The Production Process and Costs

1
The Production Process and Costs

• Andreja Cirman

2
The Theory and Estimation of Production

• The Production Function
• The Cost Function

3
The Production Function

• A production function defines the relationship
  between inputs and the maximum amount that can be
  produced within a given time period with a given
  technology.
• Mathematically, the production function can be
  expressed as
• Qf(K, L)
• Q is the level of output
• K units of capital
• L units of labour
• f( ) represents the production technology

4
The Production Function

• When discussing production, it is important to
  distinguish between two time frames.
• The short-run production function describes the
  maximum quantity of good or service that can be
  produced by a set of inputs, assuming that at
  least one of the inputs is fixed at some level.
• The long-run production function describes the
  maximum quantity of good or service that can be
  produced by a set of inputs, assuming that the
  firm is free to adjust the level of all inputs

5
Production in the Short Run

• When discussing production in the short run,
  three definitions are important.

• Total Product
• Marginal Product
• Average Product

6
Production in the Short Run

• Total product (TP) is another name for output in
  the short run.
• The marginal product (MP) of a variable input is
  the change in output (or TP) resulting from a one
  unit change in the input.
• MP tells us how output changes as we change the
  level of the input by one unit.

7
Production in the Short Run

• The average product (AP) of an input is the total
  product divided by the level of the input.
• AP tells us, on average, how many units of output
  are produced per unit of input used.

8
Production in the Short Run

• Consider the two input production function
  Qf(X,Y) in which input X is variable and input Y
  is fixed at some level.
• The marginal product of input X is defined as
• holding input Y constant.

9
Production in the Short Run

• The average product of input X is defined as
• holding input Y constant.

10
Production in the Short Run

• The table below represents a firms production
  function, Qf(X,Y)

11
Production in the Short Run

• In the short run, let Y2. The row highlighted
  below represents the firms short run production
  function.

12
Production in the Short Run

• Rewriting this row, we can create the following
  table and calculate values of marginal and
  average product.

13
Calculation of Marginal Product
14
Calculation of Marginal Product
15
Calculation of Average Product
16
Calculation of Average Product
17
Production in the Short Run

• The figures illustrate TP, MP, and AP
  graphically.

18
Production in the Short Run

• If MP is positive then TP is increasing.
• If MP is negative then TP is decreasing.
• TP reaches a maximum when MP0

19
Production in the Short Run

• If MP gt AP then AP is rising.
• If MP lt AP then AP is falling.
• MPAP when AP is maximized.

20
The Law of Diminishing Returns

• Definition
• As additional units of a variable input are
  combined with a fixed input, at some point the
  additional output (i.e., marginal product) starts
  to diminish.

21
Diminishing Returns
8
10
11
10
8
5
4
-4
22
The Law of Diminishing Returns

• Reasons

23
The Three Stages of Production

• Stage I
• From zero units of the variable input to where
  AP is maximized
• Stage II
• From the maximum AP to where MP0
• Stage III
• From where MP0 on

24
The Three Stages of Production
25
Optimal Level of Variable Input Usage

• Consider the following short run production
  process.

Where is Stage II?
26
Optimal Level of Variable Input Usage
Stage II
27
Optimal Level of Variable Input Usage

• What level of input usage within Stage II is best
  for the firm?
• The answer depends upon how many units of output
  the firm can sell, the price of the product, and
  the monetary costs of employing the variable
  input.

28
Optimal Level of Variable Input Usage

• In order to determine the optimal input usage we
  assume that the firm operates in a perfectly
  competitive market for its input and its output.
• Product price, P2
• Variable input price, w10,000

29
Optimal Level of Variable Input Usage

• Define the following
• Total Revenue Product (TRP) QP
• Marginal Revenue Product (MRP)
• Total Labor Cost (TLC) wX
• Marginal Labor Cost (MLC)

30
Optimal Level of Variable Input Usage
31
Optimal Level of Variable Input Usage
32
Optimal Level of Variable Input Usage

• A profit-maximizing firm operating in perfectly
  competitive output and input markets will be
  using the optimal amount of an input at the point
  at which the monetary value of the inputs
  marginal product is equal to the additional cost
  of using that input.
• Where MRPMLC.

33
Optimal Level of Variable Input Usage

• When the firm employs multiple variable inputs,
  the firm should choose the level of the inputs
  which equates the marginal product per dollar
  across each of the inputs. Mathematically,

34
Technology advancement
C
Q
100
B
O3
A
O2
50
O1
L
0
2
3
4
5
6
7
8
9
10
1
35
Production in the Long Run

• In the long run, all inputs are variable.
• Isoquant defines cominations of inputs that yield
  the same level of product

36
Isoquant
K
E
5
4
3
A
B
C
2
Q3 90
D
Q2 75
1
Q1 55
1
2
3
4
5
L
37
Marginal rate of technical substitution (MRTS)
K
7 6 5 4 3 2 1 0
?K3
?L1
?K1
?L1
?K1/3
?L1
L
0 1 2 3 4 5 6
7
38
Perfect Substitution
K
Q2
Q1
Q3
L
39
No substitution (Leontief isoquants)
K
K1 0
Q3
Q2
Q1
L1
L
40
Production in the Long Run

• The long run production process is described by
  the concept of returns to scale.
• Returns to scale describes what happens to total
  output as all of the inputs are changed by the
  same proportion.

41
Production in the Long Run

• If all inputs into the production process are
  doubled, three things can happen
• output can more than double
• increasing returns to scale (IRTS)
• output can exactly double
• constant returns to scale (CRTS)
• output can less than double
• decreasing returns to scale (DRTS)

42
Returns to scale
increasing
K
6 5 4 3 2 1 0
30
20
10
L
0 5 10
15
43
Returns to scale
decreasing
6 5 4 3 2 1 0
K
30
20
10
L
0 5 10
15
44
Production in the Long Run
One way to measure returns to scale is to use a
coefficient of output elasticity

• If Egt1 then IRTS
• If E1 then CRTS
• If Elt1 then DRTS

45
Production in the Long Run

• Economists hypothesize that a firms long run
  production function may exhibit at first
  increasing returns, then constant returns, and
  finally decreasing returns to scale.

46
The Theory and Estimation of Cost
47
The Theory and Estimation of Cost

• The Short Run Relationship Between Production and
  Cost
• The Short Run Cost Function
• The Long Run Relationship Between Production and
  Cost
• The Long Run Cost Function
• The Learning Curve
• Economies of Scope
• Other Methods to Reduce Costs

48
SR Relationship Between Production and Cost

• A firms cost structure is intimately related to
  its production process.
• Costs are determined by the production technology
  and input prices.
• Assume the firm is a price taker in the input
  market.

49
SR Relationship Between Production and Cost

• In order to illustrate the relationship, consider
  the production process described in the table.

50
SR Relationship Between Production and Cost

• Total variable cost (TVC) is the cost associated
  with the variable input, in this case labor.
  Assume that labor can be hired at a price of
  w500 per unit. TVC has been added to the table.

51
SR Relationship Between Production and Cost

• Plotting TP and TVC illustrates that they are
  mirror images of each other.
• When TP increases at an increasing rate, TVC
  increases at a decreasing rate.

52
SR Relationship Between Production and Cost

• Total fixed cost (TFC) is the cost associated
  with the fixed inputs.
• Total cost (TC) is the cost associated with all
  of the inputs. It is the sum of TVC and TFC.
• TCTFCTVC

53
SR Relationship Between Production and Cost

• Marginal cost (MC) is the change in total cost
  associated a change in output.

• MC can also be expressed as the change in TVC
  associated with a change in output.

54
SR Relationship Between Production and Cost

• Marginal Cost has been added to the table.
• When MP is increasing, MC is decreasing.
• When MP is decreasing, MC is increasing.

55
The Short Run Cost Function

• A firms short run cost function tells us the
  minimum cost necessary to produce a particular
  output level.
• For simplicity the following assumptions are
  made
• the firm employs two inputs, labor and capital
• labor is variable, capital is fixed
• the firm produces a single product
• technology is fixed
• the firm operates efficiently
• the firm operates in competitive input markets
• the law of diminishing returns holds

56
The Short Run Cost Function

• The following average cost functions will be
  useful in our analysis.
• Average total cost (AC) is the average per-unit
  cost of using all of the firms inputs.
• Average variable cost (AVC) is the average
  per-unit cost of using the firms variable
  inputs.
• Average fixed cost (AFC) is the average per-unit
  cost of using the firms fixed inputs.

57
The Short Run Cost Function

• Mathematically,
• AVC TVC/Q
• AFC TFC/Q
• ATCTC/Q(TFCTVC)/QAFCAVC

58
The Short Run Cost Function
59
The Short Run Cost Function

• Graphically, these results are be depicted in the
  figure below.

60
The Short Run Cost Function

• Important Observations
• AFC declines steadily over the range of
  production.
• In general, AVC, AC, and MC are u-shaped.
• MC measures the rate of change of TC
• When MCltAVC, AVC is falling
• When MCgtAVC, AVC is rising
• When MCAVC, AVC is at its minimum
• The distance between AC and AVC represents AFC

61
The LR Relationship Between Production and Cost

• In the long run, all inputs are variable.
• In the long run, there are no fixed costs
• The long run cost structure of a firm is related
  to the firms long run production process.
• The firms long run production process is
  described by the concept of returns to scale.

62
The LR Relationship Between Production and Cost

• Economists hypothesize that a firms long-run
  production function may exhibit at first
  increasing returns, then constant returns, and
  finally decreasing returns to scale.
• When a firm experiences increasing returns to
  scale
• A proportional increase in all inputs increases
  output by a greater percentage than costs.
• Costs increase at a decreasing rate

63
The LR Relationship Between Production and Cost

• When a firm experiences constant returns to scale
• A proportional increase in all inputs increases
  output by the same percentage as costs.
• Costs increase at a constant rate
• When a firm experiences decreasing returns to
  scale
• A proportional increase in all inputs increases
  output by a smaller percentage than costs.
• Costs increase at an increasing rate

64
The LR Relationship Between Production and Cost

• This graph illustrates the relationship between
  the long-run production function and the long-run
  cost function.

65
The Long-Run Cost Function

• Long run marginal cost (LRMC) measures the change
  in long run costs associated with a change in
  output.
• Long run average cost (LRAC) measures the average
  per-unit cost of production when all inputs are
  variable.
• In general, the LRAC is u-shaped.

66
The Long-Run Cost Function

• When LRAC is declining we say that the firm is
  experiencing economies of scale.
• Economies of scale implies that per-unit costs
  are falling.
• When LRAC is increasing we say that the firm is
  experiencing diseconomies of scale.
• Diseconomies of scale implies that per-unit costs
  are rising.

67
The Long-Run Cost Function

• The figure illustrates the general shape of the
  LRAC.

68
The Long-Run Cost Function

• Reasons for Economies of Scale
• Increasing returns to scale
• Specialization in the use of labor and capital
• Indivisible nature of many types of capital
  equipment
• Productive capacity of capital equipment rises
  faster than purchase price

69
The Long-Run Cost Function

• Reasons for Economies of Scale

• Economies in maintaining inventory of
• replacement parts and maintenance personnel
• Discounts from bulk purchases
• Lower cost of raising capital funds
• Spreading promotional and RD costs
• Management efficiencies

70
The Long-Run Cost Function

• Reasons for Diseconomies of Scale

• Decreasing returns to scale
• Disproportionate rise in transportation costs
• Input market imperfections
• Management coordination and control
• problems
• Disproportionate rise in staff and indirect
• labor

71
The Long-Run Cost Function

• In the short run, the firm has a fixed level of
  capital equipment or plant size.
• The figure illustrates the SRAC curves for
  various plant sizes.
• Once a plant size is chosen, per-unit production
  costs are found by moving along that particular
  SRAC curve.

72
The Long-Run Cost Function

• In the long run the firm is able to adjust its
  plant size.
• LRAC tells us the lowest possible per-unit cost
  when all inputs are variable.
• What is the LRAC in the graph?

73
The Long-Run Cost Function

• The LRAC is the lower envelope of all of the SRAC
  curves.
• Minimum efficient scale is the lowest output
  level for which LRAC is minimized.

74
The Learning Curve

• Measures the percentage decrease in additional
  labor cost each time output doubles.
• An 80 percent learning curve implies that each
  time output doubles, the labor costs associated
  with the incremental output will decrease to 80
  of their previous level.
• The figure illustrates an 80-percent learning
  curve.

75
The Learning Curve

• A downward slope in the learning curve indicates
  the presence of the learning curve effect.
• workers improve their productivity with practice
• The learning curve effect acts to shift the SRAC
  downward.

76
Economies of scale and learning curve
cost per unit
Economies of scale
A
B
AC1
C
learning effect
AC2
production in units
77
Economies of Scope

• The reduction of a firms unit cost by producing
  two or more goods or services jointly rather than
  separately.

78
Other Methods to Reduce Costs

• The Strategic Use of Cost
• Reduction in the Cost of Materials
• Using IT to Reduce Costs
• Reduction of Process Costs
• Relocation to Lower-Wage Countries or Regions
• Mergers, Consolidation, and Downsizing
• Layoffs and Plant Closings

79
Estimating Cost Functions
80
Estimating Cost Functions

• Statistical Techniques
• Engineering Cost Techniques

81
Statistical techniques

• using multiple regression analysis
• linear, polynomial, logarithmic functions etc.

82
Statistical techniques-example
83
Statistical techniques-example
84
Engineering Cost Techniques

• Estimating cost function using knowledge of
  production technology
• Attempts to determine the lowest cost combination
  of labor, capital equipment and raw materials
  required to produce various levels of output

85
Engineering Cost Techniques
86
Engineering Cost Techniques - Example
87
Profit Maximization and Competitive Supply
88
Do Firms Maximize Profits

• profit is likely to dominate desicions in owner
  managed firms
• managers in larger companies may be more
  concerned with goals such as
• revenue maximization
• dividend pay-out
• on the long run they must have profit as one of
  their highest priorities

89
Profit maximization condition MR MC
90
Competitive Firm
91
Competitive Firm Incurring Losses
92
Adequate Condition for Profit Maximization P gt
AVCmin

• Even if PMRMC, the company may operate with
  profit/loss
• if PgtATCmin -gt PROFIT
• if PATCmin, -gt ZERO PROFIT
• if AVCminltPltATCmin, -gt LOSS, however lower than
  it would be if the firm had not operated
• if PAVCmin, the company is indifferent to stay
  in business or to shut down, loss is equal to TFC
• if PltAVCmin, shut down

93
Firms Supply Curve

• Since firm decides upon PMC,and considers
  PgtAVCmin, its individual supply curve equals its
  MC curve above AVCmin.

94
Firms Supply Curve
95
Market Supply

• sum of individual supply curves

96
Costs for Decision Making
97
Economic costs

• Accounting costs are historic costs
• Historical cost is the cost incurred at the time
  of procurement.
• do not incorporate opportunity costs

98
Economic costs

• For business decision making we use economic
  costs
• explicit cost
• implicit cost
• Historic costs match to some extent explicit
  costs, implicit costs are opportunity costs
• Opportunity cost is the value that is forgone in
  choosing one activity over the next best
  alternative.
• Economic Profit Accounting Profit
  Opportunity Costs

99
Costs for Decisin Making

• A cost is relevant if it is affected by a
  management decision.
• A cost is irrelevant if it is not affected by a
  management decision.

100
Costs for Decisin Making

• Sunk cost does not vary with decision options

101
Incremental Analysis

• Incremental analysis is used to analyze business
  opportunities .
• Incremental cost varies with the range of options
  available in the decision making process.
• Incremental analysis uses only decision relevant
  revenues and cost

102
Incremental Analysis Process

• Incremental Analysis Process
• Define relevant revenues and costs
• Define incremental revenues and costs
• If incremental revenues exceed incremental costs,
  take the decision, otherwise reject it

103
Classification of Costs
104
Classification of Revenues
105
Examples of Incremental Analysis

• Outsourcing opportunities for small businesses A
  quantitative analysis