Consider the Cobb-Douglas production function: 1-0 Y = F (K, L) = AK L-, 0 (0,1), where Y - output, A - productivity parameter, K - capital, L - labor, 0 - capital share parameter and also the elasticity parameter. Recall that marginal products tell us what happens to output when only one of the inputs is increasing by 1 unit, holding all other inputs constant (ceteris paribus). This is exactly the meaning of partial derivatives. The returns to scale of a production function tell us what happens to output when all inputs increase by some factor > 0.