Two-good economy, can we tell if the demand of good 1 rises or falls when the price of good 2 rises (price of 1 is constant)? Suppose we have a two-good economy, and we know that good 1 is a normal good. Can we then make any meaningful observation about the demand for good 1 when we change the price of good 2 and keep the price of good 1 constant?
Check out the demand functions for three cases:


CES Utility
Leontief Utility
Cobb-Douglas Utility


You should be able to see that the first case gives you that demand for good 1 increases, the second case demand for good 1 decreases, and in case 3 it is unchanged.