Question

I'm given a utility function U=xy and MUx=y while MUy=x. Price of x is $2 and the income is $40. To maximize utility subject to the budget constraint, 5 units of y is purchased.

QUESTION: What must be the price of y and the amount of x consumed?

Thank you :)

Answer 1

$U=xy$ , $MUx=y$ ,$MUy=x$  $I=40$

At utility maximisation: $\frac{MUx}{MUy}=\frac{Px}{Py}$

$\frac{y}{x}=\frac{2}{Py}$

$2x=Py\times y$

$x=\frac {Py\times y}{2}$

Budget constraint: $Px\times x+Py\times y=I$

$2x+Py\times y=40$ and $y=5$

$\frac{2(5\times Py)}{2}+Py\times 5=40$

$10Py=\$40$

$Py=\$4$

Calculating for the amount of x consumed:

$x=\frac{\$4\times 5}{\$2}$

$x=10 units$