Economics homework help. Module 3: Learning & Assessment Activities
During this module you will:

Discuss:

• M3D1 Discussion: Boeing and a Most Important Input

# Module 3: Module Notes: Production and the Organization of the Firm

In Module Two, consumer behavior was examined in developing tools used to forecast demand. In Module Three, we move to the process of production and the organization of the firm. Mathematical and graphical tools are used to demonstrate principles governing the efficient use of resources. You should focus on the practical application of these devices. Tools introduced in this module are derived from the technical character of the production process.
Production is the process of transforming inputs into an output. This transformation requires the application of technology, or knowledge, in a particular area. Technology is encompassed in the production function, which is the technical relationship that defines the maximum amount of output that can be produced with a given set of inputs. We consider production using capital and labor, denoting the quantity of capital as K and the quantity of labor as L. The level of output produced is represented as Q. Capital encompasses physical resources such as machines in which the firm has invested financial resources (or capital). Mathematically, the production function can be written as:
Q = F(K, L)
The technical nature of the production function will determine maximum levels of output obtainable given certain combinations of inputs. The manager may choose to maximize output for a given cost or to minimize cost for a given output. In either case, market prices in combination with the technology of production will dictate appropriate input combinations.
Total product (TP) is the maximum level of output that can be produced with a given amount of inputs. Differing levels of output can be depicted graphically as production isoquants, which isolate a certain quantity of output that can be produced using efficient combinations of inputs. Isoquants capture the tradeoff among combinations of inputs that yield the same output in the long run when all inputs are variable. The marginal rate of technical substitution (MRTS) is the rate at which a producer can substitute between two inputs and maintain the same level of output. The MRTS is the absolute value of the slope of the isoquant which is:
MRTSKLKL = MPL
MPx

This method of representing production is a general way of stating that the tradeoff between two inputs is based on the degree to which one can be traded for another in technological, practical, or physical terms. A manager substitutes one input for the other, optimally, by comparing the technical tradeoff between the inputs against the cost of one input in relation to the other. Marginal product is the amount of goods produced when, with other inputs held constant, the manager increases the use of an input by one unit. To maximize profits when labor or capital vary in the short run, a manager should hire labor until the value of the marginal product of labor equals the wage rate w, and should utilize capital until the value of the marginal product of capital equals the rental rate r.
While the manager rarely puts pencil to paper to carry out these computations, this assessment is applied widely in determining resource use. Figure 1 below illustrates the fact that as the usage of an input increases, marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns). To maximize profits, a manager should use inputs at levels at which the marginal benefit equals the marginal cost.

More specifically, when the cost of each additional unit of labor is w, the manager should continue to employ labor up to the point where VMPL = w in the range of diminishing marginal product. Changes in technology affect the level of output available using all technically efficient combinations of inputs, as well as the rate at which one can be traded for the other. In Figure 2, this is seen as movement to successively higher isoquants. The slope of the isoquant, on the other hand, is determined by the ratio by which existing technology allows one input to be traded for the other. The firm could invest high levels of capital in a mechanized production line that minimizes the number of workers required to produce a certain level of output, as at point “A.” Alternatively, the firm could settle on a more labor-intensive solution, represented by point “B.” Both would equally yield an output of 100 units.

There are strategies that allow managers to become familiar with the production process that they are uniquely involved in (and additional information is available optional reading for this module)3. Technologies of production advance continuously, requiring ongoing efforts to deepen knowledge in areas that pertain to a firm’s products. For example, computer-aided design and manufacturing (meaning the use of software applications to create detailed instructions that control machine tools for manufacturing parts) has vastly increased productivity in many different industries in recent decades; this module’s optional reading explores the extensive impact innovation and research in this area has had on production technology4. However, managers also have less obvious ways of enhancing production processes. For instance, in 2014, economists studying the productivity gains of a steel mill with a high proportion of fixed capital, few workers to create large gains in productivity, and static physical machinery and facilities found that, after allocating productivity gains to investment and employee incentive plans, there was a “large unexplained component [of increased productivity, over the years studied]…Learning by experimentation, or tweaking, [seemed] to be behind the continual and gradual process of productivity growth.”5 Both learning-by-doing and other forms of technological advance alter the technical relationship between input and output, and any method of organizing production is also considered technology. Mangers may seek to improve production by introducing these advancements.
Decisions by managers to enhance the firm’s competitive position through the adoption of new technologies or other improvements in production techniques support profits. Most improvements confer cost, however, which may increase the firm’s vulnerability to economic downturns, when production lags and consumers are more cautious in their purchasing decisions. There are issues related to cost that are of concern to managers as they develop production strategies over time. A significant factor in the ability of the firm to compete successfully is the level of fixed factors of production such as facilities and machinery that are deployed in the production process. Like long-term financing contracts, fixed factors of production generate fixed costs that are not easily altered in the short run. The short run is defined as the time frame in which fixed factors of production, such as facilities, cannot be altered. In the longer term, the nature or level of these factors can be changed, and in fact the long run is defined as the horizon over which the manager can adjust all factors of production. At low levels of output, high fixed costs imply that the firm may not be able to price goods competitively.
Fixed costs are defrayed by increasing production and sales. As the scale of production increases, however, variable costs such as labor and electricity that grow along with output will rise in tandem with the level of production. As components of total cost (TC), the differing character of fixed and variable costs is critical, and for this reason pricing or production managers must recognize factors such as these that affect the competitive position of a firm. A firm’s competitive position is also affected by its ability to procure inputs efficiently. Effective managers procure inputs in a way that maximizes efficiency in order to increase or maintain a firm’s competitive advantage over rival firms. Managers must consider when it is optimal to acquire inputs (1) via spot exchange, (2) by writing contracts with input suppliers, or (3) by producing the inputs within the firm (vertical integration). Managers must also ensure that the firm’s employees put forth the maximum effort consistent with their capabilities, and so need to consider tools for incentivizing productivity.
A manager’s efforts to improve production or increase efficiency by improving input procurement, increasing the role of fixed factors of production, or incentivizing productivity growth will be constrained by features of the production process itself. In this module, principal tradeoffs implied by a structure or technology are illustrated by the three forms that a production function may take:
Linear: Q = F(K,L) = aK + bL, where a and b are constants.
Leontief: Q = F(K,L) = min(aK,bL), where a and b are constants
Cobb-Douglas: Q = F(K,L) = KaLbwhere a and b are constants
Given the commonly used algebraic production function forms, we can compute the measures of productivity as follows:
Linear:
Marginal products: MPK = a and MPL = b
Average products: APK =  aK+bL         and APL =   aK+bL
K                                L
Leontief:
Inputs must be used in fixed proportions; the manager cannot substitute between capital and labor and maintain the same level of output.
Cobb-Douglas:
Marginal products: MPK = aKa-1Lb and MPL = bKa-1Lb
Average products: APK = KaLb and                APL =  KaLb
K                           L
Managers may apply these functions to determine objective criteria for determining input combinations based on market and technical criteria. Say, for instance, that the firm produces output that can be sold at a price of \$60, and the Cobb-Douglas production function is given by Q = F(K, L) = K½L½. If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is \$10? The answer is that the manager must set the value of the marginal product of labor equal to the wage rate and solve for L. Since the production function is Cobb-Douglas, the manager knows that MPL = bKa Lb -1. Recalling that x½ is mathematically equivalent to ?x, and observing that a = ½, b = ½, K= 1, and MPL = .5L(½) – 1, so that MPL = .5L-(½) , and MPL = .5/L(½). Since P = \$60, we know that VMPL = P × MPL = \$60 x (.5L-(½) = \$30/(?L). Setting \$30/(?L) equal to the wage, we get \$30/(?L) = \$10. If we square both sides of this equation, we get 900/L = \$100. Thus the profit-maximizing quantity of labor, in this example, is L = 900/100 = 9 units.
In addition to the production function, certain other tools illustrate how alternative inputs can be used to produce a single level of output using cost-minimizing combinations of inputs. As mentioned previously, in physical terms, an isoquant defines the combinations of inputs that yield a single level of output. In financial terms, similarly, an isocost curve isolates combinations of inputs that yield a single level of output at a fixed cost. For given input prices, isocost curves farther from the origin are associated with higher costs, just as isoquants farther from the origin are associated with higher levels of output. Changes in input prices change the slopes of isocost lines; the slope of the isocost curve is defined by the relative cost of the two inputs, similar to the way in which the slope of an isoquant is determined by MRTSKL. To minimize costs, a manager chooses a level of output where ratio of the marginal product per dollar spent on an input is exactly equal to its cost, for all inputs. Equivalently, a manager should employ inputs such that the marginal rate of technical substitution equals the ratio of input prices:
MP  =     w
MP          r
In sum, a conceptual understanding of these principles aids a manager in selecting and procuring inputs, and employing them at a level and with an intensity that equalizes the ratio of their relative physical contributions to the production process, to their relative costs. You will have an opportunity to investigate each of these concepts in more depth in your reading materials and in the context of this module’s associated discussion, homework activity, and optional readings.
Now you have an opportunity to apply the concepts of production and organization in the accompanying case study discussion.

ASSIGNMENT:

# M3D1: Boeing and a Most Important Input

When preparing for your discussion post on this case, it is recommend you read through it several times.

• Read through it the first time to familiarize yourself with the case.
• On the second read, consider your assigned role in the situation, and let that guide your perspective. Look deeper at the details: facts, problems, organizational goals, objectives, policies, strategies.
• Next, consider the concepts, theories, tools and research you need to use to address the issues presented.
• Then, complete any research, analysis, calculations, or graphing to support your decisions and make recommendations.

The commercial airline industry is extremely competitive. Market liberalization in Europe and Asia has enabled low-cost airlines to gain significant market shares, placing downward pressure on airfares. American air carriers face aggressive foreign competitors which offer competitive products and have access to most of the same customers and suppliers. With government support, Airbus has historically invested heavily to create a family of products to compete with American offerings. Regional jet makers Embraer and Bombardier, coming from the less than 100-seat commercial jet market, continue to develop larger and more capable airplanes. Competitors from Russia, China, and Japan are developing commercially viable jets. Many of these competitors have historically enjoyed access to government-provided financial support that reduces commercial risks associated with airplane development activities and enables airplanes to be brought to market more quickly than otherwise possible, resulting in intense pressures on pricing and other competitive factors. While productivity gains boosted profit margins, Boeing took more aggressive measures. Boeing operates facilities in the Puget Sound region. It also maintains operations in Oregon, Utah, California, and Florida. In 2013, Boeing announced the transfer of some 4,300 engineering jobs to California, Alabama, Missouri, and South Carolina. A long-negotiated agreement between Boeing and certain of its skilled employees facilitated Boeing’s move across state lines by incorporating provisions to help members affected by Boeing’s move. In return, Boeing reduced pension commitments to new employees. The Society of Professional Engineering Employees in Aerospace (SPEEA) was the last major employee group to retain a traditional pension; however, SPEEA agreed to switch new hires from the traditional pension to a defined-contribution plan, but retained the current pension for existing employees.