Case 7Bond Construction Company Upon completing a bachelor's degree program in civil engineering in 2009, Allen Bond opened his own construction business that specializes in building garages for residential homes. By 2015, the firm had grown substantially and employed, in addition to Bond, 21 carpenters who were paid $30,000 per year. This was the entire employment complement of the firm; all managerial, accounting, and clerical functions were provided by Mr. Bond. During 2015, the company built 368 garages. Excluding materials, which are provided by the customer, each garage sells for $2000. The firm has a large stock of capital equipment including trucks, tools, and surveying instruments. Bond has developed a measure for a unit of capital that includes one truck and specified amount of other equipment, including a ladder, several power tools, and an air compressor. Currently, the price to rent one of these units is $6000 per year, and the firm currently uses 10 units. Bond feels this is the limit to as large as he wants his company to get. Bond believes that if he takes on additional capital he will have to hire additional supervisors and staff personnel to help him with his work. Costs of capital and labor are the only significant explicit expenses that the firm has. Bond used a $100,000 inheritance to start the business and is quite pleased that he received several offers in the past month to sell the firm for $300,000. The firm's external accountant prepared an income statement for 2015 that shows an accounting profit of $6000 after paying Bond a salary of $40,000. The market interest rate is 8%. Bond has just completed a managerial economics course in the evening school program at the local community college. Although he is not sure he understood everything, the class did make him aware of many problems he had not considered before. For example, is Bond Construction really earning a profit? Is the current usage of labor optimal? The pressures of managing this business are beginning to bother Bond, and he is wondering if he would be happier simply taking a job at Hectel, Inc., a very large engineering firm in the area. Every year the personnel manager calls him with a job offer. In January of 2015, the salary offer was $75,000. Bond thinks he should have taken the job. Bond decides to hire a consultant to make a thorough economic analysis of the firm's operation. Unfortunately, he has kept very few records that might be used for economic analysis, although records were maintained on output and inputs of capital and labor for each of the seven years of operation, shown below. Capital (Units Labor Input (Worker-Yrs) Note: The labor input includes Bond's time. Output Year (No. of Garages) 2009 30 2010 2011 62 2012 2013 170 2014 2015 368 121 Bond thinks that the cubic production function will describe the production process: Q=aK L +bK?L? 241 10 Bond has retained you as a consultant and that the information provided above is all that is available. The first thing you do is estimate the inverse demand function from local data on housing starts, number of competitors, etc: P = 10,000 - 17.321Q Next, you run a regression to estimate the production function. The following is your Excel printout. SUMMARY OUTPUT Regression Statistics Multiple R 0.875412 R Square 0.766347 Adjusted R 0.519616 Standard E 64.99507 Observatio ANOVA Regressior Residual Total SS 69276.2 21121.8 90398 F ignificance F 8.19961 0.03845 2 5 7 MS 34638.1 4224.36 Coefficients'andard Ernt Stat P-value Lower 95% Upper 95% ower 95.09/pper 95.0% Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A X Variable -0.000155 4.87E-05 -3.188604 0.024303 -0.00028 -3.01E-05 -0.00028 -3.01E-05 X Variable 0.041706 0.010489 3.976217 0.01057 0.014744 0.068669 0.014744 0.068669 Requirements: What is the estimated production equation? Does this cubic production function conform to economic theory? Explain why or why not. Determine the actual economic profit earned by the firm in 2015. Given the estimated production equation, what is the average production (APL) equation? At what labor usage is APL maximized? Remember capital (K) will remain constant at 10 units. What is the marginal product (MPL) equation? At what labor usage is MPL maximized? Equal to zero? Again, K will remain constant at 10. Given that capital usage is 10, has Bond used the optimal amount of labor in 2015? Explain why or why not. If not, what is the optimal amount of labor? If the optimal amount of labor is used then what will be the estimated number of garages built in 2016? Given this number, what price should Bond charge for a garage (round to the nearest whole dollar)? Given this price and quantity, what will be Bond's economic profit for 2016?