Problem Set #4 Production 1. Optimal Use of a Single Input. Julian Smyth is manages production at Taft)' Apple Inc., a company that produces a variety of tafty/fiuit candies. Over the last several months, he has varied then number of employees on his caran1el apple production line, and found the following relationship. Labor TP MP MRP a. In the column labeled MP, calculate the mar•ginal product oflabor. (Note, make your first entry in row 6, as the change between 5 and 6 units oflabor) b. Suppose the apples sell tor $5 (per dozen) box. Calculate the Marginal Revenue Product ( 1/fRP) c. Iflabor costs $225 per day, how many laborers should the firm hire'' Number ------------------------------------- 2. Optimal Use of a Single Input. A graphical representation. a. In the coordinate axes provided below, illustrate the general relationship between MRP and the Price of Labor. IdentifY the equilibrium quantity of labor to hire. (Not<:, your graph nc:ed not use the: numbc:rs in problem 3. Just be certain to include ranges that illustrate gains from specialization and the law of diminishing returns in your graph. $ Q b. Suppose that the candy workers union agrees to way concessions, that make the price oflabor fall. In the coordinate axes below illustrate the etlect on the equilibrium quantity of labor $ Q c. Finally. suppose that the price of caramel apples increases. Illustrate the eflt:ct of this ch mge on the equilibriwn quantity oflabor c:mployed. $ Q 3. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroof. into automobiles. 1l1e process can use a combination of skilled labor and unskilled labor. Given his current mix of employees, the marginal product of the last unit of skilled labor is 3 sumoofs per day, and tht: marginal product of the last unit of unskilled labor is 1 sunroof per day. CmTent market rates for skilled and unskilled labor are $40 and $10, respectively. Is Julian using a least cost combination of inputs? If not, which of type oflabor should he use relatively more'' Comparison Expression: _ Result: _ 4. Retmns to Scale. Jake's Free Runoff Bottled Water Company Produces with the Long Run Production Function Q = (KL)2il a. Currentlv K = 4 and L = 4. IfJake's doubles inputs to K=8 md L=8, will it realize increasing, constant or decreasmg retums to scale (circle one)'' b. As a result does Jake's enjoy economies of scale, diseconomies of scale, or does Jake's appear t be operating at Efficient Scale? (circle one)
