Suppose a firm produces joules of energy using either wind turbines or coal power plant. Both technologies use a single input: capital to produce energy and have the following production functions: Wind: f(c) = c2 if c 5 Coal: f (c) = c1/2 Suppose the firm can freely switch between using one means of production to the other. Graph the joint production function for the firms use of both technologies below, assuming the firm behaves in a way that is technically efficient: For the joint production function: What is the relationship between how the marginal product changes as more of the input ( c), and how returns to scale change as more ( c) is used