A company has a production function: $$y=x_1^{\alpha}x_2^{1-\alpha}$$
where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its production costs when it produces y> 0 units of the output.
I have in a problem found that MC: $$MC=\frac{\partial c}{\partial y}=w_1((\frac{w_2\alpha}{w_1(1-\alpha)})^{1-\alpha})+w_2((\frac{w_1(1-\alpha)}{w_2 \alpha})^\alpha)$$
We see that marginal costs only depending on $w_1$ and $w_2$ and thus not on y. So we have that the marginal costs are constant. But why is that the case? What is the economic interpretation? I think maybe I should use returns to scale?