Assume the production function in an economy is Y = AK,where Y = output,A = productivity,and K = capital.This means that

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The production function Y =AK implies that the output(Y) depends on the productivity (A) and the capital (K). Since there is no variable for labor, we can assume this to be a simple model of a "neoclassical" economy where labor is in fixed supply. With this assumption, the marginal product of capital (MPK) is also constant, which means that adding more capital will not increase the productivity of the previous unit of capital used. Hence, the marginal productivity of capital is constant.

Assume the Production Function in an Economy Is Y =