Pr | m t Due Friday 3r17r23 by 6 pm in my mailbox. outside my office. or send scan by email Please show the calculations used to arrive at your answers. Draw graphs neatly and label axes and points clearly. In general, leave numbers in fractional form while solving problems. Flound final answers to the first decimal place if necessary. A. Albuja Enterprises uses the production technology 0 = lm.) = \\22K2 + 4L2 A unit of capital K costs rand a unit of labor f. costs w. The firm wants to produce 0' units of output in order to maximize profits. (1) Set up the cost minimization problem for Albuia. (2) Solve for the input demand functions for capital and labor. K: K(w,r,0') and L = wa,r,0') [Simplify as much as possible]. (3) What is the cost function C(w,r,0') for Albuia [Simplify]? (4) a. Explain carefully what a cost function is. b. Why do we often write the cost function as just 0(0)? B. Kiwan Inc. has the cost function C(O) = 1000 + 1000 + 1002, where O = the quantity of output produced. (1) Write expressions for Average Fixed Cost (AFC), Average Variable Cost (AVG), Average Total Cost (ATC), and Marginal Cost (MC). (2) a. Graph the four cost functions found in (1). b. Indicate the firm's short-run supply curve on the graph. c. Write down the formula for the inverse supply curve. d. At what price is the firm indifferent between shutting down and staying open in the short run? (3) Solve for the quantity that minimizes ATC using one of the two possible methods; then check answer using the other method. (4) a. Write down an expression for Kiwan's profit function. Then derive the formula for the quantity that will maximize the profit function (is. q': qu), where p = unit price). b. Graph the profit function for Kiwan if the unit price of O is $500. Then graph the profit function if the unit price of O is $100. Be sure the important points of the functions are illustrated, i.e. the maximum point and points of zero profit