5. Answer ALL parts of this question. Suppose a firm can sell it's output at p per unit and that its production function is given by y= AKL, where K> 0 is capital input measured in machine-hours, L> 0 is labor input measured in worker-hours and A, a, ß> 0 are parameters. The firm is perfectly competitive and the factor prices are r per hour and w per hour. (a) Show by partial differentiation that the production function has the property of increasing marginal productivity of capital (if a > 1) and of labor (if ß > 1). Explain the economic significance of this. Does it explain why we normally assume that a and 3 are less than 1? 10 marks (b) Suppose that a = 1/3 and 8 = 1/3. i. Write down an expression for the profit function in terms of K and L (recall that the profit is given by the difference between the total rev- enue and the total cost). ii. Find (K*, L) that solve firm's profit maximization problem. iii. Are the second order conditions satisfied? iv. What is the value of firm's profit at (K*, L)? Is it increasing or decreas- ing in w? Is your finding reasonable? 25 marks tiv a IS es rc in