About Production function and law of production in short run and long run

1. THEORY OF PRODUCTION
Subject : CC03 – Managerial Economics
Class : S1 MBA (2017-19Batch)
Presented By : MUHAMMED NOWFAL
Designation : Assistant Professor
Department : Department of Management Studies
Institute : KMM College of Arts and Science – Kochi

2. LEARNING OBJECTIVES
The objective of this chapter is to make you learn about following production
related aspects
 Meaning of production and other basic terms
 Meaning and use of Production function
 Law of Production under short run
 Long run production function
 Least cost combination of inputs
 Law of returns to scale
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3. PRODUCTION – MEANING
 Process by which resources (men, material, capital, time etc.) are transformed into a
different or more useful commodity or services.
 Transforming input into output with value added.
 An input is a good or service that is used into the process of production – Production
process requires wide variety of inputs depending on the nature of the product
• Capital, Land (Stock Variable) Labour, time etc. (Flow Variables)
 An output is any good or service that comes out of production process.
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4. FIXED AND VARIABLE INPUTS
 Fixed Inputs/Fixed Factors
 Economic sense – inputs whose supply is inelastic in the short run
 Technical sense – inputs that remain fixed for a certain level of output
 Variable input / Variable factor
 Economic sense – inputs whose supply is elastic in short run
 Technical sense – inputs that changes with the change in output
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5. SHORT RUN AND LONG RUN
 Time period involved in the production process
 Short Run – period of time in which the supply of certain inputs is fixed –
production can be increased only by changing variable inputs
 Long Run – period of time in which the supply of all inputs is elastic i.e. all
inputs are variable - Amount of time needed to make all production inputs
variable
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6. PRODUCTION FUNCTION
 Functional (Technological) relationship between inputs and outputs in physical terms.
 Qualitative relationship between inputs and outputs
 Indicates the highest output that a firm can produce for every specified
combination of inputs given the state of technology.
 Shows what is technically feasible when the firm operates efficiently.
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7. PRODUCTION FUNCTION
For the sake of convenience and simplicity in the analysis of input output
relationship, production function is expressed as
Q= f (L, K)
Q = Output, K = Capital, L = Labor
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Empirical Production function :
Q= f (Ld, L, K, M, T, t)

8. PRODUCTION FUNCTION – COAL
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9. PRODUCTION FUNCTION – CONT.
1. Short fun production function – single variable production function
Q = f (L) (with constant K)
2. Long run production function
Q=f (L, K)
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10. PRODUCTION FUNCTION – ASSUMPTIONS
 Perfect divisibility of both inputs and outputs
 There are only two factors of production
 Limited substitution of one factor or the other
 A given technology
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11. ISOQUANTS
• Curves showing all possible combinations of inputs that yield the same output
• Locus of points representing various combination of two inputs i.e. capital and labour,
yielding the same output
• Assumptions
• There are only two inputs i.e. L and K to produce commodity X
• The two inputs can be substituted one for another but at a diminishing rate
• Technology of production is given
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12. PROPERTIES OF ISOQUANTS
 Isoquants have a negative slop
 The negative slop of the isoquant implies substitutability between inputs
 Isoquants are convex to the origin
 Convexity of isoquants implies not only the substitution between inputs but also diminishing
MRTS between inputs
 Isoquants do not intersect nor tangent to each other
 If they do, it violates law of production
 Upper isoquants represent higher level of output
 Upper isoquant represents a larger input combination
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13. FORMS OF ISOQUANTS -1 & 2
• Linear isoquants
 It implies perfect substitutability between the two inputs L and K
 i.e. MRTS between L and K remains constant throughout
 i.e. if Q=f(L,K) then Q=aK+bL
 Slop of Isoquant = -b/a (MRTS)
• Fixed Factor proportion or L shaped isoquants
 Such an isoquant implies zero substitutability between L and K, instead it assumes perfect
complementarity between L and K
 Is assumes there is only one technique of production and capital and Labour can be
combined only in a fixed proportion
 Fixed proportion production function is given as Q = f(L,K) = min (aK,bL)
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14. FORMS OF ISOQUANTS -3
• Kinked or Linear Programming Isoquants
 It implies that to double the production would require doubling both the inputs, L and K
 This shows that substitution of factors can be seen at the kinks since there are a few
processes to produce any one commodity.
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Technique K L K/L (Ratio)
1 OA 10 2 10:2
2 OB 6 3 6:3
3 OC 4 6 4:6
4 OD 3 10 3:10

15. ISOQUANT MAP
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Isoquant map is a set of isoquants, each isoquants shows different combinations of
two inputs L and K that can be used to produce a given level of output.

16. LAWS OF PRODUCTION
• Laws of production state the nature of relationship between output and input
• Input output relationship under short run (Laws of Variable Proposition), long run
( Laws of Returns to Scale)
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17. LAW OF DIMINISHING RETURNS
(LAWS OF VARIABLE PROPOSITION)
• This law state that when more and more units of a variable input are applied to a
given quantity of fixed inputs, the total output may initially increase at an increasing
rate and then at a constant rate but it will eventually increase at a diminishing rate
• i.e. when a firm is using two inputs such as Labour and capital – increases the labour
but capital is constant, the marginal productivity of labour may initially increase, but
it does decrease eventually
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18. LAW OF DIMINISHING RETURNS –
ASSUMPTIONS
 The state of technology is given
 Labour is homogeneous
 Input price, wages and interest are given
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19. LAW OF DIMINISHING RETURNS - Cont.
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20. LAW OF DIMINISHING RETURNS - Cont.
1. With additional workers, output (Q) increases, reaches a maximum, and then
decreases.
2. The average product of labor (AP), or output per worker, increases and then
decreases.
3. The marginal product (MP) of labor or output of the additional worker
increases rapidly initially and then decreases and becomes negative.
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L
Q
InputLabor
Output
AP 
L
Q
InputLabor
Output
MPL







21. LAW OF DIMINISHING RETURNS -
THREE STAGES OF PRODUCTION
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22. LAW OF DIMINISHING RETURNS –
FACTORS BEHIND THIS LAW
• Reasons for increasing returns
 Indivisibility of fixed factor – it results in under utilization of capital if labour is less
than optimum number
 Greater specialization or division of labour – until optimum capital labour ratio is
reached
 Once the optimum capital labour ratio is achieved employment of additional worker
amounts to substitution of capital with labour (Technically one factor can substitute
another only up to a certain limit)
 I.e. with an increase in labour, capital per unit of labour decreases – this results
decrease in marginal productivity of labour
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23. APPLICATION OF THIS LAW IN BUSINESS
• Graphical representation of this law help in identifying rational and irrational stages
of business decisions
• It give answer to questions like
• How much labour to employ to maximize the output
• what number of workers to apply to a given fixed input so that per unit cost is minimized and
output is maximized
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24. LAW OF RETURNS TO SCALE
• This law state the behavior of output in response to a proportional and simultaneous
change in inputs
• Increasing inputs proportionately and simultaneously is, in fact, an expansion of the
scale of production.
• An increase in scale means that all factor inputs are increased in the same proportion.
• In returns to scale, all the necessary factor inputs are increased or decreased to the
same extent so that whatever the scale of production, the proportion among the factors
remains the same.
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25. LAW OF RETURNS TO SCALE
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26. LAW OF RETURNS TO SCALE
Diagrammatic representation
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27. INCREASING RETURNS TO SCALE
• IRS prevails when output increases faster than inputs, i.e., percentage increase in
output exceeds percentage increase in inputs.
• This implies that output increases more than proportionately to the increase in
input and the rate of increase in output goes on increasing with each subsequent
increase in input.
• For e.g. if all the inputs of production are increased by 100% the output increases
by 150% and so on. In this kind of input-output relationship IRS exists.
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28. INCREASING RETURNS TO SCALE Cont.
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29. INCREASING RETURNS TO SCALE – Reasons
• Indivisibility of machinery and managerial power
• when scale of production is increased by increasing all inputs, the productivity of indivisible
factor increases exponentially, this results in increasing returns to scale.
• Higher degree of specialization
• The use of specialized labor and management helps in increasing productivity per units of
inputs by utilizing their cumulative efforts and thus contributes in increasing returns to scale.
• Dimensional relations
• In some cases, due to increased dimensions, output rises faster than inputs, which leads to
increasing returns to scale.
• Marketing economies
• The greater requirements of inputs and the corresponding increase of outputs lead to various
marketing economies i.e supply of quality raw material, cheaper price for raw materials -
These factors finally help to increase output fast
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30. CONSTANT RETURNS TO SCALE
• When the increase in output is proportional to increase in inputs, it
exhibits constant returns to scale
• For example, if both the inputs ( L,K) are doubled, and the output also
doubled
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31. CONSTANT RETURNS TO SCALE – Cont.
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32. CONSTANT RETURNS TO SCALE – REASONS
• The constant returns to scale arise due to the limits of economies to scale
• The producers are unable to efficiently manage the inputs with gradual increase in
scale.
• After certain time period when economies of scale end and diseconomies are yet
to begin, the returns to scale appear to be constant.
• Various communication and coordination, management (personnel, financial,
marketing) problems increase with increase in input and output, which leads to
diseconomies.
• Constant returns to scale are transitional stage between increasing and decreasing
returns to scale.
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33. DECREASING RETURNS TO SCALE
• The decreasing return to scale prevails when the output increases slower
than inputs and vice-versa.
• when output increases less than proportionately to increase in inputs (capital and
labor) and the rate of rise in output goes on decreasing, it is called decreasing
return to scale.
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34. DECREASING RETURNS TO SCALE Cont.
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35. DECREASING RETURNS TO SCALE – REASONS
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• Decreasing returns to scale arises mainly because of diseconomies of scale
• Managerial inefficiency
• Emergence of difficulties in co-ordination and control
• Difficulty in effective and better supervision
• Delays in management decisions.
• Inefficient and mis-management due to over growth and expansion of the firm.
• Productivity and efficiency declines unavoidably after a point
• Exahaustability of natural resources

36. COBB – DOUGLAS PRODUCTION FUNCTION
• The Cobb–Douglas production function is a particular functional form of
the production function, widely used to represent the technological relationship between
the amounts of two or more inputs, particularly physical capital and labor, and the amount
of output that can be produced by those inputs.
• The Cobb–Douglas form was developed and tested against statistical evidence by Charles
Cobb and Paul Douglas during 1927–1947
Expressed as Q(L,K) = AKα Lβ
Q is the quantity of products, L is the quantity of labor, K is the quantity of capital, A is a
positive constant, β and α are constants between 0 and 1.
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37. COBB – DOUGLAS PRODUCTION FUNCTION – Cont.
• In the case of the Cobb-Douglas production function:
MP (∂Q/∂L) = Aβ L(β-1) Kα
RETURNS TO SCALE
• If β+α=1 , the production function has constant returns to scale.
• If β+α > 1 , the production function has increasing returns to scale.
• If β+α < 1 , the production function has decreasing returns to scale.
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38. REFERENCES
• D N Dwiledhi, Essentials of business economics, Vikas publishing house Pvt Ltd,
New Delhi, 2009
• D.M. Mithani,Managerial Economics, 5/e, Himalaya Publishing
House,Mumbai,2011
• Yogesh, Maheswari, Management Economics,PHI Learnings, New
PHIlearning,NewDelhi,2012
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