[1]: 147 In a model where competitive consumers optimize homothetic utility functions subject to a budget constraint, the ratios of goods demanded by consumers will depend only on relative prices, not on income or scale.
This translates to a linear expansion path in income: the slope of indifference curves is constant along rays beginning at the origin.
Hence, if all consumers have homothetic preferences (with the same coefficient on the wealth term), aggregate demand can be calculated by considering a single "representative consumer" who has the same preferences and the same aggregate income.
[1]: 152–154 Utility functions having constant elasticity of substitution (CES) are homothetic.
Preferences are intertemporally homothetic if, across time periods, rich and poor decision makers are equally averse to proportional fluctuations in consumption.
The reason is that, in combination with additivity over time, this gives homothetic intertemporal preferences and this homotheticity is of considerable analytic convenience (for example, it allows for the analysis of steady states in growth models).
These assumptions imply that the elasticity of intertemporal substitution, and its inverse, the coefficient of (risk) aversion, are constant.