Question 5. A representative rm which only can survive for one period. It has the following technology: Y = 2F(K,N), where K is the given capital stock (the representative rm owns K but no market value if the rm sells it), N is labor demand by paying competitive market wage rate to, and z 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 rm's prot function and graphically determine and mathe matically prove the prot 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 workfromhome technology that save a lot of commute time. 6.6., 2 increases (decreases). Discuss and graph the change of labor demand curve