Chapter 7 Case Problem Set A

Transcription

1 Chapter 7 Case Problem Set A Arcane Assemblies was formed in the mid-198s as the result of an unlikely partnership between Arthur Rex and Bob Merlin. After a rocky start, the company began production of a computer interface enhancer called the Wizard Card. When installed in a computer, the Wizard Card intercepts commands entered from the keyboard and uses artificial intelligence to translate them into the commands that users really intended to enter in the first place. The first versions of the product were quirky, with serious quality control problems, and Arcane Assemblies came close to bankruptcy. Fortunately, Merlin had another card up his sleeve and, after a long and intensive search, Arthur was able to find an investor willing to support its production. The investor, Holly Grail, has decided to take an active role in the business. She insists that production of the new version of the Wizard Card be planned using the methods of managerial economics. As a way to ensure that this is done, she hires a consulting engineer to analyze the alternative production methods available to the firm. The engineer identifies four types of circuit board assembly systems (A, B, C, and D) and determines the number of Wizard Cards that can be produced per month using the different combinations of labor (L) and capital (K) with each system. The results of the analysis are given in the table that follows. When Holly presents the production information to Arthur and Merlin, they are initially unsure of how to proceed. A call to the local university yields a suggestion. Why not hire a student as an apprentice? Merlin finds the offer appealing, and the others agree. The following day, you find yourself working for Arcane Assemblies. Solve Problems 1 through 7 using this information. (L) A B C D

2 1. Begin your analysis of the production possibilities table by calculating the average product (AP L ) and the marginal product (MP L ) of labor and the output elasticity of labor (E L ) for each of the four production systems. Enter these values in the tables below. Production System A L AP L MP L E L Production System B L AP L MP L E L Production System C L AP L MP L E L Production System D L AP L MP L E L

3 2. Next, plot the total product curves for each of the production systems in the graph below and then plot the average and marginal product curves for each of the production systems on the four graphs that follow. Chapter 6: Problem 2 Total Product

4 Chapter 6: Problem 2 - System A AP, MP Chapter 6: Problem 2 - System B MP, AP

5 Chapter 6: Problem 2 - System C MP, AP Chapter 6: Problem 2 - System D MP, AP

6 3. Determine the range of output that corresponds to Stage II of production for labor for each of the four production systems and enter this information in the table below. Assume that hiring more than 1 units of labor will not increase output for any of the production systems. Stage II A B C D Begins Ends

7 With preliminary analysis of the production possibilities completed, you are ready to consider costs and revenues. Arthur believes that Arcane Assemblies can sell as many Wizard Cards as it can produce at a price (net of materials costs and shipping) of $1. Holly's analysis of the local labor market indicates that any number of qualified workers can be hired for $1,8 per month. Finally, Merlin has determined the monthly rental cost of capital for the four production systems to be $8, for D, $, for C, $1, for B, and zero for A. Production system A involves no capital utilization. 4. Calculate the marginal revenue product of labor for each of the production systems and enter their values in the table below. (L) A B C D

8 . Plot the relevant portions of the four labor demand curves for each of the production systems on the graph below. Label the labor demand curves A, B, C, and D. Also plot the labor supply curve on the graph. Chapter 6: Problem 7 6 Wage (Thousands)

9 6. From the graph in Problem, determine the number of workers that Arcane Assemblies should employ (L), the total cost of labor (wl), the total cost of production (TC), total product (Q), total revenue (TR), and total profit (π) for each production system and record the values in the table below. Which production system should Arcane Assemblies use and how many units of labor should it employ? L A B C D wl TC Q TR π

10 7. Finally, show that the production system that was identified as optimal in Problem 6 is also optimal according to the general optimization principle by completing the following steps. First, determine the marginal product and marginal revenue product of capital for each of the four production systems. Assume that Arcane Assemblies employs the number of workers that was found to be optimal in Problem 6. Next, determine the marginal resource cost of each of the four production systems. Enter the values into the table below and then plot the values on the graph that follows. How are these values used to identify the optimal production system? MP A B C D MRP MRC Chapter 6: Problem 7 7 MRC, MRP (Thousands) A B C D