PPT7 Theory of Production presentation.pptx

theory of production

1. Theory of Production Amit Prakash Jha

2. Basic Questions Faced by Producer What to produce? How much to produce? How to produce?

3. Firm A firm is an entity that combines and processes resources in order to produce output that will directly or indirectly satisfy consumer demand.

4. Factors of Production

5. Land R esource that comprises of the natural resources used in production.

6. Labour A ll those people who contribute to production by working in their own interest

7. Capital Human created assets that can enhance power to perform

8. Entrepreneur An  entrepreneur  is a person who combines the other  factors of production

9. Factor payments Land ... Rent Labour ... Wages Capital ... Interest Entrepreneur ... Profit/Loss Your prior understanding of all these terms are correct, but , meaning of these terms in day to day usage are slightly different from their economic interpretation. In fact, usage of these terms in accounting is also somewhat different from their economic interpretation, a nd this may create problems. So, for the purpose of this chapter, we will stick to their economic meaning.

10. Factors of Production Land ... All natural resources and assets Labour ... Human labour Capital ... All man made resources and assets Entrepreneur ... She is the one who takes risk

11. Factor payments Rent ... Whatever firm is paying for land Wages ... Whatever firm is paying to labour Interest ... Whatever firm is paying for capital Sum of all these factor payments is called cost and this includes opportunity cost. A firm gets revenue by selling the output. If Revenue > Cost, then there is profit and loss otherwise . Profit/Loss is the reward for Entrepreneurship Some natural resources (Land) are free (example - sunshine), some are owned by government and some are privately owned.

12. Factor payments Land ... Rent (+) Labour ... Wages (+) Capital ... Interest (+) Entrepreneur ... Profit/Loss (+/-)

13. Firm... Revisited Land Labour Capital Entrepreneur Firm Output

14. Firm... Revisited (A simplified view) FIRM I NPUT INPUT INPUT OUTPUT

15. Firm... Revisited (A further simplified view) FIRM Labour Capital OUTPUT

16. Firm... Revisited (A further simplified view) FIRM L K Q

17. Production Function Firm combines the inputs K (Capital) and L (Labour) and uses a technology, defined by the function (f), to produce maximum possible output (Q).   Output Inputs Technology

18. Cobb-Douglas Production Function Firm combines the inputs K (Capital) and L (Labour) and uses a technology, defined by the function (f), to produce maximum possible output (Q). This is not purely theoretical. Production process in many firms could be approximated by this Cobb-Douglas Production Function. A, and are parameters defining the technology adopted by the firm. It will differ from firm to firm and from technology to technology.   Examples

19. Cobb-Douglas Production Function Firm combines the inputs K (Capital) and L (Labour) and uses a technology, defined by the function (f), to produce maximum possible output (Q). This is not purely theoretical. Production process in many firms could be approximated by this Cobb-Douglas Production Function. A, and are parameters defining the technology adopted by the firm. It will differ from firm to firm and from technology to technology.   Examples

20. Example   K 6 24.5 56.3 71.8 5 4 45.9 3 2 1 10 1 2 3 4 5 6 L Time period is important

21. Example   K 6 24.5 37.1 47.4 56.3 64.3 71.8 5 22.4 33.9 43.2 51.4 58.7 65.5 4 20 30.3 38.7 45.9 52.5 58.6 3 17.3 26.3 33.5 39.8 45.5 50.8 2 14.1 21.4 27.3 32.5 37.1 41.4 1 10 15.2 19.3 23 26.3 29.3 1 2 3 4 5 6 L

22. Returns to Scale  

23. Constant Returns to Scale   ... what will be the output (Q)? Now, suppose both capital and labour are doubled ... what will be the new output (Q)?   Inputs are doubled and the output is exactly doubled ... We call it Constant Returns to scale

24. Increasing Returns to Scale   is same as ... what will be the output (Q)? Now, suppose both capital and labour are doubled ... what will be the new output (Q)?   Inputs are doubled and the output is more than doubled ... We call it Increasing Returns to scale

25. Decreasing Returns to Scale   ... what will be the output (Q)? (use calculator) Now, suppose both capital and labour are doubled ... what will be the new output (Q)?   Inputs are doubled and the output is less than doubled ... We call it Decreasing Returns to scale

26. More on returns to scale  

27. An important concept Long Run In the  Long - Run , all factors of production  are variable . Short Run In the   Short - Run at least one factor of production is considered fixed. Usually, capital is considered constant in the  short - run .

28. An important concept Long Run In the  Long - Run , all factors of production  are variable. Actual time is of little importance ! ... Long run could be years or could be just weeks Short Run In the   Short - Run at least one factor of production is considered fixed. Usually, capital is considered constant in the  short - run . Actual time is of little importance ! ...Short run could be days or could be months

29. Let us start by fixing the capital (K) (Sometimes, this is called total product of labour)  

30. Average product of labour The  average product of labour  is the total  product of labour  divided by the number of units of  labour  employed, or Q/L. The  average product of labour  is a common measure of  labour  productivity. The AP L  curve is shaped like an inverted “u”. At low production levels the AP L  tends to increase as additional  labour  is added.

31. Marginal product of labour The   marginal product of labour  (MP L ) is the change in output that results from employing an added unit of  labour . It is a feature of the  production  function, and depends on the amounts of physical capital and  labour  already in use.

32. Let us start by fixing the capital (K ) We will call it production with one variable input. Capital (K) is fixed and Labour (L) is variable...  

33. Let us start by fixing the capital (K ) We will call it production with one variable input. Capital (K) is fixed and Labour (L) is variable...  

34. Production with one variable input (Assume a time frame of per month) Amount of Labour (L) Amount of Capital (K) Total Output (Q) Average Product (Q/L) Marginal Product( Δ Q/ Δ L) 10 1 10 10 2 10 30 3 10 60 4 10 80 5 10 95 6 10 108 7 10 112 8 10 112 9 10 108 10 10 100

35. Production with one variable input (Assume a time frame of per month) Amount of Labour (L) Amount of Capital (K) Total Output (Q) Average Product (Q/L) Marginal Product ( Δ Q/ Δ L) 10 -- -- 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 9 10 108 12 -4 10 10 100 10 -8

36. Total Product of Labour

37. Production with one variable input (Assume a time frame of ‘per month’) Amount of Labour (L) Amount of Capital (K) Total Output (Q) Average Product (Q/L) Marginal Product( Δ Q/ Δ L) 10 -- -- 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 9 10 108 12 -4 10 10 100 10 -8 30

38. Total Product of Labour Output is increasing with the addition of labour. It is not only increasing, but also increasing at an increasing rate.

39. Marginal Product of Labour Marginal Product of Labour is Maximum

40. Marginal Product of Labour Marginal Product of Labour is Maximum. Till this point MP is increasing.

41. Total Product of Labour

42. Production with one variable input (Assume a time frame of per month) Amount of Labour (L) Amount of Capital (K) Total Output (Q) Average Product (Q/L) Marginal Product( Δ Q/ Δ L) 10 -- -- 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 9 10 108 12 -4 10 10 100 10 -8

43. Average/Marginal Product of Labour MP AP

44. Total Product of Labour Output is still increasing with the addition of labour. And, till now marginal product is above average product

45. Total Product of Labour At this point, that is at the red dot, MP = AP

46. Total Product of Labour Stage 1 of Production

47. Production with one variable input (Assume a time frame of per month) Amount of Labour (L) Amount of Capital (K) Total Output (Q) Average Product (Q/L) Marginal Product( Δ Q/ Δ L) 10 -- -- 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 9 10 108 12 -4 10 10 100 10 -8

48. Average/Marginal Product of Labour MP AP

49. Total Product of Labour Stage 1 of Production Stage 2 of Production

50. Three Stages of Production Stage 1 of Production Stage 2 of Production Stage 3 of Production

51. Production with one variable input K is fixed Rational firm produces in the stage II. Stage III is irrational because here the output decreases, due to chaotic conditions, with addition of labour. Resources are not fully utilised in stage I, hence it is best to produce in stage II.

52. Firm... Revisited (A further simplified view) FIRM L K Q Cost Revenue

53. Firm: A simple yet complete picture FIRM L K Q Cost Revenue Total Cost = wL + rK Total Revenue = P*Q

54. Law of Diminishing Marginal Returns The law of diminishing marginal returns predicts that after some optimal level of capacity is reached, adding an additional factor of production will actually result in smaller increases in output.

55. Law of Diminishing Marginal Returns After the point where L = 3, Marginal Product of Labour diminishes

56. Total Product of Labour Stage 1 of Production Stage 2 of Production Stage 3 of Production MP = AP

57. Total Product of Labour Increasing Returns Decreasing Returns Negative Returns Peak of Marginal Product Curve

58. Problem 3 Problem 3: Assume that the following production function holds for a firm: Also, assume that K is held fixed at 4. Calculate Total Product and Marginal Product of Labour and hence, fill the following table:   L TP MP 1 2 3 4 5 6 7 8

59. Problem 3 Problem 3: Answer:   L TP MP -- 1 200 200 2 283 83 3 346 63 4 400 54 5 447 47 6 490 43 7 529 39 8 565 36

60. Problem 4 Problem 4: (Assume Unit Price, P = ₹ 2.00 and whatever is produced is sold) Calculate the TOTAL REVENUE, TR (Hint: TR = P*TP)   L TP MP Total Revenue, TR -- 1 200 200 2 283 83 3 346 63 4 400 54 5 447 47 6 490 43 7 529 39 8 565 36

61. Problem 4 Problem 4: (Assume Unit Price, P = ₹ 2.00 (Hint: TR = P*TP)   L TP MP Total Revenue, TR -- -- 1 200 200 400 2 283 83 566 3 346 63 692 4 400 54 800 5 447 47 894 6 490 43 980 7 529 39 1058 8 565 36 1130

62. So, what is the lesson? We assume that whatever is produced is actually sold. We also assume that the price is constant (P). The Price (P) times Total Product (TP) is called Total Revenue (TR). Recall that Q is equivalent to TP.

63. So, what is the lesson? We assume that whatever is produced is actually sold. We also assume that the price is constant (P). The Price (P) times Total Product (TP) is called Total Revenue (TR). Recall that Q is equivalent to TP. Can you see that Marginal Revenue (MR) is same as Price (P)?

64. So, what is the lesson? We assume that whatever is produced is actually sold. We also assume that the price is constant (P). The Price (P) times Total Product (TP) is called Total Revenue (TR). Recall that Q is equivalent to TP. Marginal Revenue: Revenue from one additional unit of the output. Can you see that Marginal Revenue (MR) is same as Price (P)? ...It Is ... Convince Yourself (for simplicity, we assume a constant price)  

65. Problem 5 Problem 5: Assume the following production function If the capital input is fixed at 3 and the output sells for ₹ 5 per unit, determine the following total, average, and marginal products, and also marginal revenue and total revenue. Do the calculations for L = 0, L = 1, L =2, ..., L = 6  

66. Problem 5 Problem 5: Assume the following production function If the capital input is fixed at 3 and the output sells for ₹ 5 per unit, determine the following total, average, and marginal products, and also marginal revenue and total revenue. Do the calculations for L = 0, L = 1, L =2, ..., L = 6 Solution: You are, in fact, required to fill the following table   L TP AP MP MR TR

67. Problem 5 (Solution) ... Remember this?   K 6 24.5 37.1 47.4 56.3 64.3 71.8 5 22.4 33.9 43.2 51.4 58.7 65.5 4 20 30.3 38.7 45.9 52.5 58.6 3 17.3 26.3 33.5 39.8 45.5 50.8 2 14.1 21.4 27.3 32.5 37.1 41.4 1 10 15.2 19.3 23 26.3 29.3 1 2 3 4 5 6 L

68. Problem 5 (Solution) ... Remember this? K =3   K 6 24.5 37.1 47.4 56.3 64.3 71.8 5 22.4 33.9 43.2 51.4 58.7 65.5 4 20 30.3 38.7 45.9 52.5 58.6 3 17.3 26.3 33.5 39.8 45.5 50.8 2 14.1 21.4 27.3 32.5 37.1 41.4 1 10 15.2 19.3 23 26.3 29.3 1 2 3 4 5 6 L

69. Problem 5 Problem 5: Assume the following production function If the capital input is fixed at 3 and the output sells for ₹ 5 per unit, determine the following total, average, and marginal products, and also marginal revenue and total revenue. Do the calculations for L = 0, L = 1, L =2, ..., L = 6 Solution: You were, in fact, required to fill the following table   L TP AP MP TR MR -- -- -- -- 1 17.3 17.3 17.3 86.50 5 2 26.3 13.2 9 131.50 5 3 33.5 11.2 7.2 167.50 5 4 39.8 10.0 6.3 199.00 5 5 45.5 9.1 5.7 227.50 5 6 50.8 8.5 5.3 254.00 5

70. One more concept... What is Marginal Revenue Product of Labour? This is gain in revenue by employing additional labour... (K is fixed)  

71. Similarly, we have Marginal Revenue Product of Capital? This is gain in revenue by employing additional capital...(L is fixed)  

72. Come back to… Marginal Revenue Product of Labour  

73. Come back to… Marginal Revenue Product of Labour  

74. Optimal Employment of Factor of Production Consider labour hiring decision: If the marginal product of labour is high then more labour will be hired and this will increase the wage rate and with more and more labour marginal product of labour will fall and equality of the two will be achieved. If the marginal product of labour is low then firm will not hire and rather retrench, this will decrease the wage rate (opposite of the previous case) and equality of the two will be achieved . The optimal (best) condition is hence, naturally given by the above equations.  

76. How firm attacks the production problem? Firm may attempt to maximize the production for a given cost Firm may attempt to minimize the cost for a given output Produce the output to maximize the profit 1 & 2 are called constrained optimization problem There isn’t any constraint, as such, in 3 except for the production function

77. Production Isoquant … A new concept Production Isoquant : Combination of inputs that will produce a specified output Now we are more realistic. We are varying both K and L. We are in long-run.  

78. Production Isoquant Q is fixed at 200  

79. Production Isoquant Q is fixed at 200 , 350 and 450 respectively  

80. Properties of Production Isoquant 1. An isoquant slopes downward Valid Isoquant Invalid Isoquant

81. Properties of Production Isoquant 2. An isoquant is convex to its origin Valid Isoquant Invalid Isoquant

82. Properties of Production Isoquant 3. Isoquants cannot intersect Valid Isoquants Invalid Isoquants

83. Properties of Production Isoquant 4.  An isoquant should not touch the axes Valid Isoquant Invalid Isoquant

84. Properties of Production Isoquant 5. Higher isoquant means higher output

85. MRTS [Marginal Rate of Technical Substitution] This concept is associated with production isoquant. MRTS is the rate that one input can be substituted for another so that a given rate of output is maintained. MRTS is always positive. (It is negative of the slope of the isoquant) (Some books may have different convention)  

86.   NOTE: In previous slide there was a negative sign in the above equation. We measure marginal product of labour and marginal product of capital as positive quantities (we assume that we are not operating with negative returns). Here, in the above equation, all quantities are positive. On isoquant, a positive change in K is associated with a negative change in L. To ensure that MRTS remains positive, we put a minus sign before in the definition of MRTS. Slope of isoquant is obviously negative and it may be interpreted as negative of the ratio of marginal product of labour and marginal product of capital or ratio of change in capital and labour (with appropriate sign). Use of calculus avoids this sign inconsistency.  

87. Production Isocost … Another concept This is the cost function and if you fix your cost at some value then, This may be interpreted as the budget line .   Budget Constraint Rate of Capital Wage Rate

88. Production Isocost Let us fix C at 4 and assume  

89. Production Isocost C is successively fixed at 3 , 4 and 5 assume  

90. Production Isocost For different prices of capital ... Low price / High price  

91. Production Isocost For different prices of labour ... Low price / High price  

92. Optimal Employment of Inputs If our budget is fixed, we can’t produce this much

93. Optimal Employment of Inputs We can produce more with this budget

94. Optimal Employment of Inputs This is optimal

95. Optimal Employment of Inputs Budget Line ( Isocost ) will be tangent to Isoquant

96. Optimal Employment of Inputs  

97. Optimality Condition  

98. Optimality Condition (another approach) These equations also lead to,