l. [20 points] Consider the representative rm's maximization problem in our real in tertemporal model with investment. As we have seen in lectures, the capital accumu lation equation is K' = (l (BK + I and the presentvalue of prots can be written as z'K'\"N"1_\" w'N' + (1 core 1 + r V = 25:\"le wN K' + (1 em + (1) where the notation follows the one in the textbook and lecture slides. The rm chooses N, N' and K' to maximize V. {a} (13} Use calculus to prove that the optimalityr conditions implied by the choice of K' can be written as 1 1 off?\" N' _\" +1 d 1 + r (2) The left side of equation [2} corresponds to the marginal cost of increasing K' by 1 unit. It reects the fact that increasing K' by one unit reduoes current prots (and therefore V} by one unit. In this question, we ask you to explain the different parts of the expression oz'K'\"_1N'l_" + 1 d and explain why it is part of the calculation of the marginal benet of increasing K'. 1 Show that equation (2) implies the rm investment rule oz'N '1'\" T = m ' '1' '3} Suppose that, because of the gradual spread of a virus in the economy, the rm anticipates that it will not be able to hire as much labour in the future period as it initially planned. Explain how this expected change in N' impacts the investment schedule. Your explanation m_ust be based on the investment rule {3)