Question

Walk through the optimization process and identify the optimal choice for this consumer in both x and y (Hint: the MUx = 2xy2 and MUy = 2x2y)

Answer 1

$U(x,y)=x^2y^2$

$P$_x$=10, P$ _y$=2,y=100$

The rule of utility maximization: $Mux/P$_x$=Muy/P$_y

$\implies2xy^2/10=2x^2y/2$

$\implies1/y=x$ ..... (i)

We know the budget constraint is:

$100=10x+2y$

Lets substitute (i)

$100=10(1/5y)+2y$

$\implies100=2y+2y$

$\implies100=4y$

$\implies y=25$

$\therefore x=1/5y$

$=1/5(25)$

$\implies x=5$

Optimal choice for consumers is;

$x=5; y=25$