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In neoclassical economics, this is the mathematical derivative of the production function. Note that the "product" (Y) is typically defined ignoring external costs and benefits. In the "law" of diminishing marginal returns, the marginal product of one input is assumed to fall as long as some other input to production does not change.
In the neoclassical theory of income distribution, in competitive markets, the marginal product of labor equals the real wage. Similarly, under the same conditions, the marginal product of capital equals its rate of return. But there have been severe criticisms of this theory.