production function. fundamental questions of managers how can production be optimised or cost...
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Production Function
Fundamental Questions of Managers
• How can production be optimised or cost minimised
• How does output behave when quantity of input is increased
• How Technology effects the cost of production
• How can least –cost combination of inputs be achieved.
• What happens to rate of return when the firm expands.
Factors of Production• Production requires use of factors – agents of production
• Economic growth is dependent upon the supply and productivity of factors.
• The good and services which are used for the production of goods – Inputs.
• What they produce – Outputs.
• The input –output analysis has become an important tool of modern economic analysis.
• Classified as – Land, Labour, Capital, Entrepreneurship
Theory of Production
• Production means creation of a valuable utility.
• Supply of product refers to the quantity supplied at the given price.
• Which depends upon– Relationship between input and output– Prices of inputs– Managerial efficiency
• Production function: The functional relationship under given technology between
input and output, per unit of time.Q = f ( L, K)
Theory of Production
• It states the maximum amount of output that can be produced with any given quantities of various inputs.
• Particular period of time
• Flow concept : Flow of inputs leads to flow of output
Types of Production Function
Types
Short –Run(Inputs kept constant
One input (Labour) is varied)
Long – Run(Varying all inputs)
Law of variable proportion
Law of returns to scale
Concepts Of Product
1) Total Product:Total output produced by given amount of factor, other
factor held constant. As the factor increases the total output increases.
2) Average Product :AP = Total Product = Q
No of Units of a Factor employed L
Avg product first rises and then falls
3) Marginal Product:The addition to the total production by the employment
of an extra unit of a factorMP = ∆Q ∆L
Units of Labour
L
Total Product
(Quintals) Q
Marginal Product
(Quintals)
Average Product
(Quintals)
1 80 80 80
2 170 90 85
3 270 100 90
4 368 98 92
5 430 62 86
6 480 50 80
7 504 24 72
8 504 0 63
9 495 -9 55
10 480 -15 48
IR
DR
Negative
Short – Run Production FunctionLaw of Variable Proportion
• One – factor varying, quantities of other factor as fixed
• Law of variable proportion: It’s the study of the effect on output of variations in factor
proportion
• As the proportion of one factor in a combination of factors is increased after a point, first the marginal and then the
average product of that factor will diminish.
• It’s a new name for Law of Diminishing returns
– The state of technology is assumed to be given / unchanged– Some inputs whose quantities is fixed– Measured in physical terms.
Stages of Law of Variable proportion
TP
MP
AP
F
Stage 1 Stage 2 Stage 3
H
D S
Amount of Variable Factor
Total Product
Stages
Stage 1.
– TP increases at an increasing rate upto a point.– MP of variable factor is rising– Point F (Point of Inflection), TP curve rises but its slopes
decline – TP is increasing at a diminishing rate. MP starts falling but its positive.
– AP reaches its highest point– MP of variable factor rises and then falls– MP of fixed factor is negative– Quantity of fixed factor is too much to the variable factor
Stages
Stage 2.– TP increases at a diminishing rate, reaches its maximum
point– MP, AP are diminishing but positive– MP becomes Zero
Stage 3.– TP slopes downwards– MP of variable factor is Negative
In which stage the Producer should Produce
• Stage 3 – NoMP of variable factor is negative
• Stage 1 – NoMP of fixed factor is negativeFull utilisation is not there
Stages ofEconomic absurdity / Economic non-sense / Non- economic regions
• Stage 2 – YesMP and AP are positive but diminishing
Causes• Increasing Returns
– Quantity of fixed factor is abundant than variable factor– Fixed factor are indivisible– With addition of variable factor , fixed factor is more effectively and intensively utilised.– More units of variable factor are employed , the efficiency of
variable factor increases –“specialisation of labour”.
• Diminishing Returns– The maximum point has reached.– The amount of the variable factor is sufficient to ensure
the efficient utilisation of fixed factor.– The contribution to the production made by the variable factor after a point become less as the additional units of the variable factor have less of fixed factor.
Causes
• Negative ReturnsNumber of variable factor become too excessive to the fixed factor Marginal Product of variable factor is negative.
• Diminishing returns occur because the factors of production are Imperfect substitutes for one another.
There is a limit to which one factor of production can be substituted for another.Elasticity of substitution between factors is not infinite.
Technological Progress and Diminishing Returns
• In today’s scenario the Technological progress can suspend theoperation of diminishing returns by continually improving the techniques of production.
Labour Force
AP2
AP1
AP3
AP4
Output
Long Run – Laws of Return to Scale• Both the factors are taken as variables
• Isoquant : is a curve representing the various combinations of two inputs that produce the same amount of outputAlso called as equal product curve
Factor Production
Labour Capital
A 1 12
B 2 8
C 3 5
D 4 3
E 5 2
IsoquantK
L
General Properties of Isoquant
• An Isoquant is downward sloping to the right: If more of one factor is used then less of the other factor
is needed for producing same level of output
• Higher Isoquant represents larger output
• No two isoquants can intersect each otherSame amount of factors can produce two levels of output
• Isoquants are convex to the originSlope of isoquants diminishes from left to right, -
Marginal rate of technical substitution
Types of IsoquantThe shapes depends upon degree of substitutability of inputs
1) Linear Isoquant: Perfect substitutability between factors of production.An output can be produced byeither using one or both
2) Input- Output Isoquant Strict complementarity's between inputs. One method of production. If a quantity of one input is increased there will be
no change in output.
Q1Q2
Q3
Q2
Q1
Marginal Rate of Technical Substitution
• MRTS = The rate at which the factors can be substituted at a margin without altering the level of output.
• MRTS L for K = No of units of capital which can be replaced by one unit of labour
Factor Combination
Units of Labour
Units of Capital
MRTS of L for K
A 1 12
B 2 8 4
C 3 5 3
D 4 3 2
E 5 2 1
MRTS L for K = Slope = ∆K = MPL
∆ L MPK
Marginal Rate of Technical Substitution
• As the output remains constant• When labour and capital are substituted for each other, the
change in output due to decrease in the amount of capital is equal to increase in output due to increase in amount of labour.
– ∆K. MPK = ∆ L.MPL
– MP = Marginal productivities of labour and capital
MRTS L for K = ∆K = MPL ∆ L MPK
Why Diminishing MRTS
• MRTS diminishes as more and more of labour is substituted for capital.
• Less of capital is required to be substituted by an additional unit of labour so as maintain the same level of output.
The Law of Returns to Scale
• Return to Scale:The resultant increase in total output as the two inputs increases.
Total output may increase proportionatelyTotal output may increase more than proportionatelyTotal output may increase less than proportionately
• Three types:– Constant– Increasing– Decreasing
Constant Return to Scale
• Percentage change in factor inputs leads to equal percentage change in output.
• Factors of production are perfectly Divisible, production function must exhibit constant returns to scale
• In some industry it is not possible to increase or diminish factors in exactly the same proportion
• Some factors supplies are scarce• Factors are indivisible, full utilisation is done only when
production happens in large scale
Constant Return to Scale
IQ1
IQ2
IQ3
QX1= 100
O
R
QX2= 200
QX3 = 300
Units of Labour
Units of Capital
a
b
c
oa = ab = bc
Increasing Returns to Scale
• Output increases in a greater proportion than the increase in the inputs
• Expanding firms experience this factor
– Indivisibility of the factors: Some factors are better utilised at large scale of output– Greater possibility of specialisation of labour and machinery– Integration of processes– Dimensional Advantage
Increasing Return to Scale
IQIQ2
IQ3
QX1= 100
O
R
QX2= 200
QX3 = 300
Units of Labour
Units of Capital
a
bc
oa > ab> bc
Decreasing Returns to Scale
• When output increases in a smaller proportion then the increase in all inputs.
– Diseconomies outnumber economies of scale:When the firm expands beyond a point of constant return, the diseconomies outnumber
( increasing difficulties of management, co-ordination and control with the expansion in scale and output)
– Limited reserves of natural resources
Decreasing Return to Scale
IQ1
IQ2
IQ3
QX1= 100
O
R
QX2= 200
QX3 = 300
Units of Labour
Units of Capital
a
b
c
oa < ab < bc
Returns of Scale in a production process
• There are three phases in production– First Stage:
Increasing returns to scale because of a greater possibility of specialisation of labour and machinery– Second stage
Constant returns to scale – Third stage:
Firms continue to expand – decreasing returns to scale due to difficulty of co-ordination and control.
Importance of Production functions in Managerial Decision Making
• Serve as the foundation for the analysis of cost
• Optimal allocation of firms resources in short-run and long-run
• Capacity Planning• Accurate forecasts of demand• Effective communication between the production and
marketing functions
Case Study –Vandana EnterprisesOwners:Kumars ( Mr Ramesh Kumar(MD) / Vandana(daughter)
No of employees: 300No of years in Business :25Business: Textile (Spinning and weaving of white linen)Target: To expand in Domestic and Export market
When the company was started, they had 350 workers, the company used old technology to produce clothes. Labour was mainly used, while machine was minimally used.The plant was modernised and mechanized over the yearsProduction: 15000 m to 60,000m everyday (maximum technical efficiency)
What should the company be doing in order to increase Sales and increase their impact in the international market.
Case Study – Vandana Enterprises
Solution:
1) To produce Bed sheets, pillow covers etc2) To improve market Information3) Machinizing the plant further
Retrench labourImport machines
4) Hire specialised labour
Case StudyPearl Diving Operation
• Company: Peter F. Smithson• Product: Pearl• No of Years : 28• Area of Operation: North Pacific ocean• Offices: Japan and Canada• Mode of Operation
– 3 Trawlers– Hired local Japanese and Canadian divers– Coast of Japan more profitable ( Time / efficiency of
Japanese divers)– Divers intensively pearled the Japan coast ( 9 times in the
same area)
Case StudyPearl Diving Operation
• Sept –Oct data• Peter not happy with
results• Not been able to
compensate for non-operation of Canada
Q. How many divers seem to be efficient
Q. How can he modify his present plan in terms of return to scale?
Trip No
Divers Employed
Oyster recovered (Kg)
1 5 25
2 12 70
3 9 52
4 6 30
5 13 75
6 4 18
7 13 78
8 16 76
9 12 76