2. Uncertainty about the future and rm's investment Consider a rm that operates for two periods using capital and labor to produce. The rm starts with K units capital and has to decide optimally its labor demand for both periods and the investment so as to maximize the discounted value of prots. When the rm chooses the investment it is uncertain about the value of future productivity. The rm thinks that with probability p the productivity is going to be high (zh), and with probability 1 p it is going to be zero, so that no production takes place in the future (no labor is hired and no capital is used, so there is no depreciation). Note that it is only protable to invest when 2' is higher than zero. Since the rm does not know for sure the value of 2' it maximizes the expected value of prots. The problem of the rm is: \"(0) 1+7" max 2F(K,N) wN I+p7rlzh> s.t.K'=(15)K+I + 1 N,N',1 1+7\" ( p) (a) What are prots in the second period if z, = 2h? (b) What are prots in the second period if z, = O? (c) What is the optimality condition for investment? Interpret it. ((1) Note that when p = 1 this problem is the same as the one in the book. How does the investment demand change when p