# How to determine demand without the price of a good?

If I have the utility function of an individual that exhibits perfect substitutes, think (U=ax+by), and I'm given the price of good x and the budget M, then how am I supposed to determine the demand for good Y if I don't have the price of good Y?

I know for Cobb-Douglas style utility functions the optimal choice of good Y is given by Y=BM/price of good Y

• just solve with X left as a function of Y... – serakfalcon Feb 23 '15 at 5:38

If $\frac{a}{p_x} > \frac{b}{p_y}$, then $x^*(M) = \frac{M}{p_x}; y^* = 0$
otherwise if $\frac{a}{p_x} < \frac{b}{p_y}$, then $x^* = 0; y^*(M) = \frac{M}{p_y}$