Consider the representative firm's maximization problem in our real in- tertemporal model with investment. As we have seen in lectures, the capital accumu- lation equation is K = (1 d)K I and the present-value of profits can be written as V = zKaN 1a wN K (1 d)K zKaN 1a wN (1 d)K/(1 r ) where the notation follows the one in the textbook and lecture slides. The firm chooses N , N and K to maximize V . (a) Use calculus to prove that the optimality conditions implied by the choice of K can be written as 1 = azKa1N 1a 1 d/(1 r)