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Utilizing the attached PDF, answer the following questions that are included in the PDF:Work the following problems in Chapter 5: Technical questions 1, 2, 3, 4, 5, and 6.Work the following problems in Chapter 6: Technical questions 1, 2, 3, 4, and 8.Work the following problems in Chapter 5: Application questions 1, 2, and 3.Work the following problems in Chapter 6: Application questions 1, 2, 3, 4 and 5.
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5
Production and Cost Analysis
in the Short Run
I
n this chapter, we analyze production and cost, the fundamental building blocks on the supply side of the market. Just as consumer behavior
forms the basis for demand curves, producer behavior lies behind the supply curve. The prices of the inputs of production and the state of tech-
nology are two factors held constant when defining a market supply curve.
Production processes (or “production functions,” as economists call them)
and the corresponding cost functions, which show how costs vary with the
level of output produced, are also very important when we analyze the behavior and strategy of individual firms and industries.
We begin this chapter with a case that discusses efficiency and costs in
the fast-food industry. Next we discuss short-run versus long-run production
and costs and present a model of a short-run production function. We also
examine economic data on the differences in productivity among firms and
industries. We then present a model of short-run cost functions and discuss
evidence on the shapes of these cost functions. We also distinguish between
the types of costs measured by accountants and the cost concepts used by
economists.
144
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Case for Analysis
Production and Cost Analysis in the Fast-Food Industry
The fast-food industry in the United States has typically used
drive-through windows to increase profitability. With 65 percent of fast-food revenue derived from drive-through windows, these windows have become the focal point for market
share competition among fast-food outlets such as Wendy’s,
McDonald’s, Burger King, Arby’s, and Taco Bell. Even chains
that did not use drive-through windows in the past, such as
Starbucks and Dunkin’ Donuts, have added them to their
stores.1
Production technology changes have included the use
of separate kitchens for the drive-through window, timers
to monitor the seconds it takes a customer to move from the
menu board to the pickup window, kitchen redesign to minimize unnecessary movement, and scanners that send customers a monthly bill rather than having them pay at each visit.
Now, in an attempt to cut costs and increase speed even further, McDonald’s franchises have tested remote order-taking.2
It takes an average of 10 seconds for a new car to pull up to
a drive-through menu after one car has moved forward. With
a remote call center, an order-taker can answer a call from a
different McDonald’s where another customer has already
pulled up. Thus, a call center worker in California may take
orders from Honolulu, Gulfport, Miss., and Gillette, Wyo. This
means that during peak periods, a worker can take up to 95
orders per hour. The trade-offs with this increased speed at
the drive-through window are employee dissatisfaction with
constant monitoring and the stress of the process, decreases in
accuracy in filling orders, and possible breakdowns in communication over long distances. However, this technology may be
expanded to allow stores, such as Home Depot, to equip carts
with speakers that customers could use to wirelessly contact a
call center for shopping assistance.
In Asia and other parts of the world where crowded cities and high real estate costs limit the construction of
1
Jennifer Ordonez, “An Efficiency Drive: Fast-Food Lanes,
Equipped with Timers, Get Even Faster,” Wall Street Journal,
May 18, 2000.
2
Matt Richtel, “The Long-Distance Journey of a Fast-Food
Order,” The New York Times (Online), April 11, 2006.
drive-throughs, McDonald’s and KFC have added motorbike
delivery as part of their growth strategy.3 Fifteen hundred of
the 8,800 restaurants in McDonald’s Asia/Pacific, Middle
East, and Africa division offer delivery, while half of the new
restaurants KFC builds in China each year will offer delivery. The delivery option requires an area in the restaurant to
assemble orders that are placed in battery-powered induction
heating boxes. Along with cold items in insulated containers, all of the orders are placed on the back of yellow and red
McDonald’s branded motorbikes or electric scooters. Most
McDonald’s delivery orders are phoned in, but the company
has started offering Internet-based ordering in Singapore and
Turkey. The number of call centers may be reduced in the
future as online ordering increases. Neither McDonald’s nor
KFC plan to use this technology in the United States, where
McDonald’s derives two-thirds of its sales from drive-through
customers.
This case illustrates how firms can use production technology to influence their costs, revenues, and profits. Because
firms in more competitive markets may not have much ability to influence the prices of their products, they may depend
more on strategies to increase the number of customers and
lower the costs of production. These strategies may involve
changing the underlying production technology, lowering
the prices paid for the inputs used, and changing the scale of
operation.
To analyze these issues, we’ll first discuss the nature of
a firm’s production process and the types of decisions that
managers make regarding production. We’ll then show how a
firm’s costs of production are related to the underlying production technology. Because the time frame affects a manager’s decisions about production and cost, we distinguish
between the short run and the long run and discuss the implications of these time frames for managerial decision making.
This chapter focuses on short-run production and cost decisions, while we analyze production and cost in the long run
later (Chapter 6).
3
Julie Jargon, “Asia Delivers for McDonald’s,” Wall Street
Journal (Online), December 13, 2011.
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PART 1 Microeconomic Analysis
Defining the Production Function
To analyze a firm’s production process, we first define a production function and
distinguish between fixed and variable inputs and the short run versus the long run.
The Production Function
Production function
The relationship between a flow
of inputs and the resulting flow of
outputs in a production process
during a given period of time.
A production function describes the relationship between a flow of inputs and
the resulting flow of outputs in a production process during a given period of time.
The production function describes the physical relationship between the inputs
or factors of production and the resulting outputs of the production process. It is
essentially an engineering concept, as it incorporates all of the technology or knowledge involved with the production process. The production function illustrates how
inputs are combined to produce different levels of output and how different combinations of inputs may be used to produce any given level of output. It shows the
maximum amount of output that can be produced with different combinations of
inputs. This concept rules out any situations where inputs are redundant or wasted
in production. The production function forms the basis for the economic decisions
facing a firm regarding the choice of inputs and the level of outputs to produce.4
A production function can be expressed with the notation in Equation 5.1:
5.1
Q = f(L, K, M c)
where
Q = quantity of output
L = quantity of labor input
K = quantity of capital input
M = quantity of materials input
Fixed input
An input whose quantity a manager
cannot change during a given
period of time.
Variable input
An input whose quantity a manager
can change during a given period
of time.
As with demand relationships, Equation 5.1 is read “quantity of output is a function
of the inputs listed inside the parentheses.” The ellipsis in Equation 5.1 indicates that
more inputs may be involved with a given production function. There may also be
different types of labor and capital inputs, which we could denote by LA, LB, LC and
KA, KB, and KC, respectively. Note that in a production function, capital (K) refers to
physical capital, such as machines and buildings, not financial capital. The monetary
or cost side of the production process (i.e., the financial capital needed to pay for
workers and machines) is reflected in the functions that show how costs of production vary with different levels of output, which we’ll derive later in the chapter.
A production function is defined in a very general sense and can apply to largescale production processes, such as the fast-food outlets in this chapter’s opening
case analysis, or to small firms comprising only a few employees. The production
function can also be applied to different sectors of the economy, including both
goods and services. In this chapter, we use very simple production functions to
illustrate the underlying theoretical concepts, while the examples focus on more
complex, real-world production processes.
Fixed Inputs Versus Variable Inputs
Managers use both fixed inputs and variable inputs in a production function. A fixed
input is one whose quantity a manager cannot change during a given time period,
while a variable input is one whose quantity a manager can change during a given
4
The production function incorporates engineering knowledge about production technology and how
inputs can be combined to produce the firm’s output. Managers must make economic decisions about what
combination of inputs and level of output are best for the firm.
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CHAPTER 5 Production and Cost Analysis in the Short Run
147
time period. A factory, a given amount of office space, and a plot of land are fixed
inputs in a production function. Automobiles or CD players can be produced in the
factory, accounting services can be undertaken in the office, and crops can be grown
on the land. However, once a manager decides on the size of the factory, the amount
of office space, or the acreage of land, it is difficult, if not impossible, to change
these inputs in a relatively short time period. The amount of automobiles, CD players, accounting services, or crops produced is a function of the manager’s use of the
variable inputs in combination with these fixed inputs. Automobile workers, steel
and plastic, accountants, farm workers, seed, and fertilizer are all variable inputs
in these production processes. The amount of output produced varies as managers
make decisions regarding the quantities of these variable inputs to use, while holding constant the underlying size of the factory, office space, or plot of land.
Short-Run Versus Long-Run Production Functions
Two dimensions of time are used to describe production functions: the short run and
the long run. These categories do not refer to specific calendar periods of time, such
as a month or a year; they are defined in terms of the use of fixed and variable inputs.
A short-run production function involves the use of at least one fixed input. At
any given point in time, managers operate in the short run because there is always
at least one fixed input in the production process. Managers and administrators
decide to produce beer in a brewery of a given size or educate students in a school
with a certain number of square feet. The size of the factory or school is fixed in the
short run either because the managers have entered into a contractual obligation,
such as a rental agreement, or because it would be extremely costly to change the
amount of that input during the time period.
In a long-run production function, all inputs are variable. There are no fixed
inputs because the quantity of all inputs can be changed. In the long run, managers
can choose to produce cars in larger automobile plants, and administrators can
construct new schools and abandon existing buildings. Farmers can increase or
decrease their acreage in another planting season, depending on this year’s crop
conditions and forecasts for the future. Thus, the calendar lengths of the short run
and the long run depend on the particular production process, contractual agreements, and the time needed for input adjustment.
Short-run production
function
A production process that uses at
least one fixed input.
Long-run production
function
A production process in which all
inputs are variable.
Managerial Rule of Thumb
Short-Run Production and Long-Run Planning
Managers always operate in the short run, but they must also have a long-run planning horizon.
Managers need to be aware that the current amount of fixed inputs, such as the size of a factory or
amount of office space, may not be appropriate as market conditions change. Thus, there are more
economic decisions for managers in the long run because all inputs can be changed in that time frame
and inputs can be substituted for each other. ■
Productivity and the Fast-Food Industry
The fast-food case that opened this chapter gave a good illustration of the differences between short- and long-run production functions. With a given technology and fixed inputs, as employees at the drive-through windows work faster to
reduce turnaround time for a drive-through customer, the quality of the service
begins to decline, and worker frustration and dissatisfaction increase. This situation represents the increased use of variable inputs relative to the fixed inputs in
the short run. The management response to these problems has been to implement
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PART 1 Microeconomic Analysis
new technologies for the production process: placing an intercom at the end of the
drive-through line to correct mistakes in orders; finding better ways for employees
to perform multiple tasks in terms of kitchen arrangement; and, most recently, outsourcing the drive-through calls to remote call centers or offering delivery in certain
countries. This situation represents the long run, in which all inputs can be changed.
Model of a Short-Run Production Function
In this section, we discuss the basic economic principles inherent in a short-run
production function, illustrated in the fast-food example. To do so, we need to
define three measures of productivity, or the relationship between inputs and output: total product, average product, and marginal product. We then examine how
each measure changes as the level of the variable input changes.
Total Product
Total product
The total quantity of output
produced with given quantities of
fixed and variable inputs.
Total product is the total quantity of output produced with given quantities of
fixed and variable inputs.5 To illustrate this concept, we use a very simple production function with one fixed input, capital (K ), and one variable input, labor (L).
This production function is illustrated in Equation 5.2.
5.2
TP or Q = f(L, K )
where
TP or Q = total product or total quantity of output produced
L = quantity of labor input (variable)
K = quantity of capital input (fixed)
Equation 5.2 presents the simplest type of short-run production function. It has
only two inputs: one fixed (K )and one variable (L). The bar over the K denotes the
fixed input. In this production function, the amount of output (Q) or total product
(TP) is directly related to the amount of the variable input (L), while holding constant the level of the fixed input (K ) and the technology embodied in the production function.
Average Product and Marginal Product
Average product
The amount of output per unit of
variable input.
Marginal product
To analyze the production process, we need to define two other productivity measures: average product and marginal product. The average product is the amount
of output per unit of variable input, and the marginal product is the additional
output produced with an additional unit of variable input. These relationships are
shown in Equations 5.3 and 5.4.
The additional output produced
with an additional unit of variable
input.
5.3
AP = TP/L or Q/L
where
AP = average product of labor
5.4
MP = ∆TP/∆L = ∆Q/∆L
where
MP = marginal product of labor
5
This variable is sometimes called total physical product to emphasize the fact that the production function
shows the physical relationship between inputs and outputs. We use total product for simplicity.
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CHAPTER 5 Production and Cost Analysis in the Short Run
149
TABLE 5.1 A Simple Production Functiona
QUANTITY OF QUANTITY OF
TOTAL
AVERAGE
CAPITAL (K)
LABOR (L)
PRODUCT (TP) PRODUCT (AP)
(1)
(2)
(3)
(4)
MARGINAL PRODUCT
(MP) (ΔTP/ΔL)
(5)
MARGINAL PRODUCT
(MP) (dTP/dL)
(6)
10
1
14
14.0
14
18
10
2
35
17.5
21
24
10
3
62
20.7
27
28
10
4
91
22.8
29
30
10
4.5
106
23.6
30
30.25
10
5
121
24.2
30
30
10
6
150
25.0
29
28
10
6.75
170
25.1875
26.67
25.1875
10
7
175
25.0
25
24
10
8
197
24.6
22
18
10
9
212
23.6
15
10
10
10
217
21.7
5
0
10
11
211
19.2
–6
–12
a
In this example, the underlying equations showing total, average, and marginal products as a function of the amount of labor, L (with the level of capital assumed
constant), are
TP = 10L + 4.5L2 − 0.3333L3
AP = 10 + 4.5L − 0.3333L2
MP = dTP/dL = 10 + 9L − 1.0L2
Table 5.1 presents a numerical example of a simple production function based
on the underlying equations shown in the table. Marginal product in Table 5.1 can
be calculated either for discrete changes in labor input (Column 5) or for infinitesimal changes in labor input using the specific marginal product equation in the
table (Column 6). Column 5 shows the marginal product between units of input
(Column 2), whereas Column 6 shows the marginal product calculated precisely
at a given unit of input. Column 6 gives the exact mathematical relationships discussed below.
Relationships Among Total, Average,
and Marginal Product
Let’s examine how the total, average, and marginal product change as we increase
the amount of the variable input, labor, in this short-run production function,
holding constant the amount of capital and the level of technology. We can see
in Table 5.1 that the total product or total amount of output (Column 3) increases
rapidly up to 4.5 units of labor. This result means that the marginal product, or the
additional output produced with an additional unit of labor (Column 6), is increasing over this range of production. Between 4.5 and 10 units of labor, the total product (Column 3) is increasing, but the rate of increase, or the marginal product, is
becoming smaller (Columns 5 and 6). Total product reaches its maximum amount
of 217 units when 10 units of labor are used, but total product decreases if 11 units
of labor are employed. The marginal product of labor is 5 as labor is increased from
9 to 10 units and –6 as labor is increased from 10 to 11 units (Column 5). Therefore,
the marginal product is zero when the total product is precisely at its maximum
value of 217 units (Column 6).
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PART 1 Microeconomic Analysis
The average product of labor, or output per unit of input (Column 4), also
increases in value as more units of labor are employed. It reaches a maximum
value with 6.75 units of labor and then decreases as more labor is used in the
production process. As you can see in Table 5.1, when the marginal product of
labor is greater than the average product of labor (up to 6.75 units of labor), the
average product value increases from 14 to 25.1875 units of output per input.
When more units of labor are employed, the marginal product becomes less than
the average product, and the average product decreases in value. Therefore, the
marginal product must equal the average product when the average product is at
its maximum value.6
Figures 5.1a and 5.1b show the typical shapes for graphs of the total, average, and
marginal product curves. These graphs illustrate the relationships in Table 5.1, but
are drawn more generally …
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