If tastes are homothetic, there exists a utility function (that represents those tastes) such that the indirect utility function is homogeneous of degree 1 in income.

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This is a well-known result in microeconomics. Homotheticity of preferences implies that the consumer's preferences can be represented by a utility function that is homogeneous of degree 1 in income. This, in turn, implies that the indirect utility function is also homogeneous of degree 1 in income.

If Tastes Are Homothetic, There Exists a Utility Function (That