Production function


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Production function

  1. 1. Pr oduction Function
  2. 2. 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.
  3. 3. 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
  4. 4. 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)
  5. 5. 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
  6. 6. Types of Production Function Types Short –Run (Inputs kept constant One input (Labour) is varied) Law of variable proportion Long – Run (Varying all inputs) Law of returns to scale
  7. 7. 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 No of Units of a Factor employed = Q 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 factor MP = ∆Q ∆L
  8. 8. Units of Labour Marginal Product (Quintals) Average Product (Quintals) L Total Product (Quintals) Q 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
  9. 9. Short – Run Production Function Law 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.
  10. 10. Stages of Law of Variable proportion H TP Total Product F Stage 1 D Stage 2 Stage 3 S AP Amount of Variable Factor MP
  11. 11. 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
  12. 12. 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
  13. 13. In which stage the Producer should Produce • Stage 3 – No MP of variable factor is negative • Stage 1 – No MP of fixed factor is negative Full utilisation is not there Stages of Economic absurdity / Economic non-sense / Non- economic regions • Stage 2 – Yes MP and AP are positive but diminishing
  14. 14. 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.
  15. 15. Causes • Negative Returns Number 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.
  16. 16. Technological Progress and Diminishing Returns • In today’s scenario the Technological progress can suspend the operation of diminishing returns by continually improving the techniques of production. AP4 AP3 Output AP2 AP1 Labour Force
  17. 17. 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 output Also called as equal product curve Factor Production Labour Capital A 1 12 B 2 8 C 3 5 D 4 3 E 5 2 Isoquant K L
  18. 18. 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 other Same amount of factors can produce two levels of output • Isoquants are convex to the origin Slope of isoquants diminishes from left to right, Marginal rate of technical substitution
  19. 19. Types of Isoquant The shapes depends upon degree of substitutability of inputs 1) 2) Linear Isoquant: Perfect substitutability between factors of production. An output can be produced by either using one or both 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. Q3 Q2 Q1 Q2 Q1
  20. 20. 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
  21. 21. 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 MRTS L for K = ∆K = ∆L MPL MPK – MP = Marginal productivities of labour and capital
  22. 22. 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.
  23. 23. The Law of Returns to Scale • Return to Scale: The resultant increase in total output as the two inputs increases. Total output may increase proportionately Total output may increase more than proportionately Total output may increase less than proportionately • Three types: – Constant – Increasing – Decreasing
  24. 24. 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
  25. 25. Constant Return to Scale IQ3 R IQ2 IQ1 c Units of Capital b QX3 = 300 a QX2= 200 QX1= 100 O Units of Labour oa = ab = bc
  26. 26. 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
  27. 27. Increasing Return to Scale IQ IQ2 R IQ3 c Units of Capital b a QX3 = 300 QX2= 200 QX1= 100 O Units of Labour oa > ab> bc
  28. 28. 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
  29. 29. Decreasing Return to Scale IQ3 IQ2 R c IQ1 Units of Capital b QX3 = 300 a QX2= 200 QX1= 100 O Units of Labour oa < ab < bc
  30. 30. 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.
  31. 31. 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
  32. 32. Case Study –Vandana Enterprises Owners: Kumars ( Mr Ramesh Kumar(MD) / Vandana(daughter) No of employees: 300 No of years in Business :25 Business: 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 years Production: 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.
  33. 33. Case Study – Vandana Enterprises Solution: 1) 2) 3) 4) To produce Bed sheets, pillow covers etc To improve market Information Machinizing the plant further Retrench labour Import machines Hire specialised labour
  34. 34. Case Study Pearl 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)
  35. 35. Case Study Pearl Diving Operation • • Sept –Oct data Peter not happy with results Not been able to compensate for nonoperation of Canada Q. How many divers seem to be efficient Q. How can he modify his present plan in terms of return to scale? Divers Employ ed Oyster recovered (Kg) 1 5 25 2 12 70 3 • Trip No 9 52 4 6 30 5 13 75 6 4 18 7 13 78 8 16 76 9 12 76