Part IV (5 points) Suppose a rm has the following production function: F (K, L) = AKiLt, which is the same rm in Part III, but now we analyze its cost structure in the long run. (A) Determine whether the production function displays constant, increasing, or decreasing returns to scale. (B) Each hour the rm needs to produce Q units of output to ship to their customers. Write out the rm's cost minimization problem. Be explicit in specifying the choice variable(s) and the constraint. (C) Solve for the rm's optimal capital to labor ratio. (D) Find the rm's long-rim total cost function. (E) Determine whether the rm has economies of scale, constant economies of scale, or diseconomies of scale. Briey explain your reason. (F) (Bonus Question) Show that every short-run average total cost curve of this rm touches the long-run curve exactly once. This illustrates that the long-run average total cost curve forms an \"envelope\" of short-run average total cost curves. Hint: There is a different short-run total cost curve for each capital level