I'm working on a problem set for my intermediate microeconomics course, but I'm having trouble deriving the compensated and uncompensated demand functions. This is the utility function:
$U(x, y, z) = aln(x) + bln(y) + z$, with goods $x$, $y$, $z$ and income $I$. I found the following optimal values:
$x = (P_z/P_x)a$, $y = (P_z/P_y)b$, $z = (I/P_z) - a - b$
Even though I followed the steps, I'm not completely sure this is right. Moreover, I have to find cross price effects and both the compensated and uncompensated demand functions, but I'm having some serious trouble solving this problem.