11.12 More on the derived demand with two inputs The demand for any input depends ultimately on the demand for the goods that input produces. This can be shown most explicitly by deriving an entire industry’s demand for inputs. To do so, we assume that an industry produces a homogeneous good, Q, under constant returns to scale using only capital and labor. The demand function for Q is given by Q ¼ D(P), where P is the market price of the good being produced. Because of the constant returns-to-scale assumption, P ¼ MC ¼ AC.

Throughout this problem let C(v, w, 1) be the firm’s unit cost function.