Title: The Production Process and Costs
1The Production Process and Costs
2The Theory and Estimation of Production
- The Production Function
- The Cost Function
3The 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
4The 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
5Production in the Short Run
- When discussing production in the short run,
three definitions are important.
- Total Product
- Marginal Product
- Average Product
6Production 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.
7Production 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.
8Production 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.
9Production in the Short Run
- The average product of input X is defined as
-
- holding input Y constant.
10Production in the Short Run
- The table below represents a firms production
function, Qf(X,Y)
11Production in the Short Run
- In the short run, let Y2. The row highlighted
below represents the firms short run production
function.
12Production in the Short Run
- Rewriting this row, we can create the following
table and calculate values of marginal and
average product.
13Calculation of Marginal Product
14Calculation of Marginal Product
15Calculation of Average Product
16Calculation of Average Product
17Production in the Short Run
- The figures illustrate TP, MP, and AP
graphically. -
18Production 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
19Production 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.
20The 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.
21Diminishing Returns
8
10
11
10
8
5
4
-4
22The Law of Diminishing Returns
23The 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
24The Three Stages of Production
25Optimal Level of Variable Input Usage
- Consider the following short run production
process.
Where is Stage II?
26Optimal Level of Variable Input Usage
Stage II
27Optimal 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.
28Optimal 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
29Optimal 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)
30Optimal Level of Variable Input Usage
31Optimal Level of Variable Input Usage
32Optimal 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.
33Optimal 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,
34Technology advancement
C
Q
100
B
O3
A
O2
50
O1
L
0
2
3
4
5
6
7
8
9
10
1
35Production in the Long Run
- In the long run, all inputs are variable.
- Isoquant defines cominations of inputs that yield
the same level of product
36Isoquant
K
E
5
4
3
A
B
C
2
Q3 90
D
Q2 75
1
Q1 55
1
2
3
4
5
L
37Marginal 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
38Perfect Substitution
K
Q2
Q1
Q3
L
39No substitution (Leontief isoquants)
K
K1 0
Q3
Q2
Q1
L1
L
40Production 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.
41Production 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)
42Returns to scale
increasing
K
6 5 4 3 2 1 0
30
20
10
L
0 5 10
15
43Returns to scale
decreasing
6 5 4 3 2 1 0
K
30
20
10
L
0 5 10
15
44Production 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
45Production 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.
46The Theory and Estimation of Cost
47The 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
48SR 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.
49SR Relationship Between Production and Cost
- In order to illustrate the relationship, consider
the production process described in the table.
50SR 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.
51SR 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.
52SR 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
53SR 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.
54SR 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.
55The 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
56The 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.
57The Short Run Cost Function
- Mathematically,
- AVC TVC/Q
- AFC TFC/Q
-
- ATCTC/Q(TFCTVC)/QAFCAVC
58The Short Run Cost Function
59The Short Run Cost Function
- Graphically, these results are be depicted in the
figure below.
60The 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
61The 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.
62The 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
63The 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
64The LR Relationship Between Production and Cost
- This graph illustrates the relationship between
the long-run production function and the long-run
cost function.
65The 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.
66The 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.
67The Long-Run Cost Function
- The figure illustrates the general shape of the
LRAC.
68The 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
69The 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
70The 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
71The 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.
72The 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?
73The 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.
74The 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.
75The 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.
76Economies of scale and learning curve
cost per unit
Economies of scale
A
B
AC1
C
learning effect
AC2
production in units
77Economies of Scope
- The reduction of a firms unit cost by producing
two or more goods or services jointly rather than
separately.
78Other 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
79Estimating Cost Functions
80Estimating Cost Functions
- Statistical Techniques
- Engineering Cost Techniques
81Statistical techniques
- using multiple regression analysis
- linear, polynomial, logarithmic functions etc.
82Statistical techniques-example
83Statistical techniques-example
84Engineering 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
85Engineering Cost Techniques
86Engineering Cost Techniques - Example
87Profit Maximization and Competitive Supply
88Do 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
89Profit maximization condition MR MC
90Competitive Firm
91Competitive Firm Incurring Losses
92Adequate 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
93Firms Supply Curve
- Since firm decides upon PMC,and considers
PgtAVCmin, its individual supply curve equals its
MC curve above AVCmin.
94Firms Supply Curve
95Market Supply
- sum of individual supply curves
96Costs for Decision Making
97Economic costs
- Accounting costs are historic costs
- Historical cost is the cost incurred at the time
of procurement. - do not incorporate opportunity costs
98Economic 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
99Costs 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.
100Costs for Decisin Making
- Sunk cost does not vary with decision options
101Incremental 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
102Incremental 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
103Classification of Costs
104Classification of Revenues
105Examples of Incremental Analysis
- Outsourcing opportunities for small businesses A
quantitative analysis