Production Economics
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Production decisions determine the types and
amounts of inputs— such as land, labor, raw and
processed
materials,
factories,
machinery,
equipment, and managerial talent—to be used in the
production of a desired quantity of output.
The production manager’s objective is to minimize
cost for a given output or, in other circumstances, to
maximize output for a given input budget.
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The Production Function
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A mathematical model, schedule (table), or graph
that relates the maximum feasible quantity of
output that can be produced from given amounts of
various inputs.
A change in technology, such as the introduction of
more automated equipment or the substitution of
skilled for unskilled workers, results in a new
production function.
Inputs - A resource or factor of production, such as a
raw material, labor skill, or piece of equipment that
is employed in a production process.
Cobb-douglas production function - A particular type
of mathematical model, known as a multiplicative
exponential function, used to represent the
relationship between the inputs and the output.
o Shows you how much output you can get for
different combination of two inputs (e.g.,
labor and capital)
The planning horizon is the amount of time an
organization will look into the future when preparing
a strategic plan; is the length of time an individual
plan ahead.
Long run - the period of time in which all the
resources employed in a production process can be
varied.
In the short run, because some of the inputs are
fixed, only a subset of the total possible input
combinations is available to the firm. By contrast, in
the long run, all possible input combinations are
available (i.e., you already have plenty of choices)
PRODUCTION FUNCTIONS WITH ONE VARIABLE INPUT
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Law of Variable proportions - “If a producer
increases the units of a variable factor while keeping
other factors fixed, then initially the total product
increases at an increasing rate, then it increases at a
diminishing rate, and finally starts declining.”
the law of variable proportions (LVP) consists of
three laws, those of increasing, diminishing and
constant returns.
Marginal and Average Product Functions
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Marginal product - The incremental change in total
output that can be obtained from the use of one
more unit of an input in the production process
(while holding constant all other inputs).
Average product - The ratio of total output to the
amount of the variable input used in producing the
output; Output/Input
The Law of Diminishing Marginal Returns
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Fixed and Variable Inputs
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A fixed input is defined as one required in the
production process but whose quantity employed in
the process is constant over a given period of time
regardless of the quantity of output produced. (rent)
The costs of a fixed input must be incurred regardless
of whether the production process is operated at a
high or a low rate of output.
A variable input is defined as one whose quantity
employed in the process changes, depending on the
desired quantity of output to be produced.
Short run - The period of time in which one (or more)
of the resources employed in a production process is
fixed or incapable of being varied.
To increase output, then, the firm must employ more
of the variable input(s) with the given quantity of
fixed input(s).
Specialization – when you hire 2 workers and they
split up the work so then they can specialize
something.
Benefit of specialization – higher marginal product.
In lengthening the planning horizon, a point is
eventually reached where all inputs are variable. This
period of time is called the long run.
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A point is eventually reached, however, where the
marginal increase in output for each worker added
to the crew begins to decline.
As you add variable resources to fixed resources the
ADDITIONAL OUTPUT will eventually decrease.
3 STAGES
o Specialization – increasing marginal product
o Product is increasing but at a decreasing
rate; output increasing but marginal product
decreasing
o Marginal product negative
Example: too much of anything may cause harm
eventually; task to do the visual aid;
Increasing Returns w/ Network Effects
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Network effects - An exception to the law of
diminishing marginal returns that occurs when the
installed base of a network product makes the
efforts to acquire new customers increasingly more
productive.
a phenomenon whereby increased numbers of
people or participants improve the value of a good
or service.
The more people are using the more valuable your
product is gonna get.
Example: FACEBOOK
The more people there is the more people you can
connect w/ makes it more valuable.
Congestion – when too much people slows down the
network.
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The greater the installed base of a network product,
such as Microsoft Office and Outlook, the larger the
number of compatible network connections and
therefore the more possible value for a new
customer. Consequently, as the software’s installed
base increases, Microsoft’s promotions and other
selling efforts to acquire new customers become
increasingly more productive.
Producing Information Services under Increasing
Returns
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It is insightful to compare the production economics
of old-economy companies that produce things to
new-economy companies that produce information.
Things, when sold, the seller ceases to own.
Information, when sold, the seller can sell again (at
least until information spillovers overwhelm the
target market).
Things must be replicated through expensive
manufacturing processes, whereas information is
replicable at almost zero incremental cost.
Things exist in one location. Information can exist
simultaneously in many locations.
The production and marketing of things are subject
to eventually diminishing returns. The marketing
(and maybe the production) of information is subject
to increasing returns.
That is, the more people who use my information,
the more likely it is that another person will want to
acquire it (for any given marketing cost), or, said
another way, the cheaper it is to secure another sale.
Production Functions w/ Multiple Variable Inputs
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The Marginal Rate of Technical Substitution
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The Relationship between Total, Marginal, and Average
Product
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Optimal input level - MRPL = MFCL
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With one of the inputs (K) fixed in the short run, the
producer must determine the optimal quantity of the
variable input (L) to employ in the production process.
Such a determination requires the introduction into the
analysis of output prices and labor costs. Therefore, the
analysis begins by defining marginal revenue product and
marginal factor cost.
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Marginal revenue product - The amount that an
additional unit of the variable production input adds
to total revenue. Also known as marginal value
added.
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In addition to indicating the quantity of output that
can be produced with any of the various input
combinations that lie on the isoquant curve, the
isoquant also indicates the rate at which one input
may be substituted for another input in producing the
given quantity of output.
Marginal rate of technical substitution (MRTS) - The
rate at which one input may be substituted for
another input in producing a given quantity of
output.
While the marginal rate of substitution tells us the
rate at which a consumer is willing to replace one
product with another, the marginal rate of technical
substitution tells us the rate at which a producer is
willing to switch one input.
DETERMINING THE OPTIMAL COMBINATION OF INPUTS
Marginal product = change output/changed input
Average product = total product/total labor
Average product is the average cost per unit
produced per set of resources
Marginal product is the cost for the very next unit to
be produced in resources
MP is increases (dec) the AP increases (dec).
DETERMINING THE OPTIMAL USE OF THE VARIABLE
INPUT
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Production isoquant - An algebraic function or a
geometric curve representing all the various
combinations of two inputs that can be used in
producing a given level of output.
Production isoquant shows all the alternative ways in
which the number of workers and various sizes of
mining equipment can be combined to produce any
desired level of output.
Choices are normally limited for two reasons: first,
some input combinations employ an excessive
quantity of one input; second, input substitution
choices are also limited by the technology of
production, which often involves machinery that is
not divisible.
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The firm needs to determine which combination will
minimize the total costs for producing the desired
output.
Isocost lines - a curve which shows various
combinations of inputs that cost the same total
amount; gives PERFECT SUBSTITUTES.
A perfect substitute can be used in exactly the same
way as the good or service it replaces.
Right angle curve = perfect complements;
production will only increase if both inputs are
increased in the same proportion.
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The total cost of each possible input combination
is a function of the market prices of these inputs.
Assuming that the inputs are supplied in perfectly
elastic fashion in competitive markets, the perunit price of each input will be constant,
regardless of the amount of the input that is
purchased.
Marginal revenue (MR) is the increase in revenue that results from
the sale of one additional unit of output.
Marginal factor cost - The amount that an additional
unit of the variable input adds to total cost.
Perfect competition is an ideal type of market structure where
all producers and consumers have full and symmetric
information, no transaction costs, where there are a large
number of producers and consumers competing with one
another.
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Once the isoquants and isocosts are specified, it is
possible to solve for the optimum combination of
inputs.
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The production decision problem can be formulated
in two different ways, depending on the manner in
which the production objective or goal is stated. One
can solve for the combination of inputs that either:
 Minimizes total cost subject to a given
constraint on output
 Maximizes output subject to a given total
cost constraint
Measuring the Efficiency of a Production Process
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Minimizing Cost subject to an Output Constraint
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Output constraint – output limitation
They occur when competitors agree to prevent,
restrict or limit the volume or type of particular
goods or services available.
The total cost of producing the required output is
minimized by finding the input combinations within
this region that lie on the lowest cost isocost line.
Equimarginal criterion = marginal product per
variable input is equal; marginal product of variable
unit per dollar is equal.
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Linear programming techniques are available to
determine the least-cost process for fixed
proportions production.
feasible region is the set of all possible points (sets
of values of the choice variables) of an optimization
problem that satisfy the problem's constraints,
potentially including inequalities, equalities, and
integer constraints.
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Three possible relationships that can exist between
the increase in inputs and the increase in outputs are
as follows:
o Increasing returns to scale: Output increases
by more than λ; that is, Q(2) > λQ(1).
o Decreasing returns to scale: Output
increases by less than λ; that is, Q(2) < λQ(1).
o Constant returns to scale: Output increases
by exactly λ; that is, Q(2) = λQ(1).
o λ equals factor increase.
Production process - A fixed-proportions production
relationship; inputs are combined in fixed proportion
to obtain the output.
Operating multiple production processes can offer a
firm flexibility in dealing with unusual orders,
interruptions in the availability of resources, or
binding resource constraints.
The isoquants of a production function with fixed
proportions are L-shaped.
Implies that fixed factors of production such as land,
labor, raw materials are used to produce a fixed
quantity of an output and these production factors
cannot be substituted for the other factors.
However, not all fixed-proportions production
processes are equally efficient. The firm will prefer to
use one or two production processes exclusively if
they offer the advantage of substantial cost savings.
One major argument given for initially increasing
returns is the opportunity for specialization in the
use of capital and labor.
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Production Process and Process Rays
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Returns to scale - the proportionate increase in
output that results from a given proportionate
increase in all the inputs employed in the production
process.
Increasing and Decreasing Returns to Scale
A Fixed Proportions Optimal Production Process
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Returns to Scale
Measuring returns to scale
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Allocative efficiency - A measure of how closely
production achieves the least-cost input mix or
process, given the desired level of output.
Technical efficiency - A measure of how closely
production achieves maximum potential output
given the input mix or process.
Overall production efficiency - A measure of
technical and allocative efficiency; is defined as the
product of technical, scale, and allocative efficiency.
Scale efficiency - the ability of each company
to. operate as close to its most productive scale size
as possible.
Equipment that is more efficient in performing a
limited set of tasks can be substituted for less
efficient all-purpose equipment. Similarly, the
efficiency of workers in performing a small
number of related tasks is greater than that of
less highly skilled, but more versatile, workers.
Decreasing returns to scale thereafter often arises
from the increasingly complex problems of
coordination and control faced by management as
the scale of production is increased.
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For example, managers may be limited in their
ability to transmit and receive status reports over
a wider and wider span of control.
Cobb-Douglas Production Function
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If β1 + β2 is less than, equal to, or greater than 1, the
Cobb-Douglas production function will exhibit
decreasing, constant, or increasing returns,
respectively.
Empirical studies of the Cobb-Douglas Production
Function
SUMMARY
 A production function is a schedule, graph, or
mathematical model relating the maximum quantity
of output that can be produced from various
quantities of inputs.
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For a production function with one variable input,
the marginal product is defined as the incremental
change in total output that can be produced by the
use of one more unit of the variable input in the
production process.
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For a production function with one variable input,
the average product is defined as the ratio of total
output to the amount of the variable input used in
producing the output; QUANTITY PER V-INPUT.
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The law of diminishing marginal returns states that,
with all other productive factors held constant, the
use of increasing amounts of the variable factor in
the production process beyond some point will result
in diminishing marginal increases in total output.
Increasing returns can arise with network effects
especially involving information economy goods and
industry standards.
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In the short run, with one of the productive factors
fixed, the optimal output level (and optimal level of
the variable input) occurs where marginal revenue
product equals marginal factor cost.
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Marginal revenue product is defined as the amount
that an additional unit of the variable input adds to
total revenue. Marginal factor cost is defined as the
amount that an additional unit of the variable input
adds to total cost.
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A production isoquant is either a geometric curve or
algebraic function representing all the various
combinations of inputs that can be used in producing
a given level of output.
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The marginal rate of technical substitution is the
rate at which one input may be substituted for
another input in the production process, while total
output remains constant. It is equal to the ratio of the
marginal products of the two inputs.
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In the long run, with both inputs being variable,
minimizing cost subject to an output constraint (or
maximizing output subject to a cost constraint)
requires that the production process be operated at
the point where the marginal product per dollar input
cost of each factor is equal (EQUIMARGINAL
CRITERION).
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The degree of technical efficiency of a production
process is the ratio of observed output to the
maximum potentially feasible output for that
process, given the same inputs.
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The degree of allocative efficiency of a production
process is the ratio of total cost for producing a given
output level with the least-cost process to the
observed total cost of producing that output.
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Physical returns to scale is defined as the
proportionate increase in the output of a production
process that results from a given proportionate
increase in all the inputs.
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The Cobb-Douglas production function, which is
used extensively in empirical studies, is a
multiplicative exponential function in which output
is a (nonlinear) increasing function of each of the
inputs, with the sum of the exponential parameters
indicating the returns to scale.