42+y} +y$

 

ii.). Marginal Naira will yield:

z = $\frac{420-92y+3y^{2} }{4(y-5)}$