Problem 5: The Firm [15 marks) Consider the following modified version of the model of the firm studied in class. The firm lives for two periods, producing output Y in the first period, and output Y' in the second period by operating the following technologies: Y = F(K, nd), and y' = Z' H(K), where K (K") denote physical capital in the first (second) period, nd is labour demanded in the first period, and z (zl) denotes total factor productivity (henceforth TFP) in the first (second) period. The function F is increasing in both arguments, it is concave, and it satisfies constant returns to scale. The function H is increasing and concave. The firm hires labour in a competitive market at the wage w. Capital in the first period K is fixed, and physical capital depreciates at a rate of 100%, so that K' = I, where I denotes investment. Assume that the level of future total factor productivity is uncertain. Specifically, z' = Zh with probability oH (0,1), and z' = z[ with probability L = 1-h, where Zz