Homothetic preferences

In economics, a consumer is said to have homothetic preferences when its preferences can be represented by a homothetic utility function.^[1] Both homogeneous and homothetic preferences are common functional forms used to represent consumer preferences when analyzing the demand for consumption of various goods and services. A homothetic function is a monotonic transformation of a function which is homogeneous of degree 1. However, since ordinal utility functions are only defined up to a monotonic transformation, there is little distinction between the two concepts in practice. 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.

Intratemporally vs. intertemporally homothetic preferences

Intratemporally homothetic preferences means that, in the same time period, consumers with different incomes but facing the same prices will demand goods in the same proportions.

Intertemporally homothetic preferences means that, across time periods, rich and poor decision makers are equally averse to proportional fluctuations in consumption.

Models of modern macroeconomics and public finance often assume the constant-relative-risk-aversion form for within period utility (also called the power or isoelastic form). 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. This may have significant implications, for example when evaluating the costs of business cycles or evaluating a policy change in a dynamic general equilibrium model with heterogeneous agents.

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