A university cafeteria produces square meals, using only one input and a rather remarkable production process. We are not allowed to say what that ingredient is, but an authoritative kitchen source says that “fungus is involved.” The cafeteria’s production function is f(x) = x2, where x is the amount of input and f(x) is the number of square meals produced.
(a) Does the cafeteria have increasing, constant, or decreasing returns to scale?
(b) How many units of input does it take to produce 144 square meals? ____. If the input costs w per unit, what does it cost to produce 144 square meals? ____.
(c) How many units of input does it take to produce y square meals? _____. If the input costs w per unit, what does it cost to produce y square meals? ______.
(d) If the input costs w per unit, what is the average cost of producing y square meals? AC(w, y) = ______.