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.
If consumers make choices on a constrained budget, the marginal net utility derived from the consumption of the good 1 would be relatively higher than the good 2 after its price hike.
Thus, an indirect effect of the increase of the price of the good 2 would be an increase of the demand for good 1 as consummer preferences realign toward it.