Let's consider a middleman firm in the business of producing ethanol. Assume that the firm can produce its own corn (the feedstock) or it can purchase corn from third-party farmers. The firm processes the corn into ethanol on its own. To maintain consistency with your notes, let's call our feedstock Xh (in-house) and Xm (third party). Suppose the inverse demand curve is P = 105 -Q and the production function is Q = f(X) = (Xh + Xm)2. The cost of producing corn in-house is Ch(Xh) = 1.5X2. The cost function of a third-party producer is Cm(Xm) = X'm. Finally, the cost of processing feedstock from either source is Cp(X) = 5(Xh + Xm)2. For this middleman, find the: 1. Marginal productivity of the input. 2. Marginal revenue of the output (remeber - this is Q, not X) 3. Marginal outlay