1. Introductory Microeconomics (ES10001) Topic 4: Production and Costs

2. 1.Introduction We now begin to look behind the Supply Curve Recall: Supply curve tells us: Quantity sellers willing to supply at particular price per unit; Minimum price per unit sellers willing to sell particular quantity Assumed to be upward sloping

3. 1.Introduction We assume sellers are owner-managed firms (i.e. no agency issues) Firms objective is to maximise profits Thus, supply decision must reflect profit-maximising considerations Thus to understand supply decision, we need to understand profit and profit maximisation

4. Revenue Costs of Production q*q* ‘Optimal’ Output Figure 1: Optimal Output

5. 2.Profit Profit = Total Revenue (TR) - Total Costs (TC) Note the important distinction between Economic Profit and Accounting Profit Opportunity Cost (OC) - amount lost by not using a particular resource in its next best alternative use. Accountants ignore OC - only measure monetary costs

6. 2.Profit Example: self-employed builder earns £10 and incurs £3 costs; his accounting profit is thus £7 But if he had the alternative of working in MacDonalds for £8, then self-employment ‘costs’ him £1 per period. Thus, it would irrational for him to continue working as a builder

7. 2.Profit Formally, we define accounting profit as: where TC a = total accounting costs. We define economic profit as: where TC = TC a + OC denotes total costs

8. 2.Profit Thus: Thus, economists include OC in their (stricter) definition of profits

9. 2.Profit Define Normal (Economic) Profit That is, where accounting profit just covers OC such that the firm is doing just as well as its next best alternative.

10. 2.Profit Define Super-normal (Economic) Profit: Supernormal profit thus provides true economic indicator of how well owners are doing by tying their money up in the business

11. 3.The Production Decision Optimal (i.e. profit-maximising) q (i.e. q * ) depends on marginal revenue (MR) and marginal cost (MC) Define:MR = Δ TR / Δ q MR = Δ TC / Δ q Decision to produce additional (i.e. marginal) unit of q (i.e. Δ q = 1) depends on how this unit impacts upon firm’s total revenue and total costs

12. 3.The Production Decision If additional unit of q contributes more to TR than TC, then the firm increase production by one unit of q If additional unit of q contributes less to TR than TC, then the firm decreases production by one unit of q Optimal (i.e. profit maximising) q (i.e. q * ) is where additional unit of q changes TR and TC by the same amount

13. 3.The Production Decision Strategy: MR > MC => Increase q MR Decrease q MR = MC => Optimal q (i.e. q * ) Thus, two key factors: Costs firm incurs in producing q Revenue firm earns from producing q We will look at each of these factors in turn.

14. 3.The Production Decision Revenue affected by factors external to the firm. essentially, the environment within which it operates Is it the only seller of a particular good, or is it one of many? Does it face a single rival? We will explore the environments of perfect competition, monopoly and imperfect competition But first, we explore costs

15. 4.Costs If the firm wishes to maximise profits, then it will also wish to minimise costs. Two key factors determine costs of production: Cost of productive inputs Productive efficiency of firm i.e. how much firm pays for its inputs; and the efficiency with which it transforms these inputs into outputs.

16. 4.Costs Formally, we envisage the firm as a production function: q = f(K, L) Firm employs inputs of, e.g., capital (K) and labour (L) to produce output (q) Assume cost per unit of capital is r and cost per unit of labour is w

17. K L q = f(K, L) Figure 2: The Firm as a Production Function InputsOutput r w

18. 4.Costs Assume for simplicity that the unit cost of inputs are exogenous to the firm Thus, it can employ as many units of K and L it wishes at a constant price per unit To be sure, if w = £5, then one unit of L would cost £5 and 6 units of L would cost £30 Consider, then, productive efficiency

19. 5. Productive Efficiency We describe efficiency of the firm’s productive relationship in two ways depending on the time scale involved: Long Run:Period of time over which firm can change all of its factor inputs Short Run:Period of time over which at least one of its factor is fixed. We describe productive efficiency in: Long Run:‘Returns to Scale’ Short Run:‘Returns to a Factor’

20. 6.Returns to Scale Describes the effect on q when all inputs are changed proportionately e.g. double (K, L); triple (K, L); increase (K, L), by factor of 1.7888452 Does not matter how much we increase capital and labour as long as we increase them in the same proportion

21. 6.Returns to Scale Increasing Returns to Scale: Equi-proportionate increase in all inputs leads to a more than equi- proportionate increase in q Decreasing Returns to Scale: Equi-proportionate increase in all inputs leads to a less than equi- proportionate increase in q Constant Returns to Scale: Equi-proportionate increase in all inputs leads to same equi- proportionate increase in q

22. 6.Returns to Scale What causes changes in returns to scale? Economies of Scale: Indivisibilities; specialisation; large Scale / better machinery Diseconomies of Scale: Managerial diseconomies of Scale; geographical diseconomies Balance of two forces is an empirical phenomenon (see Begg et al, pp. 111-113)

23. 6.Returns to Scale How do returns to scale relate to firm’s long run costs? Efficiency with which firm can transform inputs into output in the long run will affect the cost of producing output in the long run And this, will affect the shape of the firms long run total cost curve

24. c 0 q LTC 10 20 30 5 10 15 Figure 3: LTC & Constant Returns to Scale

25. c 0 q LTC 10 20 30 5 12 25 Figure 4: LTC & Decreasing Returns to Scale

26. c 0 q LTC 10 20 30 5 8 10 Figure 5: LTC & Increasing Returns to Scale

27. 6.Returns to Scale LTC tells firm much profit is being made given TR; but firm wants to know how much to produce for maximum profit. For this it needs to know MR and MC So can LTC tell us anything about LMC? Yes!

28. 6.Returns to Scale Slope of line drawn tangent to LTC curve at particular level of q gives LMC of producing that level of q 1.e.

29. c 0 q LTC q 0 q 1 x Figure 6a: LTC & LMC Tan x =  LTC /  q

30. c 0 q LTC q 0 q 1 x Figure 6b: LTC & LMC Tan x =  LTC /  q

31. c 0 q LTC q 0 q 1 x Figure 6c: LTC & LMC Tan x =  LTC /  q

32. c 0 q LTC Figure 6d: LTC & LMC Tan x = LMC(q 0 ) q0q0 x

33. c 0 q LTC Figure 6e: IRS Implies Decreasing LMC q 0 q 1

34. c 0 q LMC Figure 7: IRS Implies Decreasing LMC q 0 q 1

35. 6.Returns to Scale Similarly, slope of line drawn from origin to point on LTC curve at particular level of q gives LAC of producing that level of q 1.e.

36. c 0 q LTC q 0 x Figure 8: LTC & LAC Tan x = LAC(q 0 )

37. c 0 q LTC z Figure 9: IRS Implies Decreasing LAC Tan x = LAC(q 0 ) x

38. c 0 q LAC Figure 10: IRS Implies Decreasing LAC q 0 q 1

39. 6.Returns to Scale Generally, we will assume that firms first enjoy increasing returns to scale (IRS) and then decreasing returns to scale (DRS) Thus, there is an implied ‘efficient’ size of a firm i.e. when it has exhausted all its IRS q mes - ‘minimum efficient scale’

40. c 0 q LTC Figure 11: IRS and then DRS q mes

41. 6.Returns to Scale Note the relationship between LMC and LAC: q < q mes  LMC < LAC q = q mes  LMC = LAC q > q mes  LMC > LAC

42. c 0 q LTC Figure 12a: IRS and then DRS LMC < LAC

43. c 0 q LTC Figure 12b: IRS and then DRS LMC < LAC LAC =LMC

44. c 0 q LTC Figure 12c: IRS and then DRS LMC < LAC LAC =LMC LMC > LAC

45. c 0 q LTC Figure 12d: IRS and then DRS LAC > LMC LAC =LMC LMC > LAC q mes

46. 6.Returns to Scale Thus: LAC is fallingif:LMC < LAC LAC is flat if:LMC = LAC LAC is rising if: LMC > LAC

47. c 0 q LTC q0 q mes LMC LAC Figure 13: IRS Implies Decreasing LAC

48. 7. Returns to a Factor Returns to a factor describe productive efficiency in the short run when at least one factor is fixed Usually assumed to be capital Short-run production function:

49. 7. Returns to a Factor Increasing Returns to a Factor: Increase in variable factor leads to a more than proportionate increase in q Decreasing Returns to a Factor: Increase in variable factor leads to a less than proportionate increase in q Constant Returns to a Factor: Increase in variable factor leads to same proportionate increase in q

50. q 0 L CRF DRF IRF Figure 14: Returns to a Factor Short-Run Production Function:

51. 7. Returns to a Factor Implications for short-run total cost curve Constant returns to a factor implies we can double q by doubling L; if unit price of L is constant, this implies a doubling of cost Similarly, if returns to a factor are increasing (i.e. less than doubling of costs) or decreasing (more than doubling of costs)

52. c 0 q SRTC CRF SRTC IRF SRTC DRF TFC Figure 15: Returns to a Factor

53. 7. Returns to a Factor Fixed and Variable Costs Since in the short run at least one factor is fixed, the costs associated with that factor will also be fixed and so will not vary with output Thus, in the short run, costs are either: Fixed:Do not vary with q (e.g. rent) Variable: Vary with q (e.g. energy, wages)

54. 7. Returns to a Factor Formally: Or:

55. 7. Returns to a Factor The ‘Law of Diminishing Returns’ Whatever we assume about the returns to scale characteristics of a production function, it is always that case that decreasing returns to a factor (i.e. diminishing returns) will eventually set in Intuitively, it becomes increasingly difficult to raise q by adding increasing quantities of a variable input (e.g. L) to a fixed quantity of the other input (e.g. K)

56. c 0 q STVC STC SFC Figure 16: Returns to a Factor

57. c 0 q SMC SAVC SAC SAFC Figure 17: Returns to a Factor

58. 8. Long- & Short-Run Costs What is the relationship between long-run and short- run costs? The latter are derived for a particular level of the fixed input (i.e. capital) We can examine the relationship via the tools we developed in our study of consumer theory

59. 8. Long- & Short-Run Costs We envisage the firm as choosing to maximise its output subject to a cost constraint or: Minimising its costs subject to an output constraint N.B. Assumption of competitive markets

60. 8. Long- & Short-Run Costs Formally: Max q = f(K, L) s.t c = wL + rK = c 0 or: Min c = wL + rK s.t q = f(K, L) = q 0 N.B. Duality!

61. 8. Long- & Short-Run Costs First, consider the production function We envisage this as a collection of all efficient production techniques Production Technique: Using particular combination of inputs (K, L) to produce output (q) Consider the following:

62. 8. Long- & Short-Run Costs Assume firm has two production techniques (A, B) both of which exhibit CRS Technique A requires 2 units of K and 1 unit of L to produce 1 unit of q Technique B requires 1 unit of K and 2 units of L to produce 1 unit of q;

63. K 0 L 1q1q 2q2q 1L 2L Figure 18: Production Techniques 4K4K 2K f a (2K, 1L) Production Technique A (CRS)

64. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 4L Figure 19: Production Techniques 4K4K 2K f a (2K, 1L) Production Technique A (CRS) Production Technique B (CRS)

65. 8. Long- & Short-Run Costs We assume that firm can combine the two techniques For example, produce 1 unit of q via Production Technique A and 1 unit of q via Production Technique B

66. K 0 L 3K 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 3L 4L Figure 20: Production Techniques 4K4K 2K f a (2K, 1L) 2q2q

67. K 0 L 3K 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 3L 4L Figure 21: Production Techniques 4K4K 2K f a (2K, 1L) 2q2q

68. 8. Long- & Short-Run Costs By combining techniques A and B in this way, the firm has effectively created a third technique i.e. Technique ‘AB’ Technique AB requires 1.5 unit of K and 1.5 unit of L to produce 1 unit of q

69. K 0 L 3K 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 3L 4L Figure 22: Production Techniques 4K4K 2K f a (2K, 1L) 2q2q f ab (1K, 1L)

70. K 0 L 3K 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 3L 4L Figure 22: Production Techniques 4K4K 2K f a (2K, 1L) 2q2q f ab (1K, 1L) 4/3q 2/3q

71. 8. Long- & Short-Run Costs If the firm is able to combine the two production techniques in any proportion, then it will be able to produce 2 units of q (or indeed, any level of q) by any combination of K and L We can thus begin to derive the firm’s isoquont map Isoquont: Line depicting combinations of K and L that yield the same level of q

72. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 1.5L 2L 3L 4L Figure 23: Production Techniques Isoquont Map (i) 4K4K 2K f a (2K, 1L) 2q2q 3K3K 1.5q 3.5K 0.5K 0.5q

73. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 1.5L 2L 3L 4L Figure 23: Production Techniques Isoquont Map (ii) 4K4K 2K f a (2K, 1L) 2q2q 3K3K 1.5q 3.5K 0.5K 0.5q

74. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 4L Figure 24: Production Techniques Isoquont Map (iii) 4K4K 2K f a (2K, 1L)

75. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 4L Figure 25: Production Techniques Isoquont Map (iv) 4K4K 2K f a (2K, 1L) 1q1q 2q2q

76. K 0 L 1q1q 1q1q f b (1K, 2L) 2q2q 2q2q 1K 1L 2L 4L Figure 26 Production Techniques Isoquont Map (v) 4K4K 2K f a (2K, 1L) 1q1q 2q2q

77. K 0 L Figure 27: Production Techniques Isoquont Map (vi) 1q1q 2q2q

78. 8. Long- & Short-Run Costs Consider discovery of production technique C Technique C also exhibits CRS But Technique C requires more inputs than Technique AB to produce q It is therefore technically inefficient and would not be adopted by a profit maximising firm

79. K 0 L 1q1q 1q1q f c (1K, 1L) f b (1K, 2L) 2q2q 2q2q Figure 28: Production Techniques f a (2K, 1L) 1q1q 2q2q 1q1q 2q

80. 8. Long- & Short-Run Costs Only technically efficient production techniques (such as Technique D) would be adopted Thus, the firm’s isoquont will never be concave towards the origin and will in general be convex

81. K 0 L 1q1q 1q1q f d (1K, 1L) f b (1K, 2L) 2q2q 2q Figure 29: Production Techniques f a (2K, 1L) 1q1q 2q2q 1q1q 2q2q

82. K 0 L 1q1q 1q1q f d (1K, 1L) f b (1K, 2L) 2q2q 2q2q Figure 30: Production Techniques Isoquont Map (vii) f a (2K, 1L) 1q1q 2q2q 1q1q 2q2q

83. K 0 L 1q1q 1q1q f d (1K, 1L) f b (1K, 2L) 2q2q 2q2q Figure 31: Production Techniques Isoquont Map (viii) f a (2K, 1L) 1q1q 2q2q 1q1q 2q2q

84. K 0 L Figure 32: Production Techniques Isoquont Map (viv) 1q1q 2q2q

85. 8. Long- & Short-Run Costs The more technically efficient techniques there are, each using K and L in different proportions, then the more kinks there will be in the isoquont and the more it will come to resemble a smooth curve, convex to the origin Analogous to consumer’s indifference curve

86. K 0 L q0q0 q1q1 Figure 33: Production Techniques Isoquont Map (x)

87. 8. Long- & Short-Run Costs We can measure the firms Returns to Scale in terms of isoquonts by moving along a ray from the origin i.e. returns to scale implies that firm is in the long run and can change both K and L inputs Thus:

88. K 0 L q 1 q2q2 Figure 34: Returns to Scale q3q3 1L 2L 3L 1K1K 3K3K 2K2K A

89. 8. Long- & Short-Run Costs CRS: q 2 = 2q 1 q 3 = 3q 1 IRS: q 2 > 2q 1 q 3 > 3q 1 DRS: q 2 < 2q 1 q 3 < 3q 1

90. 8. Long- & Short-Run Costs We can measure the firm’s Returns to a Factor (i.e. K) by moving along a horizontal line from the particular level of K being held fixed Note that firm will always incur decreasing returns to a factor, irrespective of its returns to scale In what follows, we have CRS but DRF - successively larger increases in L are required to yield proportionate increases in q

91. K 0 L 1q1q 2q2q Figure 35: Returns to a Factor 3q 1L 2L 3L 1K1K 3K3K 2K2K A B C A’A’ C’C’ A

92. 8. Long- & Short-Run Costs Analogous to consumer’s budget constraint, we can also derive the firm’s isocost curve Isocost curve: line depicting equal cost expended on inputs c = rK + wL Firm’s optimal choice - tangency condition

93. 8. Long- & Short-Run Costs Recall - firm’s problem: Max q = f(K, L) s.t c = wL + rK = c 0 or: Min c = wL + rK s.t q = f(K, L) = q 0

94. K 0 L q1q1 c1/wc1/w c1/rc1/r Figure 36: Optimal Input Decision E1E1 L1L1 K1K1

95. 8. Long- & Short-Run Costs Consider SR / LR cost of producing q SR cost (say, when K = K 1 ) is higher than LR cost except for one particular level of q In the following example, c 1 is minimum cost of producing q 1 in both SR and LR Rationale? Given (r, w), K 1 is optimum (i.e. cost- minimising) level of K with which to produce q 1

96. K 0 L q 0 q1q1 Figure 37: LRTC and SRTC q2q2 E 0 E 1 E 2 c2c2 c1c1 c0c0 K1K1 A

97. 8. Long- & Short-Run Costs Thus, for every level of q ≠ q 1, short-run costs exceed long-run costs Assuming increasing returns and then decreasing returns to both scale and to a factor, it must be the case that the short-run total cost curve (for a particular level of K) lays above the long-run total cost curve except at one particular level of output Thus:

98. c 0 q LTC Figure 38: LRTC and SRTC STC(K * ) q1q1 E1E1

99. 8. Long- & Short-Run Costs Consider underlying marginal cost curves At q 1, slopes of the SRTC and LRTC curve are equal such that SRMC = LRMC For all q ) q 1, slope SRTC ) LRTC such that SRMC cuts LRMC from below and to the left of q 1

100. 8. Long- & Short-Run Costs Now consider underling average cost curves SRAC = LRAC at q 1 whilst SRAC > LRAC for all q ≠ q 1 such that SRAC and LRAC are tangent at q 1 N.B. Tangency does not imply that SRAC is at a minimum at q 1, only that SRAC will fall/rise more rapidly than LRAC as q expands/contracts (i.e. not implication that SRAC will rise in absolute terms)

101. c 0 q LAC SAC 1 Figure 40: LRAC Envelopes the SRAC q 1 LMC SMC 1

102. 8. Long- & Short-Run Costs Now consider change in fixed level of capital Recall - each short-run total cost curve is drawn for a specific level of fixed capital As fixed level of K rises, level of q at which SRTC = LRTC also rises

103. K 0 L q 0 q 1 Figure 37: LRTC and SRTC c1c1 c0c0 K0K0 K 1 A

104. 8. Long- & Short-Run Costs If both LRAC & SRAC are u-shaped, then it must be the case that the former is an envelope of the latter

105. c 0 q LAC SAC 1 SAC 2 SAC 3 SAC 4 SAC 5 SAC 6 Figure 39: LRAC Envelopes the SRAC q mes

106. 8. Long- & Short-Run Costs Note the tangencies between the LRAC curve and the various SRAC curves Implication - SRAC will fall and rise more rapidly than LRAC as q contracts or expands

107. c 0 q LAC SAC 1 SAC 3 SMC 2 Figure 40: LRAC Envelopes the SRAC q 1 q 2 = q mes q 3 LMC SMC 1 SMC 3 SAC 2

108. V4. Final Comments We now turn our attention to the revenue side of the firm’s profit maximising decision We need to understand how revenue changes as we change output i.e. Marginal Revenue (MR) And how MR is determined by market environment within which the firm operates