Allen Bond used a $100,000 inheritance to open his own construction business in January, 1995. The firm specializes in building a standard-design utility (or storage) building for residential homes.

From a small beginning in 1995 when it employed only four carpenters, leased only one unit of capital, and built only 25 of its standard-design utility buildings, the firm has grown substantially. In 2020, the firm employs 75 carpenters, leases 25 units of capital, and, by the end of the year, will have built 823 of its utility buildings which sell for $2,750 each.

The 75 carpenters are paid $25,000 per year and constitute the entire labor component of the firm since all managerial, accounting, and clerical functions are handled by Mr. Bond. Mr. Bond has developed a measure for a unit of capital that includes one truck and a specified amount of other equipment, including a ladder, several power tools, an air compressor, etc. Mr. Bond currently leases 25 units of capital at $5,000 per unit. Labor and capital inputs can be varied daily and are the only significant explicit expenses incurred by the firm since building materials for each utility building are supplied by the customer.

In particular, Mr. Bond is concerned about whether the current mix of labor and capital is optimal for the production process employed by Bond, Inc. Additionally, Mr. Bond now realizes that the business environment in which he operates is much more complex than he had previously considered. For example, skilled carpenters have recently organized and their salaries will increase to $30,000 per year beginning in 2021, the cost of capital will increase to $7,500 per unit, and the demand for utility buildings is expected to slow because new builders are including plenty of storage space in new structures. Finally, the city commission has just passed an ordinance restricting the construction of utility buildings after 2021 that will essentially eliminate the industry in the city that Bond, Inc., serves. For all practical purposes, with no assets and a "doomsday" future ahead of it, Bond, Inc., has no market value.

Mr. Bond anticipates retiring at the end of 2025, but the pressures of managing his business are beginning to bother him. His own projections are that because recent developments, growth will slow to 5% per year over the remaining five years the industry can exist. Increasingly, he is wondering if he would not be happier simply accepting a job offer from a local firmBobcats, Inc., a very large construction firm. Last year the personnel manager offered Mr. Bond and annual salary of $190,000 and has already called again this year to offer Mr. Bond a five-year contract, beginning in January of 2021, at a beginning annual salary of $190,000 with 5% annual increases.

Mr. Bond has hired your consulting group to make a thorough economic analysis of the firm's operation and to help him decide how to spend the next five years. Unfortunately, he has kept very few records that might be used for economic analysis. Records were maintained on output and inputs of capital and labor for each of the 26 years of operation. In the attached table, Q represents the number of utility buildings constructed each year, L is the average number of carpenters employed during the year, and K is the average number of units of capital leased during the year.

After completing the managerial economics class, Mr. Bond thinks his process for constructing utility buildings can be described by a Cobb-Douglas production function of the form Q = AKL . He's very interested in using the available data to estimate the parameters (i.e., A, , and ) of the Cobb-Douglas production function. He wonders if his "seat-of-the pants" intuition about the labor-capital mix has been on target, or would his business have been much more profitable over the years if he had used more sophisticated analytical tools to determine the optimal labor-capital mix. From experience, he thinks building utility buildings is an increasing returns to scale operation, but he's anxious to discover what the Cobb-Douglas production function will reveal. He knows his firm has grown rapidly, but he's never really thought much about the actual compound rate of growth until he learned how to make such

computations while studying time value of money. These are just a few of the questions that Mr. Bond has been thinking about. And now he has hired your consulting team to help him with the answers. Let's get to work!

Rather than a narrative report, Mr. Bond wants your consulting team to respond directly to each of the following questions. Please answer in complete, grammatically correct, sentences. Attach supporting regression analyses, spreadsheets, computations, etc., as appendices to your responses to the questions.

Year Q L K

1995 25 4 1

1996 25 4 1

1997 50 8 1

1998 60 8 2

1999 85 8 2

2000 85 8 2

2001 115 13 3

2002 120 14 3

2003 150 16 4

2004 155 16 5

2005 175 16 5

2006 190 16 6

2007 220 20 6

2008 220 22 6

2009 245 24 7

2010 255 24 8

2011 285 28 10

2012 315 30 11

2013 320 31 12

2014 380 32 13

2015 385 33 13

2016 465 42 15

2017 475 45 16

2018 610 56 20

2019 635 60 22

2020 823 75 25

Based on the data, what is the estimated C-D production function for Bond, Inc.? Is this an increasing returns to scale industry as Mr. Bond suspected? Why or why not?

Using the estimated C-D production function, and given the costs of labor and capital, what is the expansion path (i.e., what is the optimal mix of labor and capital)? Casual observation suggests that over the years Mr. Bond has employed on average about 3 carpenters for every unit of capital (i.e., one unit of capital supports about three carpenters). Does it appear that his "seat-of-the-pants" intuition about the mix of labor and capital was correct? Why or why not?