e. If Billy Joe faces prices Px and Py for the two goods and has an income I to spend on them, derive his optimal demands for X and for Y. iv . Billy Joe's optimal demand for X is and his optimal demand for Y is a. X* = Py / Px ; Y* = I/PY b. X* = ( I * Py) / [Px * (Px+PY) ] Y* = ( I * Px) / [Py * (Px + PY) ] C. X* = I/Px ; Y* =0 X* = 1 / 2*Px ; Y* = 1/ 2*Py