Key Concepts in Production Analysis
• PPC, Input-Output, Fixed &Variable Inputs , Short run & Long
Production Function and its various determinants.
Law of Production
• Law of Variable Proportions
• Law of return to scale
Production Possibility Curve (PPC)
Production Possibility Curve is the curve which shows the combinations
of two goods and services that can be produced with fuller utilization of a
given amount of resources in the most efficient way and with a given
production technology. It is also known as Transformation curve. PPC is
concave to origin. This is because of the increasing opportunity cost i.e. in
accordance with the law of increasing opportunity cost.
In order to understand this, let us take an example.
A 50 0
B 48 1
C 44 2
D 35 3
E 0 4
• In the above figure, as we move downwards along the PPC from left to right (i.e.
from A to E ), we observe that in order to produce more units of capital goods, the
economy must sacrifice some amount of consumer goods. In other words, it reflects
the opportunity cost of producing one good in terms of another good. For example, a
movement from point B to point C implies that the economy is diverting resources
from the production of consumer goods to the production of capital goods. In order to
produce one additional unit of capital good, the economy is sacrificing four units (i.e.
48 – 44 units) of consumer goods. Thus, the opportunity cost of producing one
additional unit of capital goods is 4 units of consumer goods.
Input and Output:
• An input is a good or service that goes into the process of production.
Land, Labour, Capital, Management, Entrepreneur and Technology are
classified as inputs.
• An output is any good or service that comes out of the production process.
Short Run and Long Run:
• Short run refers to a period of time in which supply of certain inputs i.e.,
plant, building and machinery etc. is fixed or inelastic.
• Long run refers to a time period in which the supply of all the inputs is
elastic or variable.
Fixed Inputs & Variable Inputs:
• Fixed inputs remains fixed (constant) up to certain level of output.
• Variable inputs change with the change in output.
Production function is defined as “the functional relationship between
physical inputs ( i.e., factors of production ) and physical outputs, i.e.,
the quantity of goods produced”.
Production function may be expressed as under:
Q = f ( K,L)
Q = Output of commodity per
unit of time.
K = Capital.
L = Labour.
f = Functional Relationship.
Production function depends on :
• Quantities of recourses used.
• State of technical knowledge.
• Possible process.
• Size of firms.
• Relative prices of factors of production.
The following points may be emphasized:
• Production function represents a purely technical relationship.
• Output is the result of joint use of factors of production.
• Combination of factors depend on the state of technical
Every management has to make choice of the production function
which gives Minimum cost and maximum average profit.
Laws of Production
Laws of production are of two types:
• The law of variable proportions.
• Laws of returns to scale.
Short Run Production Function: The Law of Variable
Statement of the law:
“The law of variable proportions states that when more
and more units of the variable factor are added to a given
quantity of fixed factors, the total product may initially
increase at an increasing rate reach the maximum and
Tabular Presentation of Law of Variable Proportions
Units of Labour TP MP AP
1 80 80 80
2 170 90 85
3 270 100 90
4 368 98 92
5 430 62 86
6 480 50 80
7 505 25 72
8 505 0 63
9 495 -10 55
10 470 -25 47
Diagrammatical Presentation of Law of Variable Proportions
Assumptions of the
State of Technology
remains the same.
Input prices remain
Variable factors are
A Rational producer will never choose to produce in stage III where
Marginal Productivity of variable factor is negative. It will stop at the
end of the second stage where Marginal Productivity of the variable
factor is Zero. At this point the producer is maximizing the total output
and will thus be making the maximum use of the available variable
A producer will also not choose to produce in Stage I where he will not
be making full use of the available resources as the average product of
the variable factor continues to increase in this stage.
A producer will like to produce in the second stage. At this stage
Marginal and Average Product of the variable factor falls but the Total
Product of the variable factor is maximum at the end of this stage.
Thus stage II represents the stage of rational producer decision.
Law of Diminishing Returns and Business Decisions
Long Run Production Function: The Returns to scale
The long run production function is termed as returns to scale. In the
long run, the output can be increased by increasing all the factors in the
The laws of returns to scale is explained by the help of Isoquant
curves. An Isoquant curve is the locus of points representing various
combination of two inputs, Capital & Labour, yielding the same
Isoquant is one way of presenting the production function where two
factors of production are shown.
It represents all possible input combinations of the two factors, which are
capable of producing the same level of output.
Capital (K) MRTS L K
Tabular Presentation of MRTSLK
• It shows all the combinations of the two factors ( say labour and Capital)
that the firm can buy with a given set of prices of two factors.
• It plays an important role to determine combinations of factors, the firms
will choose for production ultimately to minimize cost.
PRICE OF LABOUR
D EE F
Producers Equilibrium or the Least Cost Combination of
• A producer desires to minimise his cost of production for producing a
given level of output with the least cost combination of factors.
How producers ultimately arrives the
point of equilibrium ?
•The equilibrium is achieved at the point
Where MRTS LK = PL/PK ie
• The slope of isoquant =Slope of
•Or , MRTS LY = MPL = PX
Or, MPL = MPK
There are three technical possibilities;
a) Total output may increase more than proportionately: Increasing returns to scale,
b) Total output may increase at a constant rate: Constant Returns to Scale,
c) Total output may increase less than proportionately: Diminishing returns to
Scarce and Exhaustible resources.
Indivisibilities of Factors,
High degree of specialization
Factors of production fully utilised.
Technology remains unchanged