What does homothetic mean? (in terms of consumption)?

Question

I have a question asking me if the utility function in question is homothetic and i have no idea what this means, I can not find this in my notes or my text book and it's bugging me. What exactly is a homothetic utility function and how does it effect the optimal consumption of two good as income rises?

Answer 1

Homothetic preference functions yield income elasticities of demand equal to 1 for all goods across all possible levels of income because all level sets (i.e., indifference curves) are radial expansions of each other when a function is homothetic. This means that the composition of preferred consumption is determined strictly by the relative prices of the goods, and not by the level or distribution of income.

Therefore, the optimal consumption of two good does not change as income rises.