# Lecture 5

```Applications of Cost Theory
Topics in this Chapter include:
• Estimation of Cost Functions using regressions
» Short run -- various methods including polynomial
functions such as cubic or quadratic functions
» Long run -- various methods including
• Engineering cost techniques
• Survivor techniques
• Linear Break-Even Analysis and Operating Leverage
• Business Risk and Risk Assessment
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Slide 1
Estimating Cost Functions
• Firms want to know what their costs are now, what their
costs will be, and what they would be at different output
levels.
• Costs issues involve the type of cost (fixed, variable,
average, etc.) and issues of time depreciation.
» Items often depreciate with use
» Items can also depreciate with passage of time
• Because prices of inputs change with inflation, must
consider deflating or detrending cost data.
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Slide 2
Short Run Cost-Output
Relationships
• Typically use TIME SERIES data for a plant or for firm,
regression estimation is possible.
• Typically use a functional form that “fits” the presumed shape.
• SRTC is often CUBIC
SRTC = a+bQ+cQ2+dQ3
cubic is S-shaped
or backward S-shaped
SRAC = a+bQ+cQ2
quadratic is U-shaped or arch shaped.
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Slide 3
Empirical Cost-Output
Polynomial: In Theory
•
•
•
•
•
Short run cost functions can be represented by a cubic
relationship
TC = a + bQ + cQ2 + dQ3
From this we can find ATC (average total cost)
ATC = TC/Q = a/Q + b + cQ + dQ2
We can also find MC (marginal cost)
MC = dTC/dQ = b + 2cQ + 3dQ2
Notice that both ATC and MC are U-Shaped as represented
by quadratic equations (to the power of 2)
Notice also that if “d” is insignificant, the form is even
simpler as the last term is zero in each of the above examples
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Slide 4
Estimating Short Run
Cost Functions: In Practice
• Example: TIME SERIES data of
total cost
• Cubic Total Cost
(to the
power of three)
TC = C0 + C1 Q + C2 Q2 + C3 Q3
Time Series Data:
TC Q
Q 2 Q3
900 20 400 8,000
800 15
225 3,375
834 19
361 6,859

 

Regression Output:
Predictor Coeff Std Err T-value
Constant 1000
Q
50
Q-squared -10
Q-cubed
2
800 1.25
20
2.5
2.5 -4.0
1
2.0
R-square = .91
N = 35
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Slide 5
PROBLEMS: 1. Write the cost regression as an equation.
2. Find the AC function. What is MC at Q=10?
3. Find the MC function. What is MC at Q=10?
1. TC = 1000 + 50 Q - 10 Q 2 + 2 Q3
t-values in the
(1.25) (2.5) (4)
(2)
parentheses
2.
AC = 1000/Q + 50 - 10 Q + 2 Q2
3.
MC = 50 - 20 Q + 6 Q2
NOTE: Total cost is S-shaped
Average cost is U-shaped
And even MC is U-shaped
Find AC at Q=10.
Find MC at Q=10.
AC = 1000/10 + 50 – 10(10) + 2(10)2 = 250
MC = 50 – 20 (10) + 6 (10)2 = 100 = 450
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Slide 6
Estimating LR Cost Relationships
• Use a CROSS SECTION
AC
of firms
» SR costs usually uses a
time series
• Assume that firms are near
their lowest average cost
for each output
• A quadratic curve of a
cross section of ACs for
various firms can be used.
LRAC
Q
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Slide 7
Economies of Scope
in Banking
• Economies of scope occur when producing two or more products jointly by
one firm is less than the cost of producing them separately.
• Banking offers economies of scope through offering people who can help
customers with checking, savings, credit cards, mortgages, car loans, trust
accounts, and many other services.
• Banks are expanding into other fields, including brokerage, insurance, bill
paying, foreign exchange hedging, and other services expanding economies of
scope.
• Work by Jeffry Clark used a logarithmic cost function such as:
• Ln TC = a + b• Ln Consumer Lending + c •Ln Mortgage Lending
• He found evidence for Economies of Scope in banking up to about \$100
million in assets.
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Slide 8
Engineering Cost Approach
• Engineering Cost Techniques offer an alternative to fitting lines
through historical data points using regression analysis.
• It uses knowledge about the efficiency of machinery.
• Some processes have pronounced economies of scale, whereas other
processes (including the costs of raw materials) do not have
economies of scale.
• Size and volume are mathematically related, leading to engineering
relationships. Large warehouses tend to be cheaper than small ones
per cubic foot of space.
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Slide 9
Survivor Technique
• The Survivor Technique examines what size of firms are
tending to succeed over time, and what sizes are
declining.
• This is a sort of Darwinian survival test for firm size.
• Presently many banks are merging, leading one to
conclude that small size offers disadvantages at this time.
• Dry cleaners are not particularly growing in average size,
however.
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Slide 10
Break-even Analysis
• We can have multiple B/E (break-even)
points with non-linear costs & revenues.
Total
• If linear total cost and total revenue:
Cost
» TR = P•Q
» TC = F + V•Q
• where V is Average Variable
Cost
Total
• F is Fixed Cost
Revenue
• Q is Output
• cost-volume-profit analysis
B/E
B/E
Q
Figureposted
9.5 to a publicly accessible website, in whole or in part.
Slide 11
•
•
The Break-even Quantity: Q B/E
At break-even: TR = TC
PROBLEM: As a garage
» So, P•Q = F + V•Q
contractor, find Q B/E
Qb = F / ( P - V) = F/CM
» where contribution margin is: CM = ( P - V) if: P = \$9,000 per garage
V = \$7,000 per garage
& F = \$40,000 per year
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Slide 12
Answer: Q = 40,000/(2,000)= 40/2 = 20
garages at the break-even point.
Break-even Sales Volume
•
•
Amount of sales revenues that
breaks even
P•Qb = P•[F/(P-V)]
= F / [ 1 - V/P ]
Ex: At Q = 20,
B/E Sales Volume is
\$9,000•20 =
\$180,000 Sales Volume
Variable Cost Ratio
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Slide 13
Target Profit Output


Quantity needed to attain a target profit
If is the target profit,
target  = [ F + ] / (P-v)
Q
Suppose want to attain \$50,000 profit, then,
Q target  = (\$40,000 + \$50,000)/\$2,000
= \$90,000/\$2,000 = 45 garages
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Slide 14
Contribution
Analysis
•
•
Another variation is to find if added sales
through a ad campaign or new product is
justified. It looks at the incremental
cost.
Do the project if:
» (P – v) DQ > D Direct Fixed Cost
» When this inequality holds, the project
cost.
Limitations of B/E &
Contribution Analysis
Sometimes the assumptions do
not hold
1. Costs may be semi-variable
2. Many times firms sell
multiple products or small,
medium, and large varieties
3. There is uncertainty as to the
P, V, and F in the problem
4. Inconsistency in the planning
horizon
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Slide 15
Degree of Operating Leverage
or Operating Profit Elasticity
• DOL = E
» sensitivity of operating profit (EBIT)
to changes in output
• Operating  = TR-TC = (P-v)•Q - F
• Hence, DOL = Q•(Q/) =
(P-v)•(Q/) = (P-v)•Q / [(P-v)•Q - F]
A measure of the importance of Fixed Cost
or Business Risk to fluctuations in output
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Slide 16
Suppose the Contractor Builds 45
Garages, what is the D.O.L?
• DOL =
(9000-7000) • 45
.
{(9000-7000)•45 - 40000}
= 90,000 / 50,000 = 1.8
• A 1% INCREASE in Q  1.8% INCREASE in operating
profit.
• At the break-even point, DOL is INFINITE.
» A small change in Q increase EBIT by astronomically large
percentage rates
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Slide 17
Break-Even Analysis and Risk Assessment
• One approach to risk, is the probability of losing money.
• Let Qb be the breakeven quantity, and Q is the expected quantity
produced.
• z is the number of standard deviations away from the mean
• z = (Qb - Q )/
^
• 68% of the time within 1 standard deviation
• 95% of the time within 2 standard deviations
• 99% of the time within 3 standard deviations
Problem: If the breakeven quantity is 5,000, and the expected
number produced is 6,000, what is the chance of losing money if
the standard deviation is 500?
Answer: z =(5000 – 6000)/500 = -2. There is less than 2.5% chance
of losing money. Using table B.1, the exact answer is .0228 or
2.28% chance of losing money.
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Slide 18
Prices, Output, and Strategy:
Pure Competition
and Monopolistic Competition
• Pure competition is a standard against which other market
structures are compared. In it, there are many firms and the
product is perfectly undifferentiated.
 There are industries where are many firm, but the
products or service are heterogeneous or differentiated.
• Monopolistic competition is when there are many firms, but
the product or service is differentiated.
 This brand competition may involve advertising
campaigns and large promotional expenditures to stress
often minor distinctions among products
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Slide 19
Competitive Strategy Analysis
• Many industries are already competitive, but firms need to
find ways to stay competitive
• Core Competencies – technology-based expertise or
knowledge on which a firm can focus its strategy.
• Value Proposition – basis for customer willing to pay
more than cost-covering prices
» Find value in the value chain
» Find value in network relationships
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Slide 20
The Strategy Process
Figure 10.1
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Slide 21
Generic Types of Strategies
to Attain Sustainable Profits
• Product Differentiation Strategy
» A strategy that relies upon differences in products or
processes affecting perceived customer value.
» For example, Coca-Cola or Nestlé
• Cost-based Strategies
» A strategy that relies upon low-cost operations, marketing, or
distribution. For example, Southwest Airlines & Dell
Computers
• Information Technology Strategy
» Use IT capabilities to distinguish yourself from others
» For example, Allstate Insurance & GPS tracking to offer
lower insurance rates to those who don’t drive their best cars
to work
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Slide 22
The Relevant Market Concept
• A market is a group of economic agents that interact in a buyerseller relationship. The number and size of the buyers and
sellers affect the nature of that relationship.
• A popular measure of concentration is the percentage of an
industry comprised of the top 4 firms. Similarly, the market
share held by the top 4 buyers is a popular measure of buyer
concentration.
• The relationship among firms is affected by:
a. the number of firms and their relative sizes.
b. whether the product is differentiated or standardized.
c. whether decisions by firms are independent or
coordinated (collusion).
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Slide 23
Michael Porter’s Five Forces
The forces that determine competitive advantage are:
1. The Threat of Substitutes can be offset by brands, complementors,
and special functions served by the product.
2. The Threat of Entry can be reduced by high fixed costs, scale
differentiation.
3. The Power of Buyers from the threat of concentration of buyers.
4. The Power of Suppliers for the threat when concentrated suppliers
of key inputs affect profitability.
5. The Intensity of Rivalry impact profitability via market
concentration, price competition tactics, exit barriers, ratio of FC to
TC (cost fixity), and industry growth rates.
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Slide 24
Figure 10.2
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Slide 25
Break-even Sales Change Analysis
The price-cost margin percentage (PCM) is defined as
PCM = ( P – MC )/P.
A price cut may help or hurt profitability depending on price elasticities and price
cost margins.
We can ask how much quantity must change after a price cut to breakeven (from
before the price cut)?
If we cut prices 10%, to breakeven, the percentage change in quantity (DQ/Q) must
be large enough to satisfy the equation to breakeven:
PCM / (PCM – .10) < (1 + DQ/Q )
The larger is the price-cost margin percentage, the smaller will be the necessary
quantity response to justify cutting price.
 If PCM is 80%, then .8/(.8-.1) = 1.14. Hence, a 10% cut in price must be
offset by only a 14% increase in quantity to breakeven.
 If PCM is only 20%, then .2/(.2-.1) = 2. Hence, a 10% cut in price must be
offset by at least a 20% increase in quantity to breakeven. So with Hanes
underwear and low PCM discourages discounting.
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Slide 26
There is a continuum of market structures:
Pure
Monopolistic
Competition Competition
Monopoly

1.
2.
3.
4.
Best
Pure
WorstCompetition
Oligopoly
assumes:
a very large number of buyers and sellers
homogeneous product (standardized)
complete knowledge of all relevant market
information
free entry and exit (no barriers)
These assumptions imply several things about
competitive markets, including
price equals average cost in the long run.
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Slide 27

1.
2.
3.
4.

1.
2.
3.
4.
Monopoly assumes:
Only one firm in the market area
Low cross price elasticity with other products.
No interdependence with other competitors.
Substantial entry barriers
These assumptions imply that the monopoly price is well above marginal
cost. Monopoly is discussed in full in Chapter 11.
Monopolistic competition assumes:
A large number of firms, some of which may be dominant in size
Differentiated products
Independent decision making by individual firms
Easy entry and exit
These assumptions imply several things about monopolistic competition,
including that the price in the long run is equal to average cost.
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Slide 28
 Oligopoly assumes:
1. Only a few firms in the market area
2. Products may be differentiated or undifferentiated
3. There is a large degree of interdependence with
other competitors
• These assumptions imply several things about monopolies,
including that the monopoly price is well above marginal
cost.
•
After going briefly over these four market structures, this
chapter examines:
» Pure Competition
» Monopolistic Competition
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Slide 29
CHARACTERISTICS OF DIFFERENT MARKET
ORGANIZATIONS
Although not every industry fits neatly into one of
these categories, the categories do provide a useful
and convenient framework for thinking about industry
structure and behavior.
Slide 30
Price-Output Determination
Under Pure Competition
Competitive firms attempt to maximize profits.
Competitive firms cannot charge more than the market price of
others, since their product is identical to all others.
Hence, competitive firms are price takers.
Total revenue, TR, is P·Q, where price is given. Therefore,
marginal revenue, MR, is price, P.
Profit () is total revenue minus total cost, that is:
 = TR TC.
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Slide 31
Profit maximization implies that each firm produces an
output where Price = Marginal Cost (P = MC).
» To produce more than this quantity implies that
P < MC, which is not the most profitable decision.
» To produce less than where P=MC, implies that
P > MC, and the firm could increase profits by
expanding output.
• In short run, a competitive firm may earn
economic profits.
• In long run, entry pushes price down to the minimum
point of the average cost curve, so that economic
profits are zero.
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Slide 32
A Competitive Market in the Short Run
1.
If P = MC for each firm, then
each firm is doing what it thinks
maximizes profits. Firms are in
MC
MC
equilibrium.
2. Equilibrium for the industry if:
PSR
Demand equals Supply at the
AC
going price
D
• In this example, the firm is earning
Q1
economic profits as PSR > AC.
a firm
the industry
» When both (1) & (2) occur, the
market is in a Competitive
CAN EARN ECON PROFITS
IN THE SHORT RUN
Equilibrium
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Slide 33
A Competitive Market in the Long Run
• Industries which have
economics profits draw entry
and shift the MC1 curve out
to MC2 where there is no
reason for more firms to enter
or firms to exit the industry
• Price covers all cost, so in the
LR, P=AC which means that
Economic Profits are zero.
MC1
MC2
MC
entry
AC
PLR
D
a firm
the industry
ZERO ECON PROFITS
IN THE LONG RUN
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Slide 34
Long Run Competitive Markets
with external diseconomies of scale
Figure 10.5
\$/barrel for oil
Brazilian
Ethanol
Mexican
Oil
Persian
Gulf Oil
• As demand rises for products, we
find that inputs become more
expensive.
• The rising cost is not due
necessarily to the productivity of
the firms, but higher prices for what
they purchase.
• One example is the rising price for
crude oil.
• As demand in the world increases,
D2 the marginal seller of oil is ever
pricier.
D1
Quantity in million barrels per
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Slide 35
Long Run Equilibrium in an
Increasing Cost Industry
As demand shifts from D1 to D2, the price rises to P2
and the long run supply curve is upward rising. The
cause
is the upward
shift
inReserved.
AC that
firms
Learning. All
Rights
May
not beexperience.
scanned, copied or duplicated, or
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Slide 36
Price-Output Determination Under
Monopolistic Competition
• Monopolistic Competition
» MARKET STRUCTURE
• Many Firms and Many Buyers
• Easy Entry & Exit
• PRODUCT DIFFERENTIATION ! ! !
• Historical Background
» Joan Robinson “Economics of Imperfect
Competition,” 1933
» Edward Chamberlin, “Theory of Monopolistic
Competition,” 1933
• Small Groups & Large Groups
Product
Differentiation
Among Gas
Stations
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Slide 37
Product Differentiation
• Differentiation occurs when consumers perceive that a
product differs from its competition on any physical or
nonphysical characteristic, including price.
• Examples: restaurants, dealer-owned gas stations, video
rental stores, book & convenience stores, etc.
• Assumptions of the Model:
» Large number of firms
» Differentiated Product
» Conditions of Cost and Demand are Similar
» Easy Entry & Exit
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Slide 38
Basic Model of
Monopolistic Competition
• In the Short Run
» produce where MR= MC
» price on the demand curve
PM
• NOTICE:
» P > MC
» economic profits exist
P > AC
» there exists incentives for
entry into this industry
SHORT RUN DIAGRAM
MC
AC
D
QM
MR
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Slide 39
Profits in the SR Induces Entry
• Entry in this industry “steals” customers.
• Demand curve shifts inward
• RESULTS
» MR = MC (like monopoly)
» P = AC (like competition)
» Profits in LR are zero (like competition)
P
» not at Least Cost Point of AC curve (like
monopoly)
MC
AC
D
LONG RUN DIAGRAM
D’
Q
MR
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Slide 40
Properties of Monopolistic Competition
• Inefficient Production
» EXCESS CAPACITY
• not at least cost
point of AC curve
» Could Avoid Excess
Capacity by JOINTLY
PRODUCING at the
same plant
• Kroger Salt & Morton
Salt produced at the same
plant
• Sears’ Kenmore and
Whirlpool dishwashers
are built at same factory.
• Does the expectation of
zero profits in the future
stifle innovation?
• Is there too much
product differentiation?
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Slide 41
Selling and Promotional Expenses
• Suppose that the price is determined outside of the model, as with
liquor prices in some States.
• We will expand promotional activities until the extra profit
associated with the activity equals the extra cost of the promotion.
• This decision rule for Optimal Advertising is when:
Contribution Margin = Marginal Cost of Advertising
or
P – MC = k • DA/DQ
or expand advertising whenever (P – MC)( DQ/DA) > k
• where, contribution (P – MC) is the marginal profit contribution
( k • DADQ).
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Slide 42
• To sell one more unit of output will cost the price of the added
message, k, divided by the marginal product of a dollar of
• If a radio message costs \$1000, and if that message yields 5 new
items sold, then the marginal cost of advertising is \$200, (\$1000
• If it costs \$200 to sell one more car (MCA=\$200), and if the
contribution of another car sold is \$300 to profits, then we should
expand promotional expenses.
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Slide 43
Competitive Markets Under Asymmetric Information
• Used car: who knows what about it? The buyer or the
seller?
• Asymmetric Information -- unequal or dissimilar
knowledge among market participants.
• Incomplete Information -- uncertain knowledge of
payoffs, choices, or types of opponents a market player
faces.
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Slide 44
Search Goods versus Experience Goods
• Search goods are products or services whose quality is best detected through a
market search.
• Experience goods are products and services whose quality is undetected when
purchased.
• Warranties and firm reputations are used to assure quality.
• But if someone is selling his or her car, isn't it likely that the car is no good? Is it a
lemon?
» This is an explanation why used car prices are
so much lower than
new car prices.
• If one firm defrauds customers, how do the reputable firms signal that they are
NOT like the fraudulent firm?
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Slide 45
and the Notorious Firm
• Suppose that a firm may decide to produce a High
Quality or Low Quality product, and the buyer
may decide to offer a High Price or a Low Price.
• Since the firm fears that if it offers a High Quality
product but that buyers only offer a Low Price,
they only produce Low Quality products and
• This is the problem of adverse selection
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Slide 46
Notorious Firm Analysis
Payoffs in the boxes
are for the seller only
• Simultaneous decisions
Hi Price Low Price
• A risk averse decision
High
by the firm is to make a
70
Quality 130
Low Quality product SELLER
• Best for the buyer is a
Low
150
90
Quality
low price, but a high
quality good. Worst for
We end in a trap of only
the buyer is a high price
poor quality goods at
but a low quality good.
low prices.
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Slide 47
Solutions to the Problem of
• Regulation (Disclosure Laws, Truth in Lending)
• Reliance Relationships are long term, mutually beneficial
agreements, often informal.
• Brand names (a form of a “hostage” to quality)
• Nonredeployable assets are assets that have little value in
another other use
Example: Dixie Cups made with paper-cup machinery
which cannot be used for other purposes — if Dixie Cups
leak, the company is in trouble
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Slide 48
Credible Commitments
•
A credible commitment is a conditional strategy for
establishing trust by promising to make the promise-giver
worse off by violating that trust
» such as a promise of product replacement
if the product ever fails.
Examples:
1. Dooney & Bourke promise life-time replacement of handbags
2. Other firms have sometime promised: If any of my products
fail to work, I will pay the buyer three-times their purchase
price in recompense! Clearly, this commitment makes the firm
worse off if they sell shoddy goods.
3. Brand names are a “bond” or “hostage” lost if products fail to
live up to promises.
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Slide 49
Mechanisms for commitments
• Use of nonredeployable assets such as reputation. Once
lost, a good reputation is hard to rebuild.
• Entering into alliance relationships which would fall apart
if any party violated their commitments.
• using a "hostage mechanism" that is irreversible and
irrevocable can deter breaking commitments.
» Examples are "double your money back guarantees,"
and "most favored nation" clauses.
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Slide 50
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