Consider the following preferences $U(x,y)=x^{2}y$

Derive the demands of goods $x$ and $y$

Calculate the quantity demanded of both goods if $p_x=2,p_y=1,$ and $I=36$

Now assume the price of good $x$ increases up to $p_x^{\text{'}}=4$

Calculate the new optimal quantities

Calculate the substitution effect for both goods $($Hint: please note that to

calculate the substitution effect you have to calculate the quantity demanded of

both goods given the new prices but the same utility level$)$

Calculate the income effect for both goods