Suppose a firm has a production function given by Y = zK^0.3N^0.7.

(a) If z = 1 and K = 1, graph the production function. Is the marginal product of labor positive and diminishing?

(b) Now, graph the production function when z = 2 and K = 1. Explain how the production function changed from part (a).

(c) Next, graph the production function when z = 1 and K = 2. What happens now?

(d) Given this production function, the marginal product of labor is given by MPN = 0.7K0.3N-0.3. Graph the marginal product of labor for (z, K) = (1, 1), (2, 1), (1, 2), and explain what you get.