Economies of scale

A measure of scale economies is

$$S(q)=\frac{AC(q)}{MC(q)}$$

• If $S>1$, economies of scale or increasing returns to scale exist. It is equivalent to $AC(q)$ being an decreasing function of $q$

That is,

$$AC(q+\Delta q)=\frac{AC(q)q+MC(q)\Delta q}{q+\Delta q}$$

• If $S<1$, diseconomies of scale or decreasing returns to scale exist.
• If $S=1$, We have Constant Return to Scale, which essentially means constant marginal cost without fixed costs, i.e., $C(q)=kq$

Recall the picture:

The range before point $A$ exists a increasing returns to scale.