Utility Function - Solving Equation Help

Question

$$U(x, y) = 2(x+y)^{0.5} = 5$$

I have to basically solve this for X and Y. I've been advised to plug in a number for either X or Y and try to solve for the X or Y. Anybody know how to approach this?

Thanks!

Answer 1

You can solve the equation for $x$ or $y$ respectively without plugging in a number at first.

$U=2\cdot (x+y)^{0.5}\qquad |:2$

$\frac{U}2=(x+y)^{0.5}\qquad |()^2$

$\left(\frac{U}2\right)^2=x+y\qquad $

$\Rightarrow x=\left(\frac{U}2\right)^2-y$ and $y=\left(\frac{U}2\right)^2-x$

Next you can fix the utility level $(\overline U, \text{parameter})$ and draw for different values of $\overline U$ some isoquants.

In the graph the isoquants are drawn for the parameters $\overline U_1=3, \overline U_2=5, \overline U_3=7, \overline U_4=9$ and $\overline U_5=11$