Suppose the production function for widgets is given by q=kl-0.8k^2-0.2l^2 where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.
a) k=10, graph the total and average productivity of labor curves. At what level of labor inputs does this average productivity reach a maximum? How many widgets are produced at that point?
b) Again assuming k=10, graph the MPl curve. At what level of labor inputs does MPl=0?
c) Suppose capital inputs were increased to k=20. How is part a and b change?