Production Economics
• Managers must decide not only what to produce for the
market, but also how to produce it in the most efficient or least
cost manner.
• Economics offers widely accepted tools for judging whether
the production choices are least cost.
• A production function relates the most that can be produced
from a given set of inputs.
» Production functions allow measures of the marginal
product of each input.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
The Production Function
• A Production Function is the maximum feasible
quantity from any amounts of inputs
• If L is labor and K is capital, one popular
functional form is known as the Cobb-Douglas
Production Function
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 2
The Production Function (con’t)
• Q = a • K b1• L b2
is a Cobb-
Douglas
Production Function
• The number of inputs is typically greater
than just K & L. But economists simplify
by suggesting some, like materials or labor,
is variable, whereas plant and equipment is
fairly fixed in the short run.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
The Short Run
Production Function
• Short Run Production Functions:
» Max output, from a n y set of inputs
» Q = f ( X1, X2, X3, X4, X5 ... )
FIXED IN SR
VARIABLE IN SR
_
_
Q = f ( K, L) for two input case, where K is Fixed
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 4
The Short Run
Production Function (con’t)
• A Production Function with only one
variable input is easily analyzed. The
one variable input is labor, L. Q = f(
L)
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 5
• Average Product = Q / L
» output per labor
• Marginal Product = DQ/DL =Q/L = dQ/dL
» output attributable to last unit of labor applied
• Similar to profit functions, the Peak of MP
occurs before the Peak of average product
• When MP = AP, this is the peak of the AP
curve
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 6
Law of Diminishing Returns
INCREASES IN ONE FACTOR OF PRODUCTION,
HOLDING ONE OR OTHER FACTORS FIXED,
AFTER SOME POINT,
MARGINAL PRODUCT DIMINISHES.
MP
A SHORT
RUN LAW
point of
diminishing
returns
Variable input
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 7
Bottlenecks in Production
Plants
• Boeing found diminishing returns in ramping up
production.
• It sought ways to adopt lean production
techniques, cut order sizes, and outsourced work
at bottlenecked plants.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 8
Increasing Returns and Network
Effects
• There are exceptions to the law of
diminishing returns.
• When the installed base of a network
product makes efforts to acquire new
customers increasing more productive, we
have network effects
» Outlook and Microsoft Office
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Table 7.2:
Total, Marginal & Average Products
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 10
Total, Marginal & Average Products
Marginal Product
Average
Product
3
4
5
6
7
8
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
The maximum MP occurs before the maximum AP
Slide 11
• When MP > AP, then AP is RISING
» IF YOUR MARGINAL GRADE IN THIS CLASS IS HIGHER THAN
YOUR GRADE POINT AVERAGE, THEN YOUR G.P.A. IS RISING
• When MP < AP, then AP is FALLING
» IF YOUR MARGINAL BATTING AVERAGE IS LESS THAN THAT
OF THE NEW YORK YANKEES, YOUR ADDITION TO THE
TEAM WOULD LOWER THE YANKEE’S TEAM BATTING
AVERAGE
• When MP = AP, then AP is at its MAX
» IF THE NEW HIRE IS JUST AS EFFICIENT AS THE AVERAGE
EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOESN’T
CHANGE
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 12
Three stages of production
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 13
Three stages of production
• Stage 1: average product rising.
» Increasing returns
• Stage 2: average product declining (but marginal
product positive).
» Decreasing returns
• Stage 3: marginal product is negative, or total
product is declining.
» Negative returns
L
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 14
Determining the Optimal Use of
the Variable Input
• HIRE, IF GET MORE
REVENUE THAN
COST
• HIRE if
DTR/DL > DTC/DL
• HIRE if the marginal
revenue product >
marginal factor cost:
MRP L > MFC L
• AT OPTIMUM,
MRP L = W  MFC
MRP L  MP L • P Q = W
wage
W
W  MFC
•
MRPL
optimal labor
MPL
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
L
Slide 15
Optimal Input Use at L = 6
Table 7.3
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 16
Production Functions with multiple
variable inputs
• Suppose several inputs are variable
» greatest output from any set of inputs
• Q = f( K, L ) is two input example
• MP of capital and MP of labor are the derivatives of the
production function
» MPL = Q/L = DQ/DL
• MP of labor declines as more labor is applied. Also the
MP of capital declines as more capital is applied.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 17
Isoquants & LR Production Functions
• In the LONG RUN, ALL factors are
variable
• Q = f ( K, L )
• ISOQUANTS -- locus of input
combinations which produces the
same output
» Points A & B are on the same
isoquant
• SLOPE of ISOQUANT from A to B
is ratio of Marginal Products, called
the MRTS, the marginal rate of
technical substitution = -DK /DL
ISOQUANT
MAP
K
Q3
C
B
Q2
A
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Q1
L
Slide 18
Optimal Combination of Inputs
• The objective is to minimize cost for a given output
• ISOCOST lines are the combination of inputs for a given cost,
C0
• C0 = CL·L + CK·K
• K = C0/CK - (CL/CK)·L
• Optimal where:
» MPL/MPK = CL/CK·
» Rearranged, this becomes the equimarginal criterion
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 19
Optimal Combination of Inputs
Equimarginal Criterion:
Produce where
MPL/CL = MPK/CK where
marginal products per dollar
are equal
at D, slope of
isocost = slope
of isoquant
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 20
Use of the Equimarginal Criterion
• Q: Is the following firm EFFICIENT?
• Suppose that:
» MP L = 30
» MPK = 50
» W = 10 (cost of labor)
» R = 25 (cost of capital)
• Labor: 30/10 = 3
• Capital: 50/25 = 2
• A: No!
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 21
Use of the Equimarginal Criterion
• A dollar spent on labor produces 3, and a dollar spent on
capital produces 2.
USE RELATIVELY
MORE LABOR!
• If spend $1 less in capital, output falls 2 units, but rises
3 units when spent on labor
• Shift to more labor until the equimarginal condition
holds.
• That is peak efficiency.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 22
Production Processes and Process Rays
under Fixed Proportions
• If a firm has five computers and just
one person, typically only one
computer is used at a time. You really
need five people to work on the five
computers.
• The isoquants for processes with fixed
proportions are L-shaped. Small
changes in the prices of input may
lead to no change in the process.
• M is the process ray of one worker
and one machine
people
5
4
M
3
2
1
1 2 3 4 5 6 7 8 9
computers
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 23
Allocative & Technical Efficiency
• Allocative Efficiency – asks if the firm using
the least cost combination of input
» It satisfies: MPL/CL = MPK/CK
• Technical Efficiency – asks if the firm is
maximizing potential output from a given set of
inputs
» When a firm produces at point T
rather than point D on a lower
isoquant, that firm is not
producing as much as is
technically possible.
D
T
Q(1)
Q(0)
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 24
Overall Production Efficiency
• Suppose a plant produces 93% of what the
technical efficient plant (the benchmark) would
produce.
• Suppose a plant produces 85.7% of what an
allocatively efficient plant would produce, due to
a misaligning the input mix.
• Overall Production Efficiency = (technical
efficiency)*(allocative efficiency)
• In this case: overall production efficiency =
(.93)(.857) = 0.79701 or about 79.7%.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 25
Returns to Scale
• If multiplying all inputs by  (lambda) increases the
dependent variable by,the firm has constant returns to
scale (CRS).
» Q = f ( K, L)
» So, f(K,  L) =  • Q is Constant Returns to Scale
» So if 10% more all inputs leads to 10% more output the
firm is constant returns to scale.
• Cobb-Douglas Production Functions are constant returns if
a + b =1
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 26
Cobb-Douglas Production Functions
Q = A • Ka • Lb is a Cobb-Douglas Production Function
IMPLIES:
Can be CRS, DRS, or IRS
if a + b= 1, then constant returns to scale
if a + b< 1, then decreasing returns to scale
if a + b> 1, then increasing returns to scale
Suppose: Q = 1.4 K .35 L .70
Is this production function constant returns to scale?
No, it is Increasing Returns to Scale, because 1.05 > 1.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 27
Reasons for Increasing &
Decreasing Returns to Scale
Some Reasons for IRS
Some Reasons for DRS
• The advantage of specialization in
capital and labor – become more
adept at a task
• Engineering size and volume
effects – doubling the size of
motor more than doubles its
power
• Network effects
• Pecuniary advantages of buying in
bulk
• Problems with coordination and
control – as a organization gets
larger, harder to get everyone to
work together
• Shirking increases
• Bottlenecks appear – a form of the
law of diminishing returns
appears
• CEO can’t oversee a gigantically
complex operation
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 28
Interpreting the Exponents of the
Cobb-Douglas Production Functions
• The exponents a and b are elasticities
a is the capital elasticity of output
 The a is [% change in Q / % change in K]
b is the labor elasticity of output
 The b is a [% change in Q / % change in L]
These elasticities can be written as EK and E L
Most firms have some slight increasing returns to scale.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 29
Empirical Production Elasticities
Table 7.4: Most are statistically close to CRS or have IRS
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
˟ such as management or other staff personnel.
Slide 30
Cost Analysis
The Importance of Cost Analysis
» Managers seek to produce the highest quality products at the
lowest possible cost.
» Firms that are merely satisfied with the status quo find that
competitors arise that produce at lower costs and drive them out of
business.
» The advantages once assigned to being a large firm (economies of
scale and scope) have not provided the advantages of flexibility
and agility found in some smaller companies.
» Cost analysis is helpful in the task of finding the lowest cost
methods to produce goods and services.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 31
Meaning and
Measurement of Cost
There are many cost concepts used in business. One example is
distinctions between:
Accounting vs. Economic Cost
Accounting costs involve explicit historical costs. They attempt to use
the same rules for different firms to be able to compare firm performance.
Economic costs are based on making decisions. These costs can be both
implicit and explicit.
A chief example is that economic costs include the opportunity costs of
owner-supplied resources such as time and money, which are implicit
costs.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 32
» A chief example is that economic costs include the opportunity
costs of owner-supplied resources such as time and money,
which are implicit costs.
Economic Profit = Total Revenues - Explicit Costs - Implicit Costs
» Implicit costs make economic profit lower than
accounting profit
Three Contrasts between Accounting & Economic Cost:
1. Depreciation Cost Measurement. Accounting depreciation
(e.g., straight-line depreciation) tends to have little relationship to
the actual loss of value
» To an economist, the actual loss of value is the true cost of
using machinery, though it is often hard to measure.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 33
2. Inventory Valuation. Accounting valuation depends
on its acquisition cost
» Economists view the cost of inventory as the cost of
replacement.
3. Sunk Costs of Unutilized Facilities. Empty space
may appear to have "no cost”
» Economists view its alternative use (e.g., rental value)
as its opportunity cost.
» Sunk Costs -- already paid for, or there already exists a
contractual obligation to pay
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 34
Meaning and
Measurement of Cost
There a number of cost concepts in business.
• Opportunity Cost – value of next best
alternative use.
• Explicit vs. Implicit Cost – actual
prices paid vs. opportunity cost of
owner-supplied resources.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 35
SHORT RUN COST FUNCTIONS
1. TC = FC + VC
Variable Cost (VC)
2.AFC = FC/Q
total cost (TC) is the sum of Fixed Cost
(FC) and
average fixed cost is FC divided by Q
3.AVC = VC/Q average variable cost is VC divided by Q
4.ATC = TC/Q = AFC + AVC average total cost is the sum of AFC and AVC.
5.MC = DTC/DQ =  TC/Q marginal cost is the cost of the last item produced
 Incremental cost is the extra cost of implementing a decision =
DTC of
a decision, such as adding a 2nd shift’s incremental cost
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 36
Figure 8.1
• FC is $150
• Adding FC to
VC is an upward
shift of cost to
make TC
• An S-shaped VC
gives an Sshaped TC
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 37
Short Run Cost Graphs
using AFC & AVC
MC
ATC
3.
1.
AFC
Q
2.
AVC
AVC
AFC
Q
MC intersects lowest point
of AVC and lowest point of
ATC.
When MC < AVC, AVC declines
When MC > AVC, AVC rises
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Q
Slide 38
Suppose we have found that:
TC = 100 + 60Q -3Q2 + .1Q3
• What is FC?
» 100
» Not a function of Q
• What is VC?
» VC = 60Q -3Q2 + .1Q3
• What is MC?
» MC = dTC/dQ =
60 - 6Q + .3Q2
• Notice TC is cubic or S-shaped
• Notice the MC is quadratic, which
is U-shaped.
• Notice also that VC is quadratic,
which also U-shaped
MC
AVC
Q
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 39
Long Run Cost Functions
• All inputs are variable in the long run
• LAC is long run average cost
» ENVELOPE of SAC curves
• LMC is FLATTER than SMC curves
• The optimal plant size for a given output Q2 is plant size 1 (A SR concept.)
• However, the optimal plant size occurs at Q3, which is the lowest cost point
overall. (A LR concept.)
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 40
Long Run Cost Function (LRAC)
Envelope of SRAC curves
Ave Cost
SRAC-small capital
SRAC-med. capital
SRAC-big capital
LRAC--Envelope
of SRAC curves
Variation
ofReserved.
FigureMay
8.3not be scanned, copied or
© 2011 Cengage Learning.
All Rights
duplicated, or posted to a publicly accessible website, in whole or in part.
Q
Slide 41
Economies and Diseconomies of Scale
1.
Product-level Internal Economies of Scale involves declining cost
associated a product as a firm increases production or throughput per day
due to volume discounts, specialization, mass customization , and learning
curve effects.
» Mass customization is the trend of making products partially mass
produced, and partially customized.
» Land’s End sells mass produced clothing in catalogs and in stores such as
Sears, but it also offers the service of stitching initials or names in shirts
or duffle bags – this makes the product at the same time mass produced
and customized.
» Economies offered in the mass production of items helps to offset the
expense of individually designed products.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 42
Learning Curve Relationship
• “Learning by doing" has wide application in
production processes.
• Workers and management become more efficient
with experience.
• The cost of production declines as the accumulated
past production, Q = qt, increases, where qt is the
amount produced in the tth period, and Q is the
accumulated past production.
• Airline manufacturing, ship building, and appliance
manufacturing have demonstrated the learning curve
Cengage Learning. All Rights Reserved. May not be scanned, copied or
effect. © 2011
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 43
• Functionally, the learning curve relationship can
be written C = a·Qb, where C is the input cost of
the Qth unit is a function of accumulated output.
• Taking the (natural) logarithm of both sides, we
get: log C = log a + b·log Q
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 44
• The coefficient b tells us the extent of the
learning curve effect.
» If the b = 0, then costs are at a constant level.
» If b > 0, then costs rise in output, which is
exactly opposite of the learning curve effect.
» If b < 0, then costs decline in output, as
predicted by the learning curve effect.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 45
Example
• Cookie Baskets, Inc., is a local firm that assembles gift baskets. This is a oneowner, one-worker firm. Using data on time it takes to make the tenth,
twentieth, and so on accumulated number of baskets, the manager estimates the
following regression.
Ln T = .4 - .02 • Ln Q
R2 = .834
N = 30
(3.1) (2.6)
where T is time it took to make a basket and Q is the accumulated number of
baskets made, and the parentheses contain t-statistics.
Q:
Is this firm finding any benefits of Learning by Doing?
A: Yes, the coefficient on Q is negative, so it takes less time to make baskets as
the number of baskets made grows. The coefficient is statistically significant as
the estimated t-value is 2.6.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 46
Percentage of Learning
• The proportion by which costs are reduced through
DOUBLING output is estimated as follows:
L = (C2/C1)·100%
» where C1 is the input or cost for the Q1 unit of output
and C2 is the input or cost for the Q2 unit of output
(and Q2 = 2•Q1).
• If the percentage of learning, L = 82%, then input costs
decline 18% as output doubles.
» The percentage of learning is 100% - L.
• When L = 100%, there is no percentage of learning.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 47
Economies and Diseconomies of Scale
2. Plant-level Internal Economies of Scale
involve producing several products at the same
plant. These include economies in overhead,
required reserves, investment, or interactions
among products (economies of scope).
3. Firm-level Internal Economies of Scale occur
in firms with several plants. These include
economies in distribution and transportation of a
geographically dispersed firm, or economies in
marketing,
sales
ornot beR&D
of multi© 2011 Cengage
Learning.promotion,
All Rights Reserved. May
scanned, copied
or
duplicated, or posted to a publicly accessible website, in whole or in part.
product firms.
Slide 48
Figure 8.5: U-shaped LRAC
• Flat section of the LRAC
» Displays constant returns to scale
» The minimum efficient scale (MES) is the smallest scale at which
minimum per unit costs are attained.
4. Diseconomies of Scale. Costs start to rise a large scale. These include
transportation costs, imperfections in the labor market, and problems of
coordination and control by management.
» The maximum efficient scale (Max ES) is the largest scale before
which unit costs begin to rise.
» Modern business management offers techniques to avoid
diseconomies of scale through profit centers, transfer pricing, and
tying incentives to performance.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 49
Figure 8.5
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 50
Auto Production:
Minimum Efficient Scale
• At Ford, cars made from aluminum have a
minimum efficient size of 50,000 (pt A)
• Cars made from steel have a MES of 300,000 (pt
C)
• Hence, Ford can change its products faster if it
uses aluminum, even if 10% more costly.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 51