A function (X, Y) is homogeneous of degree if, when we multiply each argument by a

A function ƒ(X, Y) is homogeneous of degree γ if, when we multiply each argument by a constant α, f(αX,αY) = α^γƒ(X, Y). Thus, if a function is homogeneous of degree zero, ƒ(αX,αY) = α⁰ƒ(X, Y) = ƒ(X, Y), because α⁰ = 1. Show that the optimality conditions for the Cobb- Douglas utility function in Solved Problem 3.6 are homogeneous of degree zero. Explain why that result is consistent with the intuition that if we double all prices and income the optimal bundle does not change?