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 &quot;no free lunch&quot;.)
Then you can apply the definition of returns to scale.