As we have seen in many places, the general Cobb-Douglas production function for two inputs is given by q=f(k,1) = Ak 18, where 0 < a <1 and 0 < <1. For this production function:

a. Show that f>0, fi > 0, fk <0, fu <0, and ff >0.

b. Show that a and e,,, = .

c. In footnote 5, we defined the scale elasticity as af (tk, tl) t at f(tk, tl)' where the expression is to be evaluated at 1. Show that, for this Cobb-Douglas function, a+B. Hence, in this case the scale elasticity and the returns to scale of the production function agree (for more on this concept see Problem 9.9).

d. Show that this function is quasi-concave.

e. Show that the function is concave for a + B1 but not concave for a + > 1.