Introductory Microeconomics (ES10001)

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
Figure 1 Optimal Output
q
Costs of Production
Revenue

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 TCa total accounting costs. We define
  economic profit as
• where TC TCa 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 ?TR / ?q
• MC ?TC / ?q
• Decision to produce additional (i.e. marginal)
  unit of q (i.e. ?q 1) depends on how this unit
  impacts upon firms 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 gt MC gt Increase q
• MR lt MC gt Decrease q
• MR MC gt 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
Figure 2 The Firm as a Production Function
r
K
q f(K, L)
L
w
Inputs Output
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 firms 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

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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 firms 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
Figure 3 LTC Constant Returns to Scale
c
LTC
15
10
5
q
0
10 20 30
25
Figure 4 LTC Decreasing Returns to Scale
c
LTC
25
12
5
q
0
10 20 30
26
Figure 5 LTC Increasing Returns to Scale
c
LTC
10
8
5
q
0
10 20 30
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
• i.e.

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Figure 6a LTC LMC
c
LTC


x
q
0
q0
q1
Tan x ?LTC / ?q
30
Figure 6b LTC LMC
c
LTC


x
q
0
q0 q1
Tan x ?LTC / ?q
31
Figure 6c LTC LMC
c
LTC


x
Tan x ?LTC / ?q
q
0
q0 q1
32
Figure 6d LTC LMC
c
LTC
x


Tan x LMC(q0)
q
0

q0
33
Figure 6e IRS Implies Decreasing LMC
c
LTC


q
0

q0
q1
34
Figure 7 IRS Implies Decreasing LMC
c


LMC
q
0
q0 q1

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
• i.e.

36
Figure 8 LTC LAC
c
LTC


x
q
0
q0
Tan x LAC(q0)
37
Figure 9 IRS Implies Decreasing LAC
c
LTC


x
z
q
0
Tan x LAC(q0)
38
Figure 10 IRS Implies Decreasing LAC
c


LAC
q
0
q0 q1

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
• qmes - minimum efficient scale

40
Figure 11 IRS and then DRS
c
LTC

q
0

qmes
41
6. Returns to Scale

• Note the relationship between LMC and LAC
• q lt qmes gt LMC lt LAC
• q qmes gt LMC LAC
• q gt qmes gt LMC gt LAC

42
Figure 12a IRS and then DRS
c
LTC

LMC lt LAC
q
0

43
Figure 12b IRS and then DRS
c
LTC

LAC LMC
LMC lt LAC
q
0

44
Figure 12c IRS and then DRS
c
LTC
LMC gt LAC

LAC LMC
LMC lt LAC
q
0

45
Figure 12d IRS and then DRS
c
LTC
LMC gt LAC

LAC LMC
LAC gt LMC
q
0

qmes
46
6. Returns to Scale

• Thus
• LAC is falling if LMC lt LAC
• LAC is flat if LMC LAC
• LAC is rising if LMC gt LAC

47

Figure 13 IRS Implies Decreasing LAC
c
LTC


q
0
LMC
LAC

q
0
qmes
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
Figure 14 Returns to a Factor
q
IRF
CRF
DRF

L
0

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
Figure 15 Returns to a Factor
c
SRTCDRF
SRTCCRF
SRTCIRF

TFC
q
0

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
Figure 16 Returns to a Factor
c
STC

STVC

SFC
q
0
57
Figure 17 Returns to a Factor
c
SMC
SAC
SAVC
SAFC
q
0
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 c0
• or
• Min c wL rK s.t q f(K, L) q0
• 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
Figure 18 Production Techniques
K
fa (2K, 1L)
2q
4K
Production Technique A (CRS)



1q
2K



L
0
1L 2L

64
Figure 19 Production Techniques
K
fa (2K, 1L)
2q
4K
Production Technique A (CRS)


fb (1K, 2L)
1q
2K

2q
Production Technique B (CRS)

1K
1q
L
0
1L 2L
4L

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
Figure 20 Production Techniques
K
fa (2K, 1L)
2q
4K
2q
3K

fb (1K, 2L)
1q
2K

2q

1K
1q
L
0
1L 2L 3L
4L

67
Figure 21 Production Techniques
K
fa (2K, 1L)
2q
4K
2q
3K

fb (1K, 2L)
1q
2K

2q

1K
1q
L
0
1L 2L 3L
4L

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
Figure 22 Production Techniques
K
fa (2K, 1L)
2q
4K
fab (1K, 1L)
2q
3K

fb (1K, 2L)
1q
2K

2q

1K
1q
L
0
1L 2L 3L
4L

70
Figure 22 Production Techniques
K
fa (2K, 1L)
2q
4K
fab (1K, 1L)
2q
3K

fb (1K, 2L)
1q
4/3q
2K

2q
2/3q

1K
1q
L
0
1L 2L 3L
4L

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 firms isoquont
  map
• Isoquont Line depicting combinations of K and L
  that yield the same level of q

72
Figure 23 Production Techniques Isoquont Map (i)
K
fa (2K, 1L)
2q
4K
2q
3.5K
1.5q
3K


fb (1K, 2L)
1q
2K

2q

1K
1q
0.5K
0.5q
L
0
1L 1.5L 2L 3L 4L

73
Figure 23 Production Techniques Isoquont Map
(ii)
K
fa (2K, 1L)
2q
4K
2q
3.5K
1.5q
3K


fb (1K, 2L)
1q
2K

2q

1K
1q
0.5K
0.5q
L
0
1L 1.5L 2L 3L 4L

74
Figure 24 Production Techniques Isoquont Map
(iii)
K
fa (2K, 1L)
2q
4K


fb (1K, 2L)
1q
2K

2q

1K
1q
L
0
1L 2L
4L

75
Figure 25 Production Techniques Isoquont Map
(iv)
K
fa (2K, 1L)
2q
4K

fb (1K, 2L)
1q
2K

2q
2q

1q
1K
1q
L
0
1L 2L
4L

76
Figure 26 Production Techniques Isoquont Map (v)
K
fa (2K, 1L)
2q
4K


fb (1K, 2L)
1q
2K
2q

2q

1q
1K
1q
L
0
1L 2L
4L

77
Figure 27 Production Techniques Isoquont Map
(vi)
K




2q


1q

L
0


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
Figure 28 Production Techniques
K
fa (2K, 1L)
2q
fc (1K, 1L)
2q

fb (1K, 2L)
1q
1q


2q
2q

1q

1q
L
0


80
8. Long- Short-Run Costs

• Only technically efficient production techniques
  (such as Technique D) would be adopted
• Thus, the firms isoquont will never be concave
  towards the origin and will in general be convex

81
Figure 29 Production Techniques
K
fa (2K, 1L)
2q
fd (1K, 1L)

2q
fb (1K, 2L)
1q


2q
2q
1q

1q

1q
L
0


82
Figure 30 Production Techniques Isoquont Map
(vii)
K
fa (2K, 1L)
2q
fd (1K, 1L)

2q
fb (1K, 2L)
1q


2q
2q
1q

1q

1q
L
0


83
Figure 31 Production Techniques Isoquont Map
(viii)
K
fa (2K, 1L)
2q
fd (1K, 1L)

2q
fb (1K, 2L)
1q


2q
2q
1q

1q

1q
L
0


84
Figure 32 Production Techniques Isoquont Map
(viv)
K



2q

1q

L
0


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 consumers indifference curve

86
Figure 33 Production Techniques Isoquont Map (x)
K



q1

q0
L
0

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
Figure 34 Returns to Scale
K
A



3K
q3
2K
1K
q2

q1
L
0

1L 2L 3L
89
8. Long- Short-Run Costs

• CRS q2 2q1
• q3 3q1
• IRS q2 gt 2q1
• q3 gt 3q1
• DRS q2 lt 2q1
• q3 lt 3q1

90
8. Long- Short-Run Costs

• We can measure the firms 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
Figure 35 Returns to a Factor
K
A


C

3K
A B
C
2K
3q
A
1K
2q

1q
L
0

1L 2L 3L
92
8. Long- Short-Run Costs

• Analogous to consumers budget constraint, we can
  also derive the firms isocost curve
• Isocost curve line depicting equal cost expended
  on inputs
• c rK wL
• Firms optimal choice - tangency condition

93
8. Long- Short-Run Costs

• Recall - firms problem
• Max q f(K, L) s.t c wL rK c0
• or
• Min c wL rK s.t q f(K, L) q0

94
Figure 36 Optimal Input Decision
K
c1/r



E1
K1

q1
L
0

c1/w
L1
95
8. Long- Short-Run Costs

• Consider SR / LR cost of producing q
• SR cost (say, when K K1) is higher than LR cost
  except for one particular level of q
• In the following example, c1 is minimum cost of
  producing q1 in both SR and LR
• Rationale? Given (r, w), K1 is optimum (i.e.
  cost-minimising) level of K with which to produce
  q1

96
Figure 37 LRTC and SRTC
K
c2
A


c1

c0
E0 E1
E2
K1
q2

q1
q0
L
0


97
8. Long- Short-Run Costs

• Thus, for every level of q ? q1, 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
Figure 38 LRTC and SRTC
c
LTC
STC(K)

E1
q
0
q1

99
8. Long- Short-Run Costs

• Consider underlying marginal cost curves
• At q1, slopes of the SRTC and LRTC curve are
  equal such that SRMC LRMC
• For all q lt (gt) q1, slope SRTC lt (gt) LRTC such
  that SRMC cuts LRMC from below and to the left at
  q1

100
8. Long- Short-Run Costs

• Now consider underling average cost curves
• SRAC LRAC at q1 whilst SRAC gt LRAC for all q ?
  q1 such that SRAC and LRAC are tangent at q1
• N.B. Tangency does not imply that SRAC is at a
  minimum at q1, 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
Figure 40 LRAC Envelopes the SRAC
c
LMC
SMC1
LAC
SAC1


q
0
q1

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
Figure 37 LRTC and SRTC
K
A



K1
q1

K0
q0
c1
c0
L
0


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
Figure 39 LRAC Envelopes the SRAC
c
SAC1
LAC

SAC2

SAC3
SAC4
SAC5
SAC6
q
0

qmes
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
Figure 40 LRAC Envelopes the SRAC
c
LMC
SMC3
SMC1
LAC
SAC1
SAC3

SMC2

SAC2
q
0
q1 q2 qmes
q3

108
9. Final Comments

• We now turn our attention to the revenue side of
  the firms 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