Suppose that we have a standard classical production function F(K,L) that exhibits constant returns to scale. Define output per worker as the ratio between output and labor: (F(K,L))/L. Prove (using the Euler equation) that, ceteris paribus, higher population causes average labor productivity to fall, i.e. show that (() (F (K,L))/L)/L < 0.

Euler equation: F(K,L) = (MPK x K) + (MPL x L)