1. Puzzle Piece # 4: Consider the same rm from Q3 from Homework 5 but this time assume the rm is operating in the long-run, i.e. it can vary K as well. As before, the rm's production function is q = 2K0'5LD'5, the wage rate is m = $18 and the rental rate of capital is r = $2. (a What is the optimal long-run relationship between K and L? (b If the rm is producing 6 units, how much labor will it employ? (d What is the (long-run) cost of producing 6 units? (e If the total cost function is linear then1 using your answer from (d), what is the slope of this line and the long-run total cost function? (f ) What are the ATC and MC curves? Sketch both curves on the same graph. (g) Comparing your answers to 3(f) above with your answer to 3(c) from Homework 5, why is the average total cost of producing 6 units the same in the short- and long-run? \"rhy is the long-run average total cost of producing a different quantity smaller than the shortrun average total cost? l l (c) How much capital will it employ? l l