Question: Call a function ((x, y) homogeneous of degree 1 if ((tx, ty) = t((x, y) for all t > 0. For example, ((x, y) =

Call a function ((x, y) homogeneous of degree 1 if ((tx, ty) = t((x, y) for all t > 0. For example, ((x, y) = x + yey/x satisfies this criterion Prove Euler's Theorem that such a function satisfies

Note: Let f(x, y) denote the value of production from x units of capital and y units of labor. Then f is a homogeneous function (e.g., doubling capital and labor doubles production). Euler's Theorem then asserts an important law of economics that may be phrased as follows: The value of production ((x, y) equals the cost of capital plus the cost of labor provided that they are paid for at their respective marginal rates ((/(x and ((/(y.

f(x, y) = rar + yof

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