| 单词 | Euler's theorem |
| 释义 | Euler's theorem A mathematical theorem relating marginal to average products. The theorem states that where a function is homogeneous of order n in its arguments, so that, for example, if y = f(x, z), then f (λx, λz) = λn f(x, z), the sum of the marginal product of each argument times its quantity equals ny. This implies that if f() is a production function with y as output and x and z the inputs, the amount of factors used times their marginal products equals total output if and only if n = 1. Thus if factors are paid their marginal products, only with constant returns to scale does the sum of factor earnings exhaust the total product. With decreasing returns to scale the entrepreneur is left with a profit, and with increasing returns to scale the firm cannot afford to pay its inputs their marginal products. Constant returns to scale are thus needed for a perfectly competitive equilibrium. |
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