Umm NS 9.2] Suppose the production function for widgets is given by q = kl 0.83:2 0.2!: where {1 represents the annual quantity of Widgets produced, R3 represents annual capital inputJ and i represents annual labor input. (a) Suppose k = 10. Graph the total and average productivity of labor curves. (Total productivity is just :3 as a mction of l). At what level of labor input does average productivity reach a maximum? How many widgets are produced at that point? (h) Again assuming that k = 10, graph the MP; curve. At what level of labor input does MP; = U? (c) Suppose capital inputs were increased to R: = 20. How would your answers to parts (a) and (b) change? {d} Does the widget production function exhibit constant. increasing. or decreasing returns to scale