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2. PROFIT MAXINIIZATION (10 POINTS) You are operating a rm that uses labor (L) and capital [IQ to produce widgets in a perfectly com- petitive market. The price of widgets is p = 3. It costs in = 4 to employ each unit of labor, and it costs Pr = 2 to employ each unit of capital. Your rm's production function is 1 1 y = IOLEK 5 where y is the number of widgets produced. (a) (3 POINTS) In the short run, your level of capital is xed at K = 8. If the rm is maximizing prots, how many units of labor will your rm employ and how many widgets will your rm produoe? (b) (2 POIN TS ) What is your rm's maximized level of prot in the short run? (c) (3 POINTS) In the long run your rm is free to choose K as well as L. If the rm is maximizing prots, how many units of labor will your rm employ and how many units of capital will your rm employ in the long run? How many widgets will your rm produce in the long run? (d) (2 POINTS) What is your rm's maximized level of prot in the long run? Is your long-run maximized level of prot greater, less than, or equal to your short-run maximized level of prot? Explain