Suppose the production function for widgets is given byq = KL- .8K2 – .IV,where q represents the annual quantity of widgets produced, K represents annual capital input,and L represents annual labor input.a. Suppose K— 10; graph the total and average productivity of labor curves. At what levelof labor input does this average productivity reach a maximum? How many widgets areproduced at that point?b. Again assuming that K= 10, graph the MPL curve. At what level of labor input doesMPL = 0?c. Suppose capital inputs were increased to K — 20. How would your answers to parts (a)and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returnsto scale?