direction of causality between Increasing returns to scale and economies of scale

Question

Does increasing returns to scale cause economies of scale OR is it the other way around?

Answer 1

They both describe different situations, and they are not necessarily causal.

1. Economies of scale are properties of the cost function. When $\partial TC/\partial Q <0$, economies of scale exist.

2. Increasing returns to scale are properties of the production function. Increasing returns to scale exist when adding more input produces disproportionately more output, so they exist when $ F(aK, aL) > aF(K, L)$.

1 does not necessarily cause 2, and other way around.