Question 5. A representative firm which only can survive for one period. It has the following technology: Y = =F(K, N). where K is the given capital stock (the representative firm owns K but no market value if the firm sells it), N is labor demand by paying competitive market wage rate w, and = is total factor productivity (TFP). Let's further assume the production function be a continuous concave function. Without loss of generality, let's assume the output good price equals to 1. (a) Write down the representative firm's profit function and graphically determine and mathe- matically prove the profit maximization condition. (10 marks) (b) Determine the labor demand curve, N, as a function of wage, w. Graph this relationship. (5 marks) (c) Suppose that the pandemic improves technology due to the improving remote work-from-home technology that save a lot of commute time. i.e., z increases (decreases). Discuss and graph the change of labor demand curve. (5 marks) 2