Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α < 1, satisfies all assumptions made in lecture 5.
1) Output increases when either the capital stock or the number of workers increase
2) Both the marginal product of capital and the marginal product of labor are decreasing
3) The marginal product of labor increases when capital increases, and the marginal product of capital increases when labor increases
4) For any constant x > 0, F(xK,xN) = xF(K,N)