• To examine the economic analysis of a firm’s
technology, different types of inputs and the process of
• To help develop an understanding of the distinction
between short run and long run production functions.
• To build up a critical appraisal of the law of variable
proportions and returns to scale.
• To introduce the concepts of isoquant, isocost line,
marginal rate of technical substitution, elasticity of
substitution and expansion path.
• To develop an understanding of technical progress and
• is the process of transformation of resources (like land,
labour, capital and entrepreneurship) into goods and
services of utility to consumers and/or producers.
• is the process of creation of value or wealth through the
production of goods and services that have economic
value to either consumers or other producers.
• process of adding value may occur
– by change in form (input to output, say steel into car), or
– by change in place (supply chain, say from factory to
– by changing hands (exchange, say from retailer to consumer).
Production of goods includes all tangible items such as
furniture, house, machine, food, car, television etc
services include all intangible items, like banking,
education, management, consultancy, transportation.
Types of Inputs
• determines the type, quantity and proportion of inputs.
• also determines the maximum limit of total output from a
given combination of inputs.
• at any point of time, technology will be given; impact of
technology can be seen only over a period of time.
Fixed and Variable Inputs:
• Production analysis of a firm uses two distinct time frames:
– the short run: refers to a period of time when the firm cannot vary
some of its inputs.
– the long run., refers to a time period sufficient to vary all of its inputs,
• Variable input : that can be made to vary in the short run,
e.g. raw material, unskilled/semi skilled labour, etc.
• Fixed input: that cannot be varied in the short run, e.g. land,
machine, technology, skill set, etc.
Factors of Production
5 factors of production
Land: anything which is gift of nature and not the result of
ii. Labour: physical or mental effort of human being that
undertakes the production process.
iii. Capital: wealth which is used for further production; it is
not a gift of nature, but is produced by human beings.
Capital is the output of one production process that
generally goes as input in another.
iv. Enterprise: The ability and action to collect, coordinate,
and utilize all the factors of production for the purpose of
economic gains. is also defined as the ability to take risk.
v. Organization: acknowledges a special kind of function,
which is a combination of highly skilled labour and
specialized human capital. It is organizational efficiency
that differentiates one company from another in terms of
• is a technological relationship between physical inputs
and physical outputs over a given period of time.
• shows the maximum quantity of the commodity that can
be produced per unit of time for each set of alternative
inputs, and with a given level of production technology.
Hence it can be said that production function is:
• Always related to a given time period
• Always related to a certain level of technology
• Depends upon relation between inputs.
• Normally a production function is written as:
Q = f (L,K,I,R,E)
where Q is the maximum quantity of output of a good being
produced, and L=labour; K=capital; l=land; R=raw
material; E= efficiency parameter.
Production Function with One
• also termed as variable proportion production function
• is essentially a short term production function in which
production is planned with one variable input (say L).
• shows the maximum output a firm can produce when only
one of its inputs can be varied, other inputs remaining fixed.
Q = f ( L, K )
• where Q = output, L = labour and K = fixed amount of
TPL = f ( K ,L)
Total product is a function of labour :
Average Product (AP) is TP product per unit of variable
Marginal Product (MP) is defined as addition in total output per
unit change in variable input. Thus marginal product of
labour (MPL) would be:
Law of Variable Proportions
Labour (’00 units)
1 2 3 4 5 6 7 8 9
states that as the quantity of the variable factor is increased
with other fixed factors, the marginal product and average
product of the variable factor will eventually decline.
Law of Variable Proportions
Increasing Returns to the
Variable Factor: very first stage.
MP>0 and MP>AP
Diminishing Returns to a
Variable Factor: the second
stage. MP>0 and MP<AP
Negative Returns: technically
inefficient stage of production
and a rational firm will never
operate in this stage. MP<0
while AP is falling but positive.
Elasticity of Substitution
• measures the percentage change in factor proportions due
to a change in marginal rate of technical substitution.
d ( K / L)
d ( MRTS )
• б is effectively a measure of the curvature of an isoquant.
• It is a pure number and independent of the units of labour
and capital, since both the numerator and denominator are
measured in the same units.
• more curved or convex is the isoquant, the lower is б.
• In Leontief (zero substitution) technology, with L shaped
isoquants, there is no substitutability between the inputs and
thus б = 0.
• In perfect substitution or linear production technology, the
MRTS does not change at all along the isoquant; б is infinite
is the line formed by joining
the tangency points
between various isocost
lines and the corresponding
highest attainable isoquants.
When the production function is homogeneous and factor
prices (and hence factor ratio) are given, the expansion
path is a straight line through the origin.
If the production function is not homogeneous, the optimal
expansion path will not be linear.
was proposed by Wicksell and tested against statistical
evidence by Charles W. Cobb and Paul H. Douglas in
Q = AK α Lβ
where α, β are constants. A is the technological parameter, α
is the elasticity of output with respect to capital and β is
the elasticity of output with respect to labour.
Properties: i. is a homogeneous of degree (α+β).
If (α+β) = 1 then Production function exhibits CRS.
If (α+β) > 1 the production function exhibits IRS.
If (α+β) < 1 the production function exhibits DRS.
ii. Isoquants are negatively sloped and convex to the origin
iii. MRTSLK is a function of input ratio.
iv. Elasticity of substitution is equal to 1.
Leontief Production Function
• represents the extreme case of perfect complements
• such production functions have ‘L’ shaped or right angled
• is also known as fixed coefficient production function.
Q = min( , )
• production technology always involves inputs labour (L)
and capital (K) in fixed proportions to produce a unit of
output and αand в are the fixed coefficients.
• a certain amount of each input is required technologically
to produce one unit to output. So, the demand for the
inputs is uniquely determined, because inputs are required
in exact quantities per unit of output.
• Any change in MRTS will not lead to any change in the
factor proportions and б = 0.
CES Production Function
• Constant Elasticity of Substitution (CES) production
function, was introduced by Arrow, Chenery, Minhas and
Solow (also known as ACMS)
Q=A[αK -ρ +(1-α)L -ρ ] -r/ρ
where A(>0) is the efficiency parameter which represents
the "size" of the production function;
α is the distribution parameter which will help us explain
relative factor shares (so 0<α<1);
ρ is the substitution parameter, which will help us derive the
elasticity of substitution and
r is the scale parameter which determines the degree of
• It is homogeneous of degree r.
(TP) and its Implications
refers to research and development and investments made to
manage technical know how.
– may be embodied or investment specific,
– may also be disembodied or investment neutral
Neutral TP: if changes in the marginal product of labour and
capital are same.
Labour augmenting TP: if MPL increases faster than the MPK.
Capital augmenting TP :if MPK increases faster than MPL.
• A production function shows the relationship between inputs
and outputs given the state of technology.
• Technical efficiency is a situation when use of more of one
input and either the same amount or more of the other input
• According to the law of variable proportions, as the quantity
of the variable factor is increased with other fixed factors,
the marginal product and the average product will eventually
• Isoquants are locus of points of different combinations of
labour and capital inputs that produce the same level of
output. MRTS is the absolute slope of an isoquant; it is
equal to the ratio of the marginal products of factor inputs.
• The isocost line represents the locus of points of all the
different combinations of labour and capital that a firm can
purchase, given the total cost and prices of the inputs. The
(absolute) slope of the isocost line is equal to the ratio of the
input prices; i.e. the relative price of labour to capital.
• The optimum level of inputs needed for objective of either
minimizing cost of producing a given level of output, or
maximizing output at a given cost would be at the point of
tangency of an isoquant and an isocost line.
• Expansion path is defined as the line formed by joining such
tangency points between the isocost lines and the highest
• If a proportional increase in all inputs yields a more than
proportional increase in output, the phenomenon is known
as increasing returns to scale; if a proportional increase in
all inputs yields an equal proportional increase in output,
then there is constant returns to scale. If a proportional
increase in all inputs yields a less than proportional
increase in output, then there is decreasing returns to scale.
• A homogeneous function one in which if each input is
multiplied by λ, then λ is factored out of the function. The
power of λ is known as the degree of homogeneity and is a
measure of returns to scale.
• Technical progress refers to improvements made in
research and development and various investments made
to manage technical know how. Technical progress is
neutral if changes in marginal products of labour and capital
are same; labour augmenting if MPL increases faster than
MPK and capital augmenting if MPK increases faster than