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
Consider that, if two goods are perfect substitutes, their marginal utilities are constant with respect to each other. Hence with two goods, you will consume only one or the other*.

If $\frac{a}{p_x} &gt; \frac{b}{p_y}$, then $x^*(M) = \frac{M}{p_x}; y^* = 0 $

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

*(assume their prices are not the inverse of their marginal utilities, in which case you are indifferent).