This document defines key concepts related to production analysis, including: 1. Production functions relate inputs like labor, capital, and technology to the quantity of output. They show the technical relationship between inputs and maximum possible output. 2. The law of diminishing marginal returns states that adding more of one variable input, while holding other inputs fixed, will eventually result in smaller increases in output. 3. Total, average, and marginal product are used to analyze how output changes with variable inputs. Total product is total output. Average product is total output divided by the input. Marginal product is the change in total output from an extra unit of input.

1. ECONOMICS FOR MANAGERS - 14MBA12
Module 2: (8 hours)
Production Analysis: Concept, Production Function: Single Variable –Law of
Variable Proportions & Two Variable Function, ISO-Quants & ISO Costs &
Equilibrium, Total, Average, & Marginal Product, Return to Scale, Technological
Progress & Production Function.
1. What is Production and Concept of Production Function?
Production is the transformation of resources into commodities over time and space. In simple words,
Production is the act of converting or transforming from input into output. It‟s a technical process
carried out by the firm.
“Production function is the name given to the relationship between rates of input of productive services
and the rate of output of product. It‟s the economist‟s summary of technical knowledge” (Stigler, 1966
P: 136)
The algebraic statement of production function is
„Q‟ = f(a,b,c,d……, n, T)
(T should have a bar at the top)
„Q‟ refers for Physical Quantity of output (Commodity produced) per unit of time
„f‟ denotes the functional relationship,
„a,b,c,… n‟, represents the quantities of various inputs (Productive Factors) per employed period.
„T‟ refers to the prevailing „Know-How Technology.
And „the bar at the top of T‟, indicates that technology is assumed to be constant.
Hence the Concept of Production Function, is a summarized description of technology possibilities,
where the given technique of production output that can be obtained from various levels of factor inputs.
2. What are the attributes of Production Function?
The attributes of Production Function include the following:
I. Flow Concept,
II. Physical Production Function,
III. State of Technology and Inputs,
IV. Inputs,
V. Some inputs are substitutes to one output,
VI. Some inputs may be specific,
VII. Factors combination for the maximum output,
VIII. Short run and Long run production function.
Flow Concept: The Production Function is a Flow Concept. It relates the flow of inputs and the resulting flows
of output of a commodity in a given period of time. Here „time‟ is taken to be functional or operational time
period.
Physical Production Function, refers to the technical relationship between the inputs and outputs expressed in
physical terms and not in monetary terms, such as in Rupees or Dollars.
State of Technology and Inputs, refers to the sum total of knowledge of the means and methods of producing
goods and services. It is the society‟s knowledge concerning the Industrial and Agricultural Arts. Thus inputs
include every type of productive resources – Land, Labor, Capital etc, also time and human energy as well as
knowledge, which are employed for producing a commodity.
Inputs, (a,b,c,d ….n) are complementary in nature as their combined productive services are transformed into
production of a specific commodity.

2. Some inputs may be specific, particularly; highly specialized factors are of specific use, as they have least
degree of substitutability.
Factors’ combination for the maximum output: This states the combination of factor input for maximum
output.
Short Run and Long Run Production Function: This is the variability of factors depends on the functional
time period under consideration. Here the short run production function pertains to the given scale of
production, while long run production function pertains to the changing scale of production.
3. What means Variable Inputs, Inputs and Fixed Inputs?
An input that is being changed in the process of production during the given time period is called
Variable inputs.
An input refers to the units of factors of production, such as Labor, Capital and Enterprise Allocated to
produce the output of a given product.
An input or the quantity of a factor of production remaining unchanged during a given time period is
called Fixed Inputs.
4. What means short run production function and long run production function?
Short Run Production Function, is the factor combination of an input, where at least one factor
remains fixed in the process of production. Short Run Production Function is denoted by Q = f(a/p0
,c0
,
…..n0
, T)
Where Stroke (/) divides between the variable and fixed components. Super scribe 0 denotes fixed
factors. This a, b, c are fixed factors, T is technology which is constant.
Long Run Production Function, operates with the changing scale of output and its size as a whole is
varied. Here all factors containing inputs tend to be variable in the process of production. This is
denoted by:
Q = f(a,b,c….n, T)
f is the functional relationship,
a,b,c …n denote the factors of inputs and
T denotes the state of technology, which is constant.
5. What is Dobb-Douglas Production Function?
C W Cobb and P H Doulas made the statistical inquiry into some of the manufacturing industries of
America and other countries, to trace the empirical relations between the changes in physical inputs and
the resulting output.
It is a generalized form of production function with two variable inputs that is labor and capital, as
follows:
Q = a[Lb
K 1-b
]
Where Q stands for Quantity of output/ Total Output,
L and K stands for Quantity of Labor employed and Capital employed respectively,
While „a‟ and „b‟ are positive constants.
„b‟ and 1-b stands for exponents of elasticity of production.
Dobb Doulas Production Function is a linear and homogenous function of degree, one which establishes
constant returns to the scale. According to this function, Return to scale is constant.
6. What is law of production?
Production process involves the transformation of all inputs into output. It is the study of combination of
different inputs producing various quantities of output under different technical reasons. Thus the
Production Function expresses the relationship between inputs and outputs. The production function is
explained by different economists in different ways to formulate laws relating to the relationship
between inputs and outputs. It can be studied in the following ways:
I. Output can be produced by keeping one factor or some factors fixed while other factors are
varied.

3. II. Another type of production function is where one factor is variable while other factors are kept
constant.
III. The third type of production function is where quantities of every input in the combination of
inputs can be varied to produce different quantities of output.
7. What means Law of Diminishing Marginal Returns?
Alfred Marshal stated, “An increase in capital and labor in the cultivation of land causes in general a less
proportionate increase in the amount of produce raised, unless it happens to coincide with an improved
in the arts of agriculture”.
The law of diminishing marginal returns was originally explained by classical economists with the
reference to agriculture. It was studied that Land is constant, while other factors were increased, but the
output did not increase proportionately. It was experienced that doubling the labor and capital cannot
reap double output, in the given piece of land. Hence additional land was required under the plough.
8. What is the Law of variable proportion and Law of non Proportional output?
The law of variable proposition, is the modern Law of Diminishing Marginal Returns, pertains to the
return to a variable factor input. The law of variable proposition assumes that one factor of production is
variable, while other factors are fixed. As the variable factor increases, while keeping other factors
constant, the variable factor may increase more than proportionately in the initial stages of production,
but finally it will not increase proportionately.
Professor Benham states the law of demand as follows:
“As the proportion of one factor in a combination of factors is increased after a point, the average and
marginal production of that factor will diminish”.
The conditions underlying the law of variable proportion is as follows:
I. Only one factor is varied and all other factors should remain constant.
II. The scale of output is unchanged, and the production plant or the size efficiency of the firm
remains constant.
III. The technique of production does not change.
IV. All units of the factor input varied are homogeneous, i.e all the units have identical
characteristics and equal efficiencies.
On the other hand, the Law of Non-Proportional Output (or Law of Variable Factor Proportion)
states, that in the short run, the variable factors will be more than proportionate initially, and after a
point, returns will be less than proportionate. This is what the law describes about the behavior in total
output resulting from increased application of variable factors to fixed factors.
9. What means Total Product, Average Product and Marginal Product?
Total Product: Total quantity of output produced by the given use of input in the production system,
per unit of time.
It is denoted: TP = F(Q, V, F)
Where TP denotes for Total Product, and
QVF denotes the quantity of the variable factor.
Average Product: Total quantity of product divided by the total units of input employed. It is per unit
product.
It is denoted: AP = TP/ QVF
Where AP refers for Average Product,
TP refers to total product of a commodity,
QVF refers to the quantity of variable factor.
Marginal Product: The addition made to the total product associated with one-unit change in a
particular single input labor. This is also called „Increment Product‟.
It is denoted: MP n = TP n – TP n-1,

4. Where MP n stands for Marginal Product, when „n‟ units of variable factor are employed,
TP refers for Total Product/ output, and refers to the number of units of variable factor employed (n =
QVF)
In Mathematical Terms it is: MP = ∆TP/ ∆QVE
In graphical terms of calculus the Marginal Product (MP) is defined as
MP = dTP/ dVF, where d = a unit change measured by the derivative of the related variable.
In a graphical display, of Product Curves on X axis and Y axis, are as follows:
I. The graphical representation shall be in X axis and Y axis,
II. The Y axis will represent the outputs, while the X axis shall represent the units of variable factor.
III. In the units of variable factors, X axis there are 3 stages – First Stage, Second Stage and Third
Stage.
IV. All MP (Marginal Product), Average Product (AP) and Marginal Product (MP) starts with 0
outputs.
V. The TP curve goes upward till the second stage and declines.
VI. The MP will start good, but within the first stage itself it declines and finally at the third stage the
curve crosses the X axis.
VII. While the Average Product, at the least gradually increases and cuts MP Curve at the last of first
stage and slightly starts decline at the third stage.
10. What is Iso-Quant or Equal Product Curve?
Equal Product Curve is also called as Production Iso-Quant. (Iso-Quant means Equal Quantity. The
equal product curve is called the iso-quant curve. It implies different combinations of inputs when
applied will produce the same quantity of output. Each combination is called as „Scale of Preference‟. A
higher Iso-quant represents higher quantity of output in compared to the lower.
Here the inputs are the L and K that is Labor and Capital.
11. What are the properties/ Characteristics of Iso-quant or equal product curve?
I. Iso quant have a negative slope, - This is because when one factor is increased the other factor
need to be decreased.
II. Iso quant are convex to origin, - This is because, the iso-quant measures the marginal rate of
technical substitute of one factor input (say labor) for the other factor input (say Capital).
III. Iso quant do not intersect, - This is because by definition, each iso-quant represents a specific
quantum of output. Therefore if two iso-quant intersect each other, it would involve logical
contradiction, as a particular iso-quant at a time may be representing a small as well as large
quantity of output. Hence to avoid the contraction it is taken care that they should not intersect.
IV. Iso quant is an oval shape curve, - This is because, it is noted that one iso-quant may have
positive upward slope at its end, when with a relative small amount of factor, relatively large
amount of other factor is combined. As such the marginal productivity of this abundant factor
tends to be negative and as such the resulting in a decline in a total output. In such cases the end
portions of the curves are regarded as uneconomical.
12. Differentiate between Equal Product Curve/ Iso-Quant Curve and Indifferent Curve?
I. Indifferent Curve indicates the level of satisfaction, while Iso-quant curve indicate the quantity
of output.
II. Indifferent Curves relate to combination between two commodities, while Iso-quant curve relate
to combinations between two factors of production.
III. Indifferent Curves cannot be easily labeled as there is no numerical measurement of satisfaction
involved, while Iso-quant curves can be easily labeled as physical units of output represented by
it are measurable.
13. What means iso-cost line?

5. Iso-cost line is a graphical device – A line showing all of the combination of the two factors (say Labor
(L) and (K) Capital) that can be purchased for a given expenditure layout by the firm.
14. What is least cost factor combination?
Every firm is interested in Least Cost Combination of factors. This is determined by comparing a
production map in relation to a given cost line. The cost line is determined by the ratio of prices of two
factors, assuming a given investment fund with the firm and given prices of factors.
The cost line is the cost constraint. (Firm‟s Budget), which is:
Cost Line Measures = PL/ PK
Where PL is the Price of Labor and
PK is the price of capital.
15. What are returns to scale?
Returns to scale refer to the long run analysis of production. It is the study of changes in the output, as a
consequence of change in the scale.
There are three stages of returns of scale, namely
I. Increasing returns to scale,: This is considered as the first stage, where the total output is more
than proportionate. (Beyond/ above)
II. Constant returns to scale: This is the second stage, where the total output is proportionate.
(Matched)
III. Diminishing returns to scale,: This is the third stage, where the total output is less than
proportionate. (Decline/ below)
16. What is Scale line?
“Scale line refers to the expansion path of optimum factor-input combinations with the increasing scale
of production”.
17. What means economies scale?
Economies of scale refer to the advantages enjoyed by the firm as a result of increase in its scale of
production.
Marshal classified economies into two types:
I. Internal Economies and
II. External Economies.
Internal Economies include
1. Technical Economies, like
a. Economies of Superior Technique,
b. Economies of increased dimension,
c. Economies of linking of process,
d. Economies of use of by-products,
e. Economies of increased specialization,
2. Managerial Economies,
3. Marketing Economies,
4. Financial Economies,
5. Labor Economies, and
6. Risk Bearing Economies
While the External Economies include:
a. Economies of localization,
b. Economies of information,
c. Economies of disintegration,
d. Economies of Government Action,
e. Economies of Physical Factors.

6. 18. What means dis-economies of scale?
Dis-economies of scale is an Economic Concept, referring to a situation in which the economies of scale
no longer function for a firm. The firm experiences increased cost per increase of output. Firm identify
that there is an increase in marginal cost when output is increased.
Dis-economies can occur due to the following reasons:
I. A specific process within a plant cannot produce the same quantity of output as another related
process. For instance, If in a product, require both Gadget „A‟ and Gadget „B‟. Dis-economies of
scale may occur if Gadget „B‟ is produced at a slower rate than Gadget „A‟.
II. As output increases, cost of transportation of goods to distance markets can increase and create
dis-economies to scale. For instance, if a firm has a large plant with higher capacity to produce
goods, the firm will need more ship to distance locations.
19. What are the reasons for diseconomies to scale?
The reasons for diseconomies to scale can be Internal Diseconomies and External Diseconomies.
Internal Diseconomies will include,
I. Worsening Labor Conditions,
II. Limited use of natural resources,
III. Limitation to efficient, large scale management.
External Diseconomies will include,
Diseconomies due to transportation as the firm may have only one firm and the products need to
be transported, Secondly is the availability of raw material goods and goods related for
manufacture goods.
20. What is the law of decreasing returns to scale, and what are its reasons?
(Same as diseconomies to scale)
There are decreasing returns to scale when the percentage increase in output is less than the percentage
in input.
Algebraically it is: ∆Q/ Q < ∆F/ F
Thus PFC < 1 under decreasing returns to scale.
Economists have considered the following causes for decreasing returns to scale:
I. Though all physical factors inputs are increased proportionately, organization and management
as a factor cannot be increased in equal proportion.
II. Business risk increases more than proportionately when the scale of production is enhanced. An
entrepreneurial efficiency has its own physical limitation.
III. When the scale of production increases beyond a limit, growing diseconomies of large scale
production set in.
IV. The increasing difficulty of managing big enterprises (Problem of supervising and co-ordination)
V. Imperfect substitutability of factors of production causes diseconomies resulting in a declining
marginal output.
21. What are the types of linear and non-linear models in production function?
The linear and non-linear models in production function applied in empirical studies, include as follows:
I. Linear Production Function,
II. Quadratic Production Function,
III. Cubic Production Function,
IV. Power Production Function, and
V. Cobb-Douglas Production Function.
Algebraically it is denoted as follows:
Linear Production Function: Q = b0 + b1V
Where if „V‟ the variable factor is labor (L) then it would be stated as: Q = b0 + b1 L
And b0 is the fixed factor input quantity, and b1 is the slope coefficient. It represents the marginal
product (MP) the variable factor.

7. Quadratic Production Function: Q = b0 + b1 V – b2 V2
This equation measures downward slopes of AP and AP curve.
Cubic Production Function: Q = b0 + b1 V + b2 V2
– b3 V3
,
This function highlights the operation of the law of non-proportional returns to the variable
factors.
Power Production Function: Q = a Vb
Where, a is the constant parameter and b is the power which is expressed in logarithmic terms, it
is been transformed to linear function: Log Q = Log a + b Log V
Cobb-Douglas Production Function: (Already explained above)
Q = f (L, K, F)
Where L = Labor,
K = Capital,
F = Fixed factor component of inputs.
In empirical measurement, it is represented with power terms as:
Q = aLb
Kc
Where Q = Total Quantity of output,
L = Labor unit - inputs.
K = Capital unit – inputs.
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