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**Let u(x) be a function homogeneous of degree one in x. Let g(y) be a function of one argument that is monotonically increasing in y. Then u(g()) is a homothetic function of y.****So a function is homothetic in y if it can be decomposed into an inner function that is monotonically increasing in y and an outer function that is homogeneous of degree one in its argument.****In consumer theory there are some useful analytic results that can come from studying homothetic utility functions of consumption.**