1. Isoquant
From Wikipedia, the free encyclopedia
In economics, an isoquant (derived from quantity and the Greek word iso,
meaning equal) is a contour line drawn through the set of points at which the
same quantity of output is produced while changing the quantities of two or
more inputs.[1][2] While an indifference curve mapping helps to solve the
utility-maximizing problem of consumers, the isoquant mapping deals with
the cost-minimization problem of producers. Isoquants are typically drawn
on capital-labor graphs, showing the technological tradeoff between capital
and labor in the production function, and the decreasing marginal returns of
both inputs. Adding one input while holding the other constant eventually
leads to decreasing marginal output, and this is reflected in the shape of the
isoquant. A family of isoquants can be represented by an isoquant map, a
graph combining a number of isoquants, each representing a different
quantity of output. Isoquants are also called equal product curves.
An isoquant shows the extent to which the firm in question has the ability to
substitute between the two different inputs at will in order to produce the
same level of output. An isoquant map can also indicate decreasing or
increasing returns to scale based on increasing or decreasing distances
between the isoquant pairs of fixed output increment, as output increases. If
the distance between those isoquants increases as output increases, the firm's
production function is exhibiting decreasing returns to scale; doubling both
inputs will result in placement on an isoquant with less than double the output
of the previous isoquant. Conversely, if the distance is decreasing as output
increases, the firm is experiencing increasing returns to scale; doubling both
inputs results in placement on an isoquant with more than twice the output of
the original isoquant.

2. As with indifference curves, two isoquants can never cross. Also, every
possible combination of inputs is on an isoquant. Finally, any combination of
inputs above or to the right of an isoquant results in more output than any
point on the isoquant. Although the marginal product of an input decreases as
you increase the quantity of the input while holding all other inputs constant,
the marginal product is never negative in the empirically observed range since
a rational firm would never increase an input to decrease output.
Shapes of Isoquants
If the two inputs are perfect substitutes, the resulting isoquant map generated
is represented in fig. A; with a given level of production Q3, input X can be
replaced by input Y at an unchanging rate. The perfect substitute inputs do not
experience decreasing marginal rates of return when they are substituted for
each other in the production function.
If the two inputs are perfect complements, the isoquant map takes the form of
fig. B; with a level of production Q3, input X and input Y can only be combined
efficiently in the certain ratio occurring at the kink in the isoquant. The firm
will combine the two inputs in the required ratio to maximize profit.
Isoquants are typically combined with isocost lines in order to solve a cost-
minimization problem for given level of output. In the typical case shown in
the top figure, with smoothly curved isoquants, a firm with fixed unit costs of
the inputs will have isocost curves that are linear and downward sloped; any
point of tangency between an isoquant and an isocost curve represents the
cost-minimizing input combination for producing the output level associated
with that isoquant.
The only relevent portion of the iso quant is the one that is convex to the
origin, part of the curve which is not convex to the origin implies negative
marginal product for factors of production. Higher ISO-Quant higher the
production

3. Economies of scale
Economies of scale, inmicroeconomics, refers to the cost advantages that a
business obtains due to expansion. There are factors that cause a producer’s
average cost per unit to fall as the scale of output is increased. "Economies of
scale" is a long run concept and refers to reductions in unit cost as the size of a
facility and the usage levels of other inputs increase.[1] Diseconomies of
scale are the opposite. The common sources of economies of scale
are purchasing (bulk buying of materials through long-term contracts),
managerial (increasing the specialization of managers), financial (obtaining
lower-interest charges when borrowing from banks and having access to a
greater range of financial instruments), marketing (spreading the cost of
advertising over a greater range of output in media markets), and
technological (taking advantage of returns to scale in the production function).
Each of these factors reduces the long run average costs (LRAC) of production
by shifting theshort-run average total cost (SRATC) curve down and to the
right. Economies of scale are also derived partially from learning by doing.
Economies of scale is a practical concept that is important for explaining real
world phenomena such as patterns of international trade, the number of firms
in a market, and how firms get "too big to fail". The exploitation of economies
of scale helps explain why companies grow large in some industries. It is also a
justification for free trade policies, since some economies of scale may require
a larger market than is possible within a particular country — for example, it
would not be efficient for Liechtenstein to have its own car maker, if they
would only sell to their local market. A lone car maker may be profitable,

4. however, if they export cars to global markets in addition to selling to the local
market. Economies of scale also play a role in a "natural monopoly."
Natural monopoly
A natural monopoly is often defined as a firm which enjoys economies of scale
for all reasonable firm sizes; because it is always more efficient for one firm to
expand than for new firms to be established, the natural monopoly has no
competition. Because it has no competition, it is likely the monopoly has
significant market power. Hence, some industries that have been claimed to
be characterized by natural monopoly have been regulated or publicly-owned.
Economies of scale and returns to scale
Economies of scale is related to and can easily be confused with the theoretical
economic notion of returns to scale. Where economies of scale refer to a firm's
costs, returns to scale describe the relationship between inputs and outputs in
a long-run (all inputs variable) production function. A production function
hasconstant returns to scale if increasing all inputs by some proportion results
in output increasing by that same proportion. Returns are decreasing if, say,
doubling inputs results in less than double the output, and increasing if more
than double the output. If a mathematical function is used to represent the
production function, and if that production function is homogeneous, returns
to scale are represented by the degree of homogeneity of the function.
Homegeneous production functions with constant returns to scale are first
degree homogeneous, increasing returns to scale are represented by degrees of
homogeneity greater than one, and decreasing returns to scale by degrees of
homogeneity less than one.
If the firm is a perfect competitor in all input markets, and thus the per-unit
prices of all its inputs are unaffected by how much of the inputs the firm
purchases, then it can be shown[2][3][4] that at a particular level of output, the
firm has economies of scale if and only if it has increasing returns to scale, has
diseconomies of scale if and only if it has decreasing returns to scale, and has
neither economies nor diseconomies of scale if it has constant returns to scale.
In this case, with perfect competition in the output market the long-run
equilibrium will involve all firms operating at the minimum point of their
long-run average cost curves (i.e., at the borderline between economies and
diseconomies of scale).
If, however, the firm is not a perfect competitor in the input markets, then the
above conclusions are modified. For example, if there are increasing returns to

5. scale in some range of output levels, but the firm is so big in one or more input
markets that increasing its purchases of an input drives up the input's per-unit
cost, then the firm could have diseconomies of scale in that range of output
levels. Conversely, if the firm is able to get bulk discounts of an input, then it
could have economies of scale in some range of output levels even if it has
decreasing returns in production in that output range.
The literature assumed that due to the competitive nature of Reverse Auction,
and in order to compensate for lower prices and lower margins, suppliers seek
higher volumes to maintain or increase the total revenue. Buyers, in turn,
benefit from the lower transaction costs and economies of scale that result
from larger volumes. In part as a result, numerous studies have indicated that
the procurement volume must be sufficiently high to provide sufficient profits
to attract enough suppliers, and provide buyers with enough savings to cover
their additional costs[5].
However, surprisingly enough, Shalev and Asbjornsen found, in their research
based on 139 reverse auctions conducted in the public sector by public sector
buyers, that the higher auction volume, or economies of scale, did not lead to
better success of the auction!. They found that Auction volume did not
correlate with competition, nor with the number of bidder, suggesting that
auction volume does not promote additional competition. They noted,
however, that their data included a wide range of products, and the degree of
competition in each market varied significantly, and offer that further
research on this issue should be conducted to determine whether these
findings remain the same when purchasing the same product for both small
and high volumes. Keeping competitive factors constant, increasing auction
volume may further increase competition[6].
Diseconomy of scale

6. Diseconomies of scale are the forces that cause larger firms and
governments to produce goods andservices at increased per-unit costs. They
are less well known than whateconomists have long understood as "economies
of scale", the forces which enable larger firms to produce goods and services at
reduced per-unit costs.[citation needed]However the political philosophy of
conservatism has long recognized the concept when applied to government.
Causes
Some of the forces which cause a diseconomy of scale are listed below:
Cost of communication
Ideally, all employees of a firm would have one-on-one communication with
each other so they know exactly what the other workers are doing.[citation
needed] A firm with a single worker does not require any communication
between employees. A firm with two workers requires one communication
channel, directly between those two workers. A firm with three workers
requires three communication channels (between employees A & B, B & C,
and A & C). Here is a chart of one-on-one communication channels required:
The one-on-one channels of communication grow more rapidly than the
number of workers, thus increasing the time, and therefore costs, of
communication. At some point one-on-one communications between all
workers becomes impractical; therefore only certain groups of employees will
communicate with one another (salespeople with salespeople, production
workers with production workers, etc.). This reduced communication slows,
but doesn't stop, the increase in time and money with firm growth, but also
costs additional money, due to duplication of effort, owing to this reduced
level of communication.
Duplication of effort
A firm with only one employee can't have any duplication of effort between
employees. A firm with two employees could have duplication of efforts, but
this is improbable, as the two are likely to know what each other is working on

7. at all times. When firms grow to thousands of workers, it is inevitable that
someone, or even a team, will take on a project that is already being handled
by another person or team. General Motors, for example, developed two in-
house CAD/CAMsystems: CADANCE was designed by the GM Design Staff,
while Fisher Graphics was created by the former Fisher Body division. These
similar systems later needed to be combined into a single Corporate Graphics
System, CGS, at great expense. A smaller firm would neither have had the
money to allow such expensive parallel developments, or the lack of
communication and cooperation which precipitated this event. In addition to
CGS, GM also used CADAM, UNIGRAPHICS, CATIA and other off-the-shelf
CAD/CAM systems, thus increasing the cost of translating designs from one
system to another. This endeavor eventually became so unmanageable that
they acquired Electronic Data Systems (EDS) in an effort to control the
situation.
Office politics
"Office politics" is management behavior which a manager knows is counter to
the best interest of the company, but is in her/his personal best interest. For
example, a manager might intentionally promote an incompetent worker
knowing that that worker will never be able to compete for the manager's job.
This type of behavior only makes sense in a company with multiple levels of
management. The more levels there are, the more opportunity for this
behavior. At a small company, such behavior would likely cause the company
to go bankrupt, and thus cost the manager his job, so he would not make such
a decision. At a large company, one bad manager would not have much effect
on the overall health of the company, so such "office politics" are in the
interest of individual managers.
Isolation of decision makers from results of their decisions
If a single person makes and sells donuts and decides to try jalapeño flavoring,
they would likely know that day whether their decision was good or not, based
on the reaction of customers. A decision maker at a huge company that makes
donuts may not know for many months if such a decision worked out or not.

8. By that time they may very well have moved on to another division or
company and thus see no consequences from their decision. This lack of
consequences can lead to poor decisions and cause an upward sloping average
cost curve.
Slow response time
In a reverse example, the single worker donut firm will know immediately if
people begin to request healthier offerings, like whole grain bagels, and be
able to respond the next day. A large company would need to do research,
create an assembly line, determine which distribution chains to use, plan an
advertising campaign, etc., before any change could be made. By this time
smaller competitors may well have grabbed that market niche.
Inertia (unwillingness to change)
This will be defined as the "we've always done it that way, so there's no need to
ever change" attitude (see appeal to tradition). An old, successful company is
far more likely to have this attitude than a new, struggling one. While "change
for change's sake" is counter-productive, refusal to consider change, even
when indicated, is toxic to a company, as changes in the industry and market
conditions will inevitably demand changes in the firm, in order to remain
successful. A recent example is Polaroid Corporation's refusal to move into
digital imaging until after this lag adversely affected the company, ultimately
leading to bankruptcy.[citation needed]
Cannibalization
A small firm only competes with other firms, but larger firms frequently find
their own products are competing with each other. A Buick was just as likely to
steal customers from another GM make, such as an Oldsmobile, as it was to
steal customers from other companies. This may help to explain why
Oldsmobiles were discontinued after 2004. This self-competition wastes
resources that should be used to compete with other firms.

9. Large market portfolio
A small investment fund can potentially return a larger percentage because it
can concentrate its investments in a small number of good opportunities
without driving up the price of the investment securities.[1] Conversely, a large
investment fund like Fidelity Magellan must spread its investments among so
many securities that its results tend to track those of the market as a whole.[2]
Inelasticity of Supply
A company which is heavily dependent on its resource supply will have trouble
increasing production. For instance a timber company can not increase
production above the sustainable harvest rate of its land. Similarly service
companies are limited by available labor, STEM (Science Technology
Engineering and Mathematics professions) being the most cited example.
Public and government opposition
Such opposition is largely a function of the size of the firm. Behavior
fromMicrosoft, which would have been ignored from a smaller firm, was seen
as an anti-competitive and monopolistic threat, due to Microsoft's size, thus
bringing about public opposition and government lawsuits.
Solutions
Solutions to the diseconomy of scale for large firms involve changing the
company into one or more small firms. This can either happen by default
when the company, in bankruptcy, sells off its profitable divisions and shuts
down the rest, or can happen proactively, if the management is willing.
Returning to the example of the large donut firm, each retail location could be
allowed to operate relatively autonomously from the company headquarters,
with employee decisions (hiring, firing, promotions, wage scales, etc.) made by
local management, not dictated by the corporation. Purchasing decisions
could also be made independently, with each location allowed to choose its
own suppliers, which may or may not be owned by the corporation (wherever
they find the best quality and prices). Each locale would also have the option

10. of either choosing their own recipes and doing their own marketing, or they
may continue to rely on the corporation for those services. If the employees
own a portion of the local business, they will also have more invested in its
success. Note that all these changes will likely result in a substantial reduction
in corporate headquarters staff and other support staff. For this reason, many
businesses delay such a reorganization until it is too late to be effective.
Cobb-Douglas Production Function
1 Introduction
In economics, the Cobb-Douglas functional form of production
functions is widely used to represent the relationship
of an output to inputs. It was proposed by Knut
Wicksell (1851 - 1926), and tested against statistical evidence
by Charles Cobb and Paul Douglas in 1928.
In 1928 Charles Cobb and Paul Douglas published a
study in which they modeled the growth of the American
economy during the period 1899 - 1922. They considered
a simplified view of the economy in which production
output is determined by the amount of labor involved
and the amount of capital invested. While there
are many other factors affecting economic performance,
their model proved to be remarkably accurate.
The function they used to model production was of the form:
P(L,K) = bL_K_
where:
• P = total production (the monetary value of all goods produced in a year)
• L = labor input (the total number of person-hours worked in a year)
• K = capital input (the monetary worth of all machinery, equipment, and buildings)
• b = total factor productivity
• _ and _ are the output elasticities of labor and capital, respectively. These values are
constants
determined by available technology.
1
Output elasticity measures the responsiveness of output to a change in levels of either
labor or

11. capital used in production, ceteris paribus. For example if _ = 0.15, a 1% increase in
labor would
lead to approximately a 0.15% increase in output.
Further, if:
_ + _ = 1,
the production function has constant returns to scale. That is, if L and K are each
increased by
20%, then P increases by 20%.
Returns to scale refers to a technical property of production that examines changes
in output subsequent to a proportional change in all inputs (where all inputs increase
by a constant factor). If output increases by that same proportional change then there
are constant returns to scale (CRTS), sometimes referred to simply as returns to scale.
If output increases by less than that proportional change, there are decreasing returns
to scale (DRS). If output increases by more than that proportion, there are increasing
returns to scale (IRS)
However, if
_ + _ < 1,
returns to scale are decreasing, and if
_ + _ > 1,
returns to scale are increasing. Assuming perfect competition, _ and _ can be shown to
be labor
and capital’s share of output.
2
2 Discovery
This section will discuss the discovery of the production formula and how partial
derivatives are
used in the Cobb-Douglas model.
2.1 Assumptions Made
If the production function is denoted by P = P(L,K), then the partial derivative
@P
@L
is the
rate at which production changes with respect to the amount of labor. Economists call it
the
marginal production with respect to labor or the marginal productivity of labor. Likewise,
the
partial derivative
@P
@K
is the rate of change of production with respect to capital and is called the
marginal productivity of capital.
In these terms, the assumptions made by Cobb and Douglas can be stated as follows:
1. If either labor or capital vanishes, then so will production.
2. The marginal productivity of labor is proportional to the amount of production per unit
of
labor.

12. 3. The marginal productivity of capital is proportional to the amount of production per
unit of
capital.
2.2 Solving
Because the production per unit of labor is
P
L
, assumption 2 says that
@P
@L
=_
P
L
for some constant _. If we keep K constant(K = K0) , then this partial differential
equation
becomes an ordinary differential equation:
dP
dL
=_
P
L
This separable differential equation can be solved by re-arranging the terms and
integrating both
sides: Z
1
P
dP = _
Z
1
L
dL
ln(P) = _ ln(cL)
ln(P) = ln(cL_)
3
And finally,
P(L,K0) = C1(K0)L_ (1)
where C1(K0) is the constant of integration and we write it as a function of K0 since it
could
depend on the value of K0.
Similarly, assumption 3 says that
@P
@K
=_
P
K
Keeping L constant(L = L0), this differential equation can be solved to get:

13. P(L0,K) = C2(L0)K_ (2)
And finally, combining equations (1) and (2):
P(L,K) = bL_K_ (3)
where b is a constant that is independent of both L and K.
Assumption 1 shows that _ > 0 and _ > 0.
Notice from equation (3) that if labor and capital are both increased by a factor m, then
P(mL,mK) = b(mL)_(mK)_
= m_+_bL_K_
= m_+_P(L,K)
If _ + _ = 1, then P(mL,mK) = mP(L,K), which means that production is also increased
by
a factor of m, as discussed earlier in Section 1.
4
3 Usage
This section will demonstrate the usage of the production formula using real world data.
3.1 An Example
Year 1899 1900 1901 1902 1903 1904 1905 ... 1917 1918 1919 1920
P 100 101 112 122 124 122 143 ... 227 223 218 231
L 100 105 110 117 122 121 125 ... 198 201 196 194
K 100 107 114 122 131 138 149 ... 335 366 387 407
Table 1: Economic data of the American economy during the period 1899 - 1920 [1].
Portions
not shown for the sake of brevity
Using the economic data published by the government , Cobb and Douglas took the
year 1899 as
a baseline, and P, L, and K for 1899 were each assigned the value 100. The values for
other years
were expressed as percentages of the 1899 figures. The result is Table 1.
Next, Cobb and Douglas used the method of least squares to fit the data of Table 1 to
the function:
P(L,K) = 1.01(L0.75)(K0.25) (4)
For example, if the values for the years 1904 and 1920 were plugged in:
P(121, 138) = 1.01(1210.75)(1380.25) _ 126.3
P(194, 407) = 1.01(1940.75)(4070.25) _ 235.8
which are quite close to the actual values, 122 and 231 respectively.
The production function P(L,K) = bL_K_ has subsequently been used in many settings,
ranging
from individual firms to global economic questions. It has become known as the Cobb-
Douglas
production function. Its domain is {(L,K) : L _ 0,K _ 0} because L and K represent labor
and capital and are therefore never negative.
3.2 Difficulties
Even though the equation (4) derived earlier works for the period 1899 - 1922, there are
currently
various concerns over its accuracy in different industries and time periods.

14. Cobb and Douglas were influenced by statistical evidence that appeared to show that
labor and
capital shares of total output were constant over time in developed countries; they
explained this
5
by statistical fitting least-squares regression of their production function. However, there
is now
doubt over whether constancy over time exists.
Neither Cobb nor Douglas provided any theoretical reason why the coefficients _ and _
should be
constant over time or be the same between sectors of the economy. Remember that the
nature of
the machinery and other capital goods (the K) differs between time-periods and
according to what
is being produced. So do the skills of labor (the L).
The Cobb-Douglas production function was not developed on the basis of any
knowledge of engineering,
technology, or management of the production process. It was instead developed
because
it had attractive mathematical characteristics, such as diminishing marginal returns to
either factor
of production.
Crucially, there are no microfoundations for it. In the modern era, economists have
insisted that
the micro-logic of any larger-scale process should be explained. The C-D production
function fails
this test.
For example, consider the example of two sectors which have the exactly same Cobb-
Douglas
technologies:
if, for sector 1,
P1 = b(L_
1 )(K_
1)
and, for sector 2,
P2 = b(L_
2 )(K_
2 ),
that, in general, does not imply that
P1 + P2 = b(L1 + L2)_(K1 + K2)_
This holds only if
L1
L2
=
K1
K2

15. and _ + _ = 1, i.e. for constant returns to scale technology.
It is thus a mathematical mistake to assume that just because the Cobb-Douglas
function applies
at the micro-level, it also applies at the macro-level. Similarly, there is no reason that a
macro
Cobb-Douglas applies at the disaggregated level.
Cobb–Douglas
A two-input Cobb–Douglas production function
In economics, the Cobb–Douglas functional form of production functions is widely used to represent the
relationship of an output to inputs. It was proposed by Knut Wicksell (1851–1926), and tested against statistical
evidence by Charles Cobb and Paul Douglas in 1900–1928.
For production, the function is
Y = ALαKβ,
where:
 Y = total production (the monetary value of all goods produced in a year)
 L = labor input
 K = capital input
 A = total factor productivity

16.  α and β are the output elasticities of labor and capital, respectively. These values are constants
determined by available technology.
Output elasticity measures the responsiveness of output to a change in levels of either labor or capital
used in production, ceteris paribus. For example if α = 0.15, a 1% increase in labor would lead to
approximately a 0.15% increase in output.
Further, if:
α + β = 1,
the production function has constant returns to scale. That is, if L and K are each increased by 20%,
Y increases by 20%. If
α + β < 1,
returns to scale are decreasing, and if
α+β>1
returns to scale are increasing. Assuming perfect competition and α + β = 1, α and β can
be shown to be labor and capital's share of output.
Cobb and Douglas were influenced by statistical evidence that appeared to show that
labor and capital shares of total output were constant over time in developed countries;
they explained this by statistical fitting least-squares regression of their production
function. There is now doubt over whether constancy over time exists.
Difficulties and criticisms
]Lack of constancy over time
Neither Cobb nor Douglas provided any theoretical reason why the coefficients α and β
should be constant over time or be the same between sectors of the economy.
Remember that the nature of the machinery and other capital goods (the K) differs
between time-periods and according to what is being produced. So do the skills of labor
(the L).
Dimensional analysis
The Cobb–Douglas model is criticized on the basis of dimensional analysis of not having
meaningful or economically reasonable units of measurement.[1] The units of the
quantities are:
 Y: widgets/year (wid/yr)

17.  L: man-hours/year (manhr/yr)
 K: capital-hours/year (caphr/yr; this raises issues of heterogeneous capital)
 α, β: pure numbers (non-dimensional), due to being exponents
 A: (widgets * yearα + β – 1)/(caphrα * manhrβ), a balancing quantity.
The model is accordingly criticized because the quantities Lα and Kβ have economically
meaningless units unless α=β=1 (which is economically unreasonable, as there are then
no decreasing returns to scale). For instance, if α=1/2, Lα has units of "square root of
man-hours over square root of years", neither of which is meaningful. Total factor
productivity A is yet harder to interpret economically.
Lack of microfoundations
The Cobb–Douglas production function was not developed on the basis of any
knowledge of engineering, technology, or management of the production process. It was
instead developed because it had attractive mathematical characteristics, such
as diminishing marginal returns to either factor of production and the property that
expenditure on any given input is a constant fraction of total cost.
Crucially, there are no microfoundations for it. In the modern era, economists have
insisted that the micro-logic of any larger-scale process should be explained. The C–D
production function fails this test.
For example, consider two sectors which have exactly the same Cobb–Douglas
technologies:
if, for sector 1,
Y1 = AL1αK1β
and, for sector 2,
Y2 = AL2αK2β,
that, in general, does not imply that
Y1 + Y2 = A(L1 + L2)α(K1 + K2)β
This holds only if L1 / L2 = K1 / K2 and α+β = 1, i.e. for constant returns
to scale technology.
It is thus a mathematical mistake to assume that just because the
Cobb–Douglas function applies at the micro-level, it also applies at the

18. macro-level. Similarly, there is no reason that a macro Cobb–Douglas
applies at the disaggregated level.