Question

on # 3. Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. 

Find out the combination of Apples and Bananas that maximize Ceja’ satisfaction

Answer 1

Maximizing utility condition is achieved where

The slope of indifference curve = slope of the budget constraint

$MRS =\frac{ P_ A} {P_ B}$

$where MRS =\frac{ MU_ A }{MU _B}$

$MU _A = 2AB ^2$

$MU _A = 2A^ 2 B$

$Now MRS = \frac{P _ A }{P _B}$

$\frac{MU_ A }{MU _B} = \frac{1 }{0.25}$

$\frac{2AB ^2 }{2A ^2 B} = \frac{1 }{0.25}$

$\frac{B}{ A} = 4$

$B = 4A$

Now Substitute the value of B= 4A in Budget constraint

$P _A A + P _B B = M$

$1A +0.25B = 20$

$1A +0.25\times4A = 20$

$1A +1A = 20$

$2A = 20$

$A = 10$

Now put A = 10 in budget constraint to calculate bundle B

$P _A A + P _B B = M$

$1\times 10+0.25B = 20$

$10+0.25B = 20$

$0.25B = 20 − 10$

$0.25B = 10$

$B = \frac{10}{0.25}$

$B = 40$

therefore the combination of apple and banana to maximize the utility are (10,40); 10 apples and 40 bananas