Euler's theorem

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f(x1, …, xn)

is homogeneous of degree n thenOne use of the theorem is to demonstrate that with constant returns to scale and competitive factor markets the total payment to factors equals the revenue of the firm. Assume there are two factors, capital, K, and labour, L. Constant returns to scale implies the production function is homogeneous of degree one so Euler's theorem givesIf the price of output is p, it follows thatCompetition on the factor market ensures that and . Hence,

rK + wL = pf(K,L)

so total payment to factors equals revenue. This argument has been used as the basis for a theory of distribution.

Subjects: Mathematics — Economics.

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