# How constant returns to scale leads to zero economic profit?

This was mentioned in my textbook Macroeconomics-Gregory Mankiw.

If the production function has the property of constant returns to scale, as is often thought to be the case, then economic profit must be zero. That is, nothing is left after the factors of production are paid.

It was mentioned that this comes out as a result of Euler's Theorem, but I don't quite understand it, can anyone please clarify this?

The argument is that if there are constant returns to scale then the marginal product of each factor of production is constant as total quantity changes. This makes the production function homogeneous in the first degree and it will look something like $$Q=\dfrac{\partial Q}{\partial A}A +\dfrac{\partial Q}{\partial B}B +\dfrac{\partial Q}{\partial C}C$$
$$PQ-\left(P\dfrac{\partial Q}{\partial A}A +P\dfrac{\partial Q}{\partial B}B +P\dfrac{\partial Q}{\partial C}C\right)=0$$
• "The argument is that if there are constant returns to scale then the marginal product of each factor of production is constant as total quantity changes." - This is not true - what you need to do is take the production function $Q(A, B, C)$ and look at the derivative with respect to $t$ of $Q(tA, tB, tC) = t Q(A, B, C)$ using the chain rule. The marginal product of each factor can change as the quantity supplied of that factor changes - no, not all constant returns to scale production functions are linear. – Starfall Feb 7 '18 at 18:58