A) Given a Cobb - Douglas production function Q = 150K0.5L 0.5 , show that when the average product of labour (APL) is at a maximum it is equal or identical to the marginal product of labour (MPL). [5 Marks] B) Show that the Cobb Douglas production function Q = 100K0.2L 08 obeys the law of diminishing marginal product with respect to capital by demonstrating that jQuery22406197562606593827_1593186374486 ?? > 0 and that ? 2? ??2 < 0. [3 Marks] C) Your company, Vision Unlimited, has estimated the following production function for your product, Q = 50K0.8L 0.2

If your required output is Q = 2,500 units, determine the equation of your production isoquant of capital (K) in terms of labour (L)? [6 Marks] II) Determine whether your production isoquant is convex to the origin by showing that ?? ?? < 0 and that ? 2? ?? 2 > 0. [4 Marks] D) For each of the following production functions, determine whether returns to scale are decreasing, constant, or increasing when capital and labor inputs are increased from K = L = 2 to K = L = 4. i) Q = 50K0.4L 0.7 [2 Marks] ii) Q = 200K +300L +400KL [2 Marks] iii) Q =100 +35K +25L [2 Marks] iv) Q = 2K 3L [2 Marks]