Homothetic preferences guarantee that the expenditure function implies linear homogeneity in wealth.

What does the evidence say?

The claim represents a standard, foundational property in microeconomic consumer theory. By definition, if preferences are homothetic (meaning the marginal rate of substitution depends only on the ratio of consumption quantities, not their absolute levels), the indirect utility function is multiplicative in income/wealth and price indices, which yields an expenditure function that is linear (homogeneous of degree one) in wealth or utility. Because this is a textbook mathematical property of utility maximization and duality, it is common knowledge in economics and does not require empirical citations from the retrieved literature.