This study source was downloaded by 100000796483839 from CourseHero com on 09 24 2022 10 39 59 GMT 05 00 https www coursehero com file 81238121 chapter 5 Economic solutionspdf AbuTurki Chapter 5 Answers to Questions and Problems Q1 A firm can manufacture a product according to the production function Q F K L K3 4L1 4 a Calculate the average product of labor APL when the level of capital is fixed at 16 units and the firm uses 16 units of labor How does the average product of labor change when the firm uses 81 units of labor b Find an expression for the marginal product of labor MPL when the amount of capital is fixed at 16 units Then illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor c Suppose capital is fixed at 16 units If the firm can sell its output at a price of 100 per unit and can hire labor at 25 per unit how many units of labor should the firm hire in order to maximize profits Answer 3 a When K 16 and L 16 0 750 25161616Q Thus APL Q L 16 16 1 When K 16 and L 81 0 750 2516818324Q Thus APL 24 81 8 27 b The marginal product of labor is 342LMPL When L 16 342161 4LMP When L 81 342812 27LMP Thus as the number of units of labor hired increases the marginal product of labor decreases 161 42 2781LLMPMP holding the level of capital fixed c We must equate the value marginal product of labor equal to the wage and solve for L Here 3 43 4 1002200LLVMPPMPLL Setting this equal to the wage of 25 gives 3 420025L Solving for L the optimal quantity of labor is L 16 Q2 Explain the difference between the law of diminishing marginal returns and the law of diminishing marginal rate of technical substitution Answer 2 The law of diminishing returns is the decline in marginal productivity experienced when input usage increases holding all other inputs constant In contrast the law of diminishing marginal rate of technical substitution is the rate at which a firm can substitute among different inputs while maintaining the same level of output This study source was downloaded by 100000796483839 from CourseHero com on 09 24 2022 10 39 59 GMT 05 00 https www coursehero com file 81238121 chapter 5 Economic solutionspdf Powered by TCPDF www tcpdf org 2 AbuTurki Q3 An economist estimated that the cost function of a single product firm is C Q 50 25Q 30Q2 5Q3 Based on this information determine a The fixed cost of producing 10 units of output b The variable cost of producing 10 units of output c The total cost of producing 10 units of output d The average fixed cost of producing 10 units of output e The average variable cost of producing 10 units of output f The average total cost of producing 10 units of output g The marginal cost when Q 10 Answer 3 d FC 50 e 231025103010510 8 250VC f 300 8 10510301025501032 C g 5 1050 10 AFC h 10 8 25010 8251010VCAVC i 830 101010 AVCAFCATC j 125 2 1015106025102 MC Q4 Explain the difference between fixed costs sunk costs and variable costs Provide an example that illustrates that these costs are in general different Answer 4 Fixed costs are associated with fixed inputs and do not change when output changes Variable costs are costs associated with variable inputs and do change when output changes Sunk costs are costs that are forever lost once they have been paid