<P> Formally, a production function F (K, L) (\ displaystyle \ F (K, L)) is defined to have: </P> <Ul> <Li> Constant returns to scale if (for any constant a greater than 0) F (a K, a L) = a F (K, L) (\ displaystyle \ F (aK, aL) = aF (K, L)) </Li> <Li> Increasing returns to scale if (for any constant a greater than 1) F (a K, a L)> a F (K, L), (\ displaystyle \ F (aK, aL)> aF (K, L),) </Li> <Li> Decreasing returns to scale if (for any constant a greater than 1) F (a K, a L) <a F (K, L) (\ displaystyle \ F (aK, aL) <aF (K, L)) </Li> </Ul> <Li> Constant returns to scale if (for any constant a greater than 0) F (a K, a L) = a F (K, L) (\ displaystyle \ F (aK, aL) = aF (K, L)) </Li> <Li> Increasing returns to scale if (for any constant a greater than 1) F (a K, a L)> a F (K, L), (\ displaystyle \ F (aK, aL)> aF (K, L),) </Li>

Law of diminishing returns vs economies of scale