Theory of
Production
Production
• Production is the process of converting inputs
into output
• Production is the process of transformation of
inputs like land, labour, capital and
entrepreneurship into goods and services of
utility to consumers and/or producers
• It is the process of creation of value or wealth
through the production of goods and services
that have economic value
Fixed Input & Variable Input
• Typically the production analysis of a firm is
done using two distinguished time frame, Short
Run (SR) and Long Run (LR)
• In SR, supply or availability of some of the
inputs of production is fixed
• In LR firm can vary all its inputs including
technology
• Based on horizon, inputs are classified as
variable and fixed
Fixed Input & Variable Input
• Fixed Input – Level cannot be altered
rapidly with production in short-run. e.g.
Plant Size, Technology
• Variable Input – Level can be altered
according to the changes in production
level. e.g. Labour, Raw Material
Factors of Production
• Land: It not only incorporate dry surface
of the earth but also natural resources
on or under the earth surface like
forests, rivers, sunlight, minerals etc.
– Return from land is called rent
• Labour: Physical or mental effort that
undertakes the production process. It
can be unskilled, semi-skilled or skilled
– Return for labour is called wages or salery
Factors of Production
• Capital: Wealth which is used for further
production and of two types
– Physical capital: equipments, buildings
– Human capital: Knowledge and investment
made by people through education and
training that help to produce better goods
and services
– Return form capital is interest
Production Function
• It is the technical relationship between inputs
and output
• A commodity may be produced by using
different combination of inputs with different
technologies
– Power can be produced from coal, gas,
renewables etc with subcritical, super-critical or
SPV technology
• Production function includes all such
technically efficient methods
Production Function
• Technical efficiency is defined as a
situation when using more of one input
with either the same amount or more of
other input must increase output
• Production function is
– Always related to a given time period
– Always related to a certain level of technology
Production Function
• Output:
Q = f(L, K, Land, Raw material, efficiency)
• In short-run, inputs like plant size,
machine and equipments cannot be
changed
• Producer can increase output in SR by
increasing only variable inputs like
labour
• In long-run all the inputs can vary
Short run Production function
• Q=f(L,K*); K* is fixed
• Total Product (TP) – in short run when the
capital input is fixed, output can be increased
by increasing labour input
– This is termed as TP of labour
• TP increases at an increasing rate at first, then
increases at a diminishing rate
• Eventually TP falls with more employment
 Law of Diminishing Marginal Productivity
Average & Marginal Products
• Average Product, APL = TP/L
• Marginal Product MPL – Additional output
obtained by increasing an unit of labour input,
combined with other fixed factors of production.
In other words, MPL = ∆TP/∆L
• When TP of labour increases at an increasing
(decreasing) rate, MPL also rises (falls).
• When TP of labour falls, MPL<0
Table showing TP, AP & MP
L
Q
AP
MP
0
0
-
-
1
52
52
52
2
112
56
60
3
170
56.7
58
4
220
55
50
5
258
51.6
38
6
286
47.7
28
7
304
43.4
18
8
314
39.3
10
9
318
35.3
4
10
314
31.4
-4
K=2
Production Function With One Variable Input
Law of Diminishing Marginal Productivity
or
Law of Diminishing Returns
• As we increase units of labour, total output
increases but not at a constant rate
• In the beginning output increases at an
increasing rate and finally it increases at
a diminishing rate
• We also have increasing and then
diminishing marginal returns
Law of Diminishing Returns
• The law thus states that when increasing
amounts of the variable input are
combined with a fixed level of another
input, a point will be reached where the
marginal product of the variable input
will decline
• This law is based on actual
observations of many production
processes
Example
• MIT study reveals that too much wind and
solar raises power system costs
• Because adding more and more solar
panels decline productivity
• https://www.utilitydive.com/news/too-much-wind-and-solar-raises-powersystem-costs-deep-decarbonizationreq/568080/?fbclid=IwAR0l_3gosJ5sOhXtdidOqEbsjSu0faN1EGMMqWo
yf7LBzEvaR62ZS6mFJqo
•
https://www.technologyreview.com/2021/07/14/1028461/solar-valuedeflation-california-climate-change/
Example
• Costs they impose on the system become
substantial once the contribution of renewables
(wind and solar) exceeds 40% of the total
electricity generation
– First, more and more solar and wind production is
“curtailed” — that is, the generator must be unplugged
from the grid during its most productive hours because
more electricity is being produced than is needed
– Second, more back-up generating capacity is
needed to fill in when the wind and solar are not
producing.
• Since that extra backup capacity is idle much of
the time, it adds costs to the system.
Production Function With One Variable Input
If adding another worker
increases output by more
than the average product
of the total labor force,
then the marginal product
of the new worker will
raise the average product
amount
Law of Diminishing Returns
• G is the point of inflection in TP curve
• G/ is the corresponding point on MPL curve where
MP attend its maximum value and starts falling
thereafter
• So, till G/ , increasing returns, MP max &
MP>AP
• Point H in TP curve is where AP=MP (H/) &
• AP reaches its maximum value
Law of Diminishing Returns
• AP starts falling to the right of H/
• G/ to J/  Region of diminishing returns;
MP>0
• At point J, TP reaches its maximum value
and falling thereafter
• At J/ MP is zero and negative thereafter
– Region of negative returns
MP & AP
• If the marginal is greater than the average,
then the average rises
• If the marginal is less than the average,
then the average declines
• If the marginal is equal to the average,
then the average does not change.
Table showing TP, AP & MP
L
1
2
3
4
5
6
7
8
9
Q
20
50
90
120
140
150
150
130
100
MPL
30
40
30
20
10
0
-20
-30
APL
20
25
30
30
28
25
21.5
16.25
11.1
Stages
IR
DR
NR
Increasing, Diminishing & Negative Returns
Managerial Decisions
• Rational firm should operate in Stage II
• Stage I represents under-utilization of firm’s
fixed inputs relative to its variables one
• Stage III represents overutilization of its fixed
inputs
• Thus capacity planning is required at the
beginning based on demand forecasting so
that plant can operate in stage II
Managerial Decisions
• Thus, good capacity planning requires
– Sophisticated techniques for estimating
and forecasting demand and demand
elasticities
– Effective communication between
production and marketing divisions as
production division proceed based on
technical point of view
• A firm produces output according to the production
function Q = 10KL2 – L3, where K denotes capital
stock and L denotes no. of workers it hires.
Suppose K = 10
Derive APL & MPL
At what level of labour does DMR sets in?
At what level of labour APL is highest?
Ans:
MPL =∂Q/ ∂L = 200L – 3L2
APL = Q/L = 10KL – L2 = 100L – L2
DMRS ∂(MPL)/ ∂L=0200-6L=0; L=33.33
Av Product max ∂(APL)/ ∂L=0 L=50
Production in the long run
How to plot??
Production in the long run
Q=F(L,K), L, K are variable
• An Isoquant (meaning equal quantity) is a
locus of points showing all possible
combinations of the inputs physically
capable of producing a given (fixed)
level of output.
• Each point is technically efficient
– Technical efficiency is defined as a situation
when using more of one input with either the
same amount or more of other input must
increase output
An isoquant
45
a
40
Units
of K
40
20
10
6
4
Units of capital (K)
35
30
25
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
20
15
10
5
0
0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
Production in the long run
• Many combinations of inputs can produce
the same level of output
• Firms will only use combinations of two
inputs that are in the economic region of
production
• Economic region of production is defined
by the portion of each isoquant that is
negatively sloped
An isoquant
45
a
40
Units
of K
40
20
10
6
4
Units of capital (K)
35
30
25
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
20
15
10
5
0
0
5
10
15
20
25
30
Units of labour (L)
35
40
45
50
Properties of Isoquants
• Higher Isoquants show higher output
more & more away from the origin
• Marginal Rate of Technical Substitution
(MRTS) measures the reduction in per unit of
one input, resulting in increase in the other
input that is just sufficient to maintain the
same level of output
• MRTS=Absolute value of the slope of the
isoquant
• MRTS of labour for Capital given by ∆K/∆L
Diminishing marginal rate of factor substitution:
(or marginal rate of technical substitution)
14
g
Units of capital (K)
12
DK = 2
MRTS = DK / DL
MRTS = 2
h
10
DL = 1
A decline in MRTS along
an isoquant for producing the
same level of output is called
the diminishing marginal rate
of substitution
8
j
MRTS = 1
k
DK = 1
6
DL = 1
4
2
isoquant
0
0
2
4
6
8
10
12
Units of labour (L)
14
16
18
20
Caselet
• A blueprint to protect labour
rights without constraining
capital | Opinion
https://www.hindustantimes.com/analysis/a-blueprint-to-protect-labour-rightswithout-constraining-capital-opinion/storyPWfCgpaUHa8Ky6cDZWz3QI.html?fbclid=IwAR0UJChp43S0Ge5W_qf4GsjOy7OcM40
0sFaBweNyfA6DpoUFD_fVAjz3W-4
Economic Region of Production
• Ridge lines separate the economic zone from
non-economic zones
• Ridge line is a locus of points on different
isoquants where MP of one of the factors is
zero.
– Upper ridge line implies that MPK is zero
– Lower ridge line implies that MPL is zero
• Production techniques are technically
efficient only inside the ridge lines
–
.
Isoquants
K
Upper Ridge Line
Economic Zone
Lower Ridge Line
L
Isoquants
• The downward sloping isoquants as we
see earlier are most common
• There, underline assumption is that the
inputs are substitute but not perfect
• What will happen when inputs are
either perfect substitute or perfect
compliments, i.e. no substitutability?
Linear Isoquants
• When there is perfect substitutability
between two factors, the isoquants
would be linear
• Q*=f(L. K) = αL + βK, where α & β are
Constant
• MPL = dQ/dL = α & MPk = dQ/dK = β
• MRTS = α / β = Constant
Right Angled Isoquants
• When capital is perfect compliment for
labour, implying non existence of any
substitutability between two factors,
such isoquants are right angled
• In this case, production technology
always involves inputs L & K in fixed
proportions to produce a unit of output
Production With Two Variable Inputs
Perfect Substitutes
Perfect Complements:
Fixed Coefficient Technology
• Producer’s objective would be
• maximize output at a given cost
(represented by isoquants) or
– to minimize cost of production a
given level of output
??
Optimal Combination of Inputs
Isocost lines represent all
combinations of two inputs that a firm
can purchase with the same total cost.
C  wL  rK
C
w
K 

L
r
r
C  Total Cost
r  Cost of Capital ( K )
w  Wage Rate of Labor ( L )
An isocost
30
Assumptions
25
Units of capital (K)
r = Rs.20 000
w = Rs10 000
TC = Rs 300000
20
a
15
10
5
TC = Rs300000
0
0
5
10
15
20
25
Units of labour (L)
30
35
40
Isocost Lines
• So, isocost line is the locus of points of all the
different combination of capital and labour
that a firm can employ, given the total cost
and prices of inputs
• If the factor prices are constant, then for different
levels of total cost, there will be a set of isocost
lines, each representing a specific level of total
cost
• The higher the total cost, the further the
isocost line will be from origin as more of
both inputs can be purchased by the firm
Optimal Combination of Inputs
Isocost Lines
AB
C = 100, w = r = 10
A’B’
C = 140, w = r = 10
A’’B’’
C = 80, w = r = 10
AB*
C = 100, w = 5, r = 10
Optimal Combination of Inputs
• The intercept of Isocost line on Capital Axis (Pt
A) is the maximum amount of capital employed
when labour is not used in production process
and is given by (C/r)
• Similarly the intercept on labour axis, point B,
(max amount of labour used in production
process when capital usage is zero) is (C/w)
• Line AB* shows a fall in w, thus more of labour
can be acquired
• Slope of AB* is (–w/r) = -(5/10) = -0.5
Producer’s Equilibrium
• To be economically efficient, a producer must
determine the combination of inputs that
produces the output at minimum cost
• The maximum output level for any firm is
determined by isoquants,
– but they would not give the minimum cost of
production,
• For this we need isocost line
Producer’s Equilibrium
• Combining isoquants and isocost lines
would help us to understand Producer’s
equilibrium
• The lowest cost of producing a given
level of output is the point where the
isoquant is tangent to isocost line
Optimal Combination of Inputs
MRTS = w/r
Producer’s Equilibrium
• The lowest cost of producing a given level of
output is given at point E, where the isoquant
corresponding to output 10Q is tangent to isocost
line AB
• At this point the firm would employ 5 units of
capital and labour each
• For line AB, 14Q is beyond the reach of the firm ,
whereas any point below AB is feasible but not
desirable
• So, necessary condition of producer’s equilibrium
is slope of isocost=slope of isoquant
Expansion Path
• Expansion path is define as the line formed by
joining the tangency points between various
isocost lines and the corresponding highest
attainable isoquants
• Also defined as the locus of equilibrium points of
the isoquant with lowest possible isocost line
• An expansion path is a long run concept and
each point of the expansion path represents a
combination of inputs that minimise cost
Optimal Combination of Inputs
MRTS = w/r
Production Function
&
Returns to Scale
• It refers to the degree by which the
level of output changes in response
to a given change in all the inputs in
a production system
• It is a LR phenomenon
• Can be constant, increasing or
decreasing returns to scale
Returns to Scale
Production Function Q = f(L, K)
Q = f(hL, hK)
If  = h, then f has constant returns to scale.
If  > h, then f has increasing returns to scale.
If  < h, the f has decreasing returns to scale.
Returns to Scale
Constant
Returns to
Scale (CRS)
Increasing
Returns to
Scale (IRS)
Decreasing
Returns to
Scale (DRS)
Increasing returns to scale
• When input prices remain constant, increasing
returns to scale results in decreasing longrun average costs (economies of scale)
• A firm that gets bigger experiences lower costs
because of increased specialization, more
efficient use of large pieces of machinery (for
example, use of assembly lines), volume
discounts, and other advantages of producing in
large quantities
– Coke, Pepsi
Empirical Production Functions
• In SR Q=f(L)K
• In SR, if we incorporate increasing,
diminishing and negative marginal returns
then
Q = a + bL + cL2 – dL3
• In empirical estimation one uses linear
production function Q = a + bL
• The function, however, exhibit no
diminishing retuns
Empirical Production Functions
• Cobb-Douglas production function is commonly
used functional form
• The function can exhibit increasing, decreasing
and constant returns
• One can directly estimate elasticity of
production
Q = aLbKc
• Estimated through regression analysis using Natural
Logarithms ln Q = a + b ln K + c ln L
Estimation of Production Functions
• Both capital and labor inputs must exist for Q to
be a positive number
• Can be increasing, decreasing, or constant
returns to scale
b + c > 1, IRTS
b + c = 1, CRTS
b + c < 1, DRTS
• Elasticities of factors are equal to their exponents
• Example: Q = 1.01 L0.76 K0.25
Indian Plywood manufactures and sells lumber, plywood, veneer,
particle board, medium-density fiberboard, and laminated beams.
The company has estimated the following multiplicative
production function for basic lumber products in the Pacific
Northwest market using monthly production data over the past
two and one-half years (30 observations):
Q = b0 Lx Ky Ez (Lab, Cap, Energy)
Each of the parameters of this model was estimated by
regression analysis. Estimated coefficients with their std errors
in brackets are as follows
b0 = 0.9 (0.6); x= 0.4 (0.1); y= 0.4(0.2); and z= 0.2 (0.1)
A. Estimate the effect on output of a 1% decline in worker hours
(holding K and E constant).
B. Estimate the effect on output of a 5% reduction in machine hours
availability accompanied by a 5% decline in energy input (holding
L constant).
C. Estimate the returns to scale for this production system.
A. -0.4%
B. = 0.4(-0.05) + 0.2(-0.05) = -0.03 or -3%
C. x+y+z = 0.4 + 0.4 + 0.2 = 1 indicating
constant returns to scale. This means
that a 1% increase in all inputs will lead
to a 1% increase in output
• Hydraulics Ltd. has designed a pipeline that provides a
throughput of 70,000 gallons of water per 24-hour
period. If the diameter of the pipeline were increased by
1 inch, throughput would increase by 4,000 gallons per
day. Alternatively, throughput could be increased by
6,000 gallons per day using the original pipe diameter
with pumps that had 100 more horsepower.
A. Estimate the marginal rate of technical substitution
between pump horsepower and pipe diameter.
B. Assuming the cost of additional pump size is $600 per
horsepower and the cost of larger diameter pipe is
$200,000 per inch, does the original design exhibit the
property required for optimal input combinations? If so,
why? If not, why not?
A. The marginal rate of technical substitution is calculated
by comparing the marginal products of "diameter," MPD,
and "horsepower," MPH:
MPD = ∂Q/ ∂D = 4,000/1 = 4,000 gal.
MPH = ∂Q/ ∂H = 6,000/100 = 60 gal.
So, MRTSDH = MPD / MPH = -66.67
[ ∂Q/ ∂D]/[∂Q/ ∂H] = -66.67
This implies ∂H = -66.67 ∂D or ∂D = -0.015 ∂H.
This means, for example, that output would remain
constant following a one inch reduction in pipe diameter
provided that horsepower were increased by 66.67.
B. Answer is No.
The rule for optimal input proportions is:
MPD /PD = MPH /PH
In this case,
MPD /PD = 4000/200000 = 0.02
MPH /PH = 60/600 = 0.1
So, MPD /PD ≠ MPH /PH
Here the additional throughput provided by the last dollar
spent on more horsepower (0.10 gallons/day) is five
times the gain in output resulting from the last dollar
spent to increase the pipe diameter (0.02 gallons/day)
Thus, horsepower and pipe diameter are not being
employed in optimal proportions in this situation.
Returns to Scale - Example
Production Function
Q = 10L0.4K0.9
•Compute Production elasticity w.r.t. L
•Compute Production elasticity w.r.t. K
•What can we say about the RTS?
Caselets
• MNREGA, labour shortage and farm
mechanization in Punjab 
Substitution
https://www.tribuneindia.com/news/punjab/growers-feel-pinch-as-farm-wages-goup/608030.html
• Nokia & Smartphone  Technology
http://www.enterprisegarage.io/2015/12/case-study-how-nokia-lost-the-smartphone-battle/
• Tata Nano failure  Consumers’
demand
•
http://www.adageindia.in/marketing/cmo-strategy/tata-nano-a-marketing-disaster-then-a-billion-dollaropportunity-now/articleshow/61839731.cms