# Returns to Scale Microeconomics

Are there any production function $$f(x_1,\ldots,x_n)$$ that is having decreasing returns to scale, given that the marginal product in every input $$i$$ in the function $$f$$ is constant?

Seems like the only function $$f$$ that fits your description $$\forall i: \frac{\partial f(\mathbf{x})}{\partial x_i} = c_i$$ is $$f(\mathbf{x}) = A + \sum x_i c_i.$$ (Frequently $$f(\mathbf{0}) = 0$$ is assumed. The assumption is referred to as "no free lunch".)