1. Theory of Production Topic 4

2. Outline There are 3 major issues to be addressed by the theory of Production – Production behaviour in the short run – Production behaviour in the Long run – Optimal combination of inputs

3. Definition of Terms Production—the process by which a commodity or commodities are transformed into a different usable commodity. Production can be of manufacturing or Services – Manufacturing involves tangible inputs/output – Services involves intangible inputs/output— Lawyers, doctors, hairdressers, consultants

4. Definition of Terms—Conti. Input—commodities that goes into the production process; Classification – labour, capital, raw materials – Fixed input—its supply is inelastic in the SR – Variable input—its supply is elastic in the SR Output—any commodity or service that comes out of the production process

5. Definition of terms—Conti. Short Run & Long Run Short Run—a period of time in which supply of certain inputs (Plant, building and machines, etc) are fixed or inelastic. – Short Run does not necessarily refer to any specific time period like 1, 2, 3 or 4 years.

6. Definition of terms Conti. The Long Run—this refers to a period of time in which the supply of all the inputs is elastic, but not long enough to permit a change in technology. – Output can be increased by varying all the inputs The very Long run—period of time that permits change in technology

7. Production Function PF describes the technological relationship between inputs and output in physical terms It represents the technology of a firm, an industry or of the economy as a whole. It is represented Mathematically as: Q = f(L, K)

8. Production function Cont. A firm can have 2 types of Production Function—SR and LR. Short Run PF – Describes technological relationship in when one input is inelastic. – Law variable proportion/diminishing returns Long Run PF—Describes technological relationship when all the input are variable – Laws of returns to scale

9. Short Run Production Function Concepts used in the Study of SR PF – Total Product—amount of total output produced by a given amount of factor, other factors held constant. – Average Product—total output produced per unit of the factor employed – Marginal Product—Addition to total production by the employment of an extra unit of factor

10. Tabular Illustration Explain the behaviour of the concepts

11. Graphical Illustration

12. Marginal Product Curve MP changes at different levels of employment

13. The Law of Variable Proportions The law of variable proportions presents the relationship between AP, MP and TP The law states that “As successive units of a variable factor are added to a given quantity of a fixed factor, there is a point beyond which the returns to the variable factor will start to decline or diminish” (Example, refer to TP in the table)

14. Behavior of the Concepts Total Product increased at an increasing rate up to employment of 3 units of labour—check the MP Total output increased up to employment of the 7 th unit of labour As labour increased from 7 to 8, output remains constant As employment increased beyond 8, output declines

15. Behaviour of Concepts Conti. Marginal Product rises up to employment of 3 units before decline. At the employment of the 4 th and 5 th units, MP falls to 98 and 62 units respectively. Beyond the employment of 8 th unit, TP diminish, while MP become negative As regards AP, it rises up to the use of 4 units, but beyond, it declines all through.

16. Geometrical Relationship between the concepts AP curve slopes upward when MP is above it AP falls when MP is below it MP cuts the AP at its peak

17. Mathematical Relationship

18. Stages of the Law of Variable Proportion Stage 1 increases to the point where AP is maximum – During this stage, MP rises and diminish – Point of inflexion—point where TP stop increasing at an increasing rate, and start increasing at a diminishing rate.

19. Stages of the Law of Proportion Cont. Stage 2—TP continues to increase at a diminishing rate until it reaches its maximum point H Both AP and MP diminishes but positive The end of stage 2 is where MP is equal to zero

20. Stages of the Law of Variable Proportion Conti. Stage 3—Total Product declines, hence, the TP curve slopes downward Marginal product becomes negative and goes below the X axis This stage is called the stage of negative returns.

21. Stages of operation Stage 1 and stage 3 are not rational – In stage 3, MP is negative, hence the only way to produce is to reduce employment of labour – In stage 1, output can be increased by employing more labour, hence, so operating at that stage will not be rational – Rational producer will only produce where MP and AP are diminishing but positive. – Stage 2 represents the rational production decision

22. Causes of the Operation of Law Variable Proportion Increasing Returns to Scale – Indivisibility of factors 1:4 – Division and specialization of labour Diminishing Returns to scale – Fixed factor of production—cooperation of factors are needed in production – Imperfect substitutes of factors Negative returns to scale – Excessive variable factor Impairs efficiency of production

23. Production with 2 variable inputs Outline – Introduction – Concept of isoquant – Marginal Rate of Technical Substitution – Properties of isoquants – Exceptions to convexity of isoquants – Elasticity of substitution – Illustrations – Output elasticities – Laws of returns to scale – Homogeneity of production function—Cobb Douglas – Graphical illustration of PF – Isoquant map and economic region of production

24. Introduction/Concepts Production with 2 variable inputs—it is a long run analysis Employment of labour and capital increases the scale of production Hence, the long run analysis is referred to as a law of Returns to Scale.

25. Isoquant An Isoquant curve is a locus of points representing the various combinations of two inputs—capital and labour—yielding the same level of output. – Input combinations for production suggests that labour and capital can be substituted for one another, but at a diminishing rate. – The equation of Isoquant is given as: ̅=(,)

26. Isoquant Graph Illustrations of different combinations of inputs.

27. Marginal Rate of Technical Substitution/Slope of Isoquant The slope of an Isoquant shows the ability of a firm to replace one input with another while holding output constant The Slope is called MRTS and it is given as:

28. Proof

29. Tabular Illustration The slope of the isoquant (–dK/dL) defines the degree of substitutability of the factors of production

30. Slope of the Isoquant The slope of the isoquant decreases (in absolute terms) as we move downwards along the isoquant, showing the increasing difficulty in substituting K for L.

31. Properties of Isoquants Isoquants have negative slope – An increase of one factor leads to a decrease of the other to enable output to be constant Isoquants cannot intersect – Intersection means a combination can produce two levels of output Isoquants are convex to the origin – It is increasingly difficult to substitute one factor for the other.

32. Exceptions to the Convexity of Isoquants Perfect Substitute (linear isoquants) Perfect Complements Isoquants (L-shaped Isoquant) Kinked or linear programming isoquants

33. Perfect Substitute/Linear Isoquant The inputs are perfect substitutes to one another It has a straight line isoquant The MRTS is constant Line AB indicates that a given output can be produced with only L or K or both. Graph

34. Perfect Complements/L-shaped Factors are combined in fixed proportions for production It takes L-shape It assumes zero substitutability If one input is increased without the other, output remains the same.

35. Kinked or Linear Programming Isoquants This isoquants assumes limited substitutability of inputs There are only very few processes of producing a commodity This kind of isoquant is used basically in linear programme

36. Elasticity of Substitution This is a better measure of substitution as compared with the MRTS—it shows the ease of substitutability It is defined as the percentage change in K/L divided by percentage change in MRTS

37. Elasticity of Substitution Cont. The value of EOS varies between zero and infinity depending on the nature of PF. – For L-Shaped ISQ = 0 – For a linear ISQ = Infinity – For homogenous PF = 1 Illustration

38. Illustration Cont.

39. Question

40. Output Elasticities Proportionate rate of change in output with respect to L or K.

41. LAWS OF RETURNS TO SCALE Given that Q 0 = f(K, L); – Increasing the function by k gives – Q 0 * = f(kK, kL) – If Q0 increases by k = constant RTS – If Q0 increases less = Decreasing RTS – If Q0 increases by more = Increasing RTS

42. RTS and Homogenous PF A production function is said to be homogenous if when each input factor is multiplied by a positive real constant k, the constant can be completely factored out – If expn = 1, homogn of degree I – If expn less than 1, homogn of degree less than I – If expn is more than 1, homogn of degree more than 1

43. Cobb-Douglas PF

44. Graphical Illustration Increasing Returns to Scale Constant Returns to Scale

45. Decreasing Returns to Scale

46. Isoquant Map & Economic Region of Production Traditional Econ. Theory concentrates on efficient region of production That region is where: – The limit of the region is where MP = 0 – Such a point is obtained by drawing a tangent to the Isoquant curve

47. Optimal Input combination Production and cost functions are required to obtain the least-cost input combinations The cost function is given as: Labour and capital cost can be obtained as: =.+. TC = Total cost of inputs K = capital input L = Labour input Pk = unit cost of capital PL = unit cost of labour

48. Optimal Input combination conti. This is shown as ff. The slope of the isocost line is given as;

49. Determination of least cost input combination The firm is in equilibrium when it maximises its output subject to the given constraint. This is achieved when the isocost line is tangential to the highest isoquant curve. In other words:

50. Expansion Path The expansion of input and output through d point of optimal factor proportions gives the optimal expansion path. This is shown in the diagram below

51. Diagram of Expansion Path Homogenous PF Non-homogenous PF