The Stackelberg Leader –Follower Model
In this model of oligopoly, firms set output, and one firm acts before the others. The leader firm
picks its output level and then the other firms are free to choose their optimal quantities given their
knowledge of the leader’s output. In some industries, historical, institutional, or legal factors
determine which firm is the first mover. For example, the firm that discovers and develops a new
product has a natural first mover advantage. ( See also the modified behavioural models)
In terms of equilibrium, the Stackelberg leader produces more output and the follower less output
than would a Cournot firm. (The Stackelberg equilibrium because the leader acts first and the
follower knows for certain its rivals output. That is, the leader’s claim that it will produce a large
quantity is credible because it has already done so. Total Stackelberg output is greater than the
Cournot output but less than the social optimum (competitive equilibrium) output. The Stackelberg
price is higher than the competitive price, but lower than the Cournot price. As a result, consumer
surplus is higher with a Stackelberg duopoly, than with a Cournot duopoly, but lower than the social
optimum. Total industry profits under Stackelberg are less than combined profits in the Cournot or
collusive equilibria.
Comparison of the major oligopoly models
The three major non-cooperative models make different assumptions about whether firms choose
output or price and whether the firms choose simultaneously or sequentially. As a result, they
predict very different firm and industry outputs, prices, profits and consumer surpluses in
equilibrium. If there is only one firm, all three models predict monopoly behaviour. The more firms,
n, in the industry the closer the Cournot and Stackelberg equilibria to the social optimum or
competitive equilibrium. The Bertrand equilibrium with homogeneous goods , however is unaffected
by the number of firms in the industry, as long as it includes at least two firms with unlimited
capacity. The Bertrand oligopoly equilibrium is the same as the social optimum. With heterogeneous
goods, the Bertrand equilibrium differs from the competitive equilibrium and the number of firms in
the industry affects prices.
The Cournot, Bertrand and Stackelberg models can be interpreted as conjectural variations models
rather than as game theory models. In each model, firms control only quantity or price. (firms form
expectations about the reactions (or variations) of other firms and this is called conjectural
variations. In the Cournot model, each firm’s conjecture is that other firms are satisfied to continue
producing (selling) their current quantity of output.
In the Stackelberg follower firms make the Cournot conjecture. The Stackelberg leader takes those
conjectures into account in making its decisions. In the Bertrand model, each firm makes the
conjecture that its rivals will not change their price in response to a change in its own price.
Cartel arrangements
The cartel is an explicit agreement between the oligopoly firms. Cartel agreements represent the
most complete form of collusion among the oligopolists. Cartel type collusions are formed with a
view to (1) eliminating uncertainty surrounding the market and (2) restraining competition and
thereby ensuring monopoly gains to the cartel group. The board of control first calculates the MC
and MR for the industry; MC for industry is the summation of MCs of individual firms. On the basis
of industry’s MR and MC, the total output for the industry is determined. The total output is then
1
allocated between the member firms on the basis of their own MC.(see diagram below). The total
profit may be different , but there will be no motivation to change in price –quantity combination,
since their individual profits are maximum.
There are two types of cartel: the centralized cartel and the market sharing cartel. As the name
implies, the market sharing cartel gives each member the exclusive right to operate in a particular
geographical area. The most well known type of cartel is the centralized cartel. This is a formal
agreement among the oligopolistic producers of a product to set the monopoly price, allocate
output among its members, and determine how profits are to be shared.
Firm 1
Firm 2
Industry (cartel)
A
MC1
8
7
MC2
ATC1
6
D
∑MC
ATC2
4
E1
E2
E
MR
0
20
Q1
0
30
Q2
0
50
Q
In the oligopoly models described previously there is no collusion. Collusion can be overt or explicit
as in centralised and market sharing cartels, or tacit or implicit as in price leadership models. IATA is
an example of a cartel as is OPEC.
Cartel Types
Two types:
(a) Market sharing – each member is given the exclusive right to operate in a particular
geographical area. and
(b) Centralized cartel- this is the most well-known type. It is a formal agreement among the
oligopolistic producers of a product to set the monopoly price, allocate output among its
members and determine how profits are to be shared. From the diagram above ∑MC is the
MC curve for the entire cartel and is obtained by summing horizontally the MC curves of the
two firms. The centralised cartel will sell at P=$8 and sell Q=50 units given at point E at
which MC intersects MR curve of the cartel. To minimise production costs, the centralised
authority will have to allocate 20 units of output to firm 1 and 30 units of output to firm 2
given respectively by point E1 at which MC1 =MR and by point E2 at which MC2 = MR. If
MC1>MC2 at the point of production, the total costs of the cartel as a whole can be reduced
by shifting production from firm 1 to firm 2 until MC1 = MC2. The result would be the same
for a multiplant monopolist operating plants 1 and 2. Firm 1 however may demand a more
equitable share of profits under the threat of withdrawing from the carte, and herein lies an
important weakness of most cartels and the reason for their failure. Cartel members also
have a strong incentive to cheat by selling more than their quota.
2
One way of making necessary adjustments in oligopolistic markets without fear of starting a price
war and without overt collusion is by price leadership. With price leadership, the firm that is
recognized as the price leader initiates a price change and then the other firms in the industry
quickly follow.
The market- sharing cartel
Suppose that the market demand function for a 2-firm equal –market-sharing cartel is Q=120-10P
and that the total cost function of duopolist 1 is TC’=0.1Q2
The half –share market faced by each duopolist is then Q’=60-5P or P’=12-0.2Q
so that TR’=P’Q’=(12-0.2Q’)Q’=12Q’-0.2Q’2
and MR’= 
d (TR' )
 12  0.4Q'
dQ'
The marginal and average total cost of each duopolist is MC ' 
ATC' 
d (TC ' )
 0.2Q'
dQ'
and
TC ' 0.1Q' 2

 0.1Q'
Q'
Q'
Setting MC’ equal to MR’, we get 0.2Q’=12-0.4Q’  0.6Q'  12  Q'  20
and P’=12-0.2(20)=$8
Therefore TR’=12(20)-0.2(20)2 =240-80=$160 and
 '  TR'TC '  160  0.1(20) 2  160  40  $120
  2( ' )  $240
The centralized Cartel model
Suppose that a two firm cartel faces the following demand function:
Q=120-10P or P=12-0.1Q and the total cost function of each member firm is respectively,
TC1  4Q1  0.1Q12 and TC 2  4Q2  0.1Q22
We can calculate MR, MC1, and MC2 as follows:
TR  PQ  (12  0.1Q)Q  12Q  0.1Q 2
d (TR)
MR 
 12  0.2Q
dQ
MC1 
d (TC1 )
d (TC 2 )
 4  0.2Q1 and MC 2 
 2  0.2Q2
dQ1
dQ2
 MC , we solve for Q
so that Q  30  10 MC
In order to add MC1 and MC2 horizontally to find
Q1=-20+5MC1 and Q2=-10+5MC2
3
1
and Q2 and get
Q  30
 MC , we have  MC  10  3  0.1Q (Strictly speaking this is the average
 MC function ). Setting  MC =MR, we get 3  0.1Q  12  0.2Q so that
Solving for
9  0.3Q and Q  30
Then P  12  0.1(30)  $9
At Q=30; MR  12  0.2(30)  12  6  $6
Setting MC1 and MC2 equal to MR, we have 4+0.2Q1=6 so that Q1=10
and 2+0.2Q2=6 so thatQ2=20 and Q=Q1+Q2=10+20=30
Therefore
 1  TR1  TC1  PQ1  4Q1  0.1Q12  9(10)  4(10)  0.1(10) 2  90  40  10  $40
 2  TR2  TC2  PQ2  2Q2  0.1Q22  9(20)  2(20)  0.1(20) 2  180  40  40  $100 and
   1   2  $40  $100  $140
Instability of cartels
The more the membership , the greater the difficulty of keeping a stable cartel. A firm that secretly
cheats (‘chiseling’) can increase its profits as long as other firms do not do the same thing and as
long as the cartel does not punish it in some way. If all firms do this the cartel breaks down. Price
concessions made secretly by a few chiselers cut into the sales of the cooperative members, thus
breaking down the cartel completely.
MODIFIED BEHAVIOURAL PRICING MODELS
These are models which incorporate one or more of the appropriate behavioral assumptions (profit
maximizing) It looks at several more complex models of pricing behaviour in imperfectly competitive
markets. They include:
(a) Price Leadership models- these are mostly under oligopoly where there is upward
adjustment of prices. One firm leads the way and will be followed within a relatively short
period by all or most of the other firms adjusting their prices to a similar degree. The leader
is a firm willing to take the risk of being the first to adjust price, and usually has good reason
to expect that other firms will follow suit. The risk here is if the firm raises price and is not
followed by other firms, it will experience an elastic demand response and lose profits. Price
leadership is possible under both product homogeneity and product differentiation; where
there is a small number of firms; restricted entry; inelastic demand for industry and firms
have almost similar cost curves.
(1) Barometric Price Leader- the leader possesses an ability to accurately predict when
climate is right for a price change e.g. following a generalized increase in labour or
materials costs, or a period of increased demand, the barometric firm judges that all
firms are ready for a price change and takes the risk of sales losses by being the first
to adjust its price. If the other firms trust the firm’s judgement they adjust prices to
the extent or if they do not they may adjust to a lesser degree, the leader reviewing
the price to that level. It does not have to be the same firm functioning as leader
always.
(2) Low Cost Price Leadership- is a firm that has a significant cost advantage over its
rivals and inherits the role of price leader largely due to the other firms’ reluctance
to incur the wrath of the lower cost firm. In the event of a price war, the other firms
would incur greater losses and be more prone to the risk of bankruptcy than would
be the lower cost firm.
4
(3) Dominant Firm Price Leadership- the dominant firm is large relative to its rivals and
its market. It is large and has several smaller firms competing with it in the industry.
Large firm may have achieved its position by being the first seller in the industry,
because it has lower costs resulting from scale economies, or by virtue of superior
management skill. If the small firms in an industry look to the dominant firm to
establish price, they can be viewed as price takers. As such their behaviour is similar
to firms in perfect competition. If they can sell all they produce at the market price,
they maximise profit by producing until P=MC. Total output supplied by all the small
firms is the sum of their marginal cost curves ( M C F ) in the diagram The smaller

firms accept the firm’s price leadership perhaps simply because they are unwilling
to risk being the first to change prices or perhaps out of fear that the dominant firm
could drive them out of business, by forcing raw materials suppliers to boycott a
particular small firm on pain of losing the order of the larger firm for example. In
such a situation the smaller firms accept the dominant firm’s choice of the price
level and simply adjust output to maximize their profits. They are more like pure
competitors. Knowing how much the smaller firms will supply at each price level,
the dominant firm can subtract this from the market demand to find how much
demand is left over at each price level. The dominant firm will choose the price level
in order to maximize its own profits from this assured or residual demand.
If the dominant firm is content to set a price and let its small rivals supply as much
as they want, the large firms can be thought of as supplying the residual demand.
 MC
Price
Cost
per unit
F
DT
DL
Po
MCL
PL
MRL
O
DL
QL
QT
DT
Quantity per period
If the dominant firm is content to set a price and let its small rivals supply as much as they
want, the large firm can be thought of as supplying the residual demand. The leader’s
demand curve is DLDL. Total demand is DTDT. MCL is dominant firm’s MC while MRL is
dominant firm’s MR. If price is set at Po, the small firms will meet total market demand and
the dominant firm will have no sales because there is no residual demand. So prices will be
set below Po. The demand curve faced the industry leader can easily be determined for any
5
price level (it is the horizontal distance between DTDT and
leader is QL. Output of small firms is QT-QL.
6
 MC
F
) Output for the price
PRICING STRATEGIES: PRICING MODELS
Predatory, skimming and sealed Bid Pricing,
Modified behavioural models.
PRICING ANALYSIS AND DECISIONS
Price is the amount of money paid for a unit or quantity of the good or service under consideration.
A “package” of other services goes with the physical commodity and include time and place of
delivery, time payment is expected by the seller, cash and quantity discounts, guarantees that go
with the product, or any rights of return of goods.
The setting of prices involves three areas of information- costs, competition and consumer demand.
Costs information is derived from internal sources whereas information on competition and
consumer demand involves the external environment. In any business a great deal of information is
potentially available about its external environment from the operations of its own staff.
PRICING STRATEGIES
This is the task of defining the initial price range and planned price movement through time that the
company will use to achieve its marketing objectives in the target market.
1. COST ORIENTED PRICING STRATEGIES
(a) Mark up pricing or cost plus pricing- also called Average Cost pricing or full cost pricing. It
is the most common method of pricing a product by manufacturing firms. The term cost plus is
often used to describe the pricing of jobs that are non-routine and difficult to “cost” in advance,
such as construction and military weapon development. Under the cost plus pricing, the firm
calculates or estimates its AVC , and then sets its price by adding on a percentage mark-up that
includes a contribution towards the firm’s fixed costs, and a profit margin. The general practice
under the mark-up pricing method is to add a fair percentage of profit margin to the AVC. The price
is set as:
P= AVC+ x% (of AVC) where x is the mark-up percentage chosen. Or
P=AVC + AVC x (m) = (1+m)AVC or (1+m)C where m is the mark-up percentage fixed so as to
cover AFC and net profit margin. The size of mark up depends on the willingness of consumers to
pay the maximizing and this level varies inversely with the value of price elasticity. Products with
higher price elasticities of demand should be expected to have relatively lower percentage mark ups
in order to make the maximum total contribution to overheads and profits. Firms find their “best”
mark up by trial and error or by adopting the same mark up that is applied by other firms or by the
price leader in the industry.
Firms usually apply higher mark-ups to products facing less elastic demand than to products with
more elastic demand. It can also be shown that cost-plus pricing leads to approximately the profit –



maximising price. If we take MR  P1 
1
Ep

 where Ep is the price elasticity of demand. Solving


7
 Ep 
 .Since profits are maximised where MR=MC, we can substitute MC
 E 1
p


for P we get P  MR
 Ep 
 . If the firm’s MC is constant and equal to C
 E  1
 p

for MR in the above equation and get P  MC 
 Ep 
 Ep 
 Ep 
 . We can then set P =(1+m)C  C 
 or 1+m  
 . Thus
 E 1
 E 1
 E 1
 p

 p

 p

we can get P  C 
we get m 
Ep
Ep 1
 1 . From this if Ep=-1.5, m=2, or 200%; if Ep=-2, m=1 or 100%. It can then be
concluded that the optimal mark-up is lower the greater is the price elasticity of demand of the
product. Firms in practice have been found to apply a higher mark-up to products with inelastic
demand than to products with elastic demand, and when increased competition has increased the
price elasticity of demand, they have been found to reduce their mark-up. It can thus be concluded
that cost-plus pricing does lead to approximately profit-maximizing prices. In a world of inadequate
and imprecise data on demand and costs, firms may simply utilize cost-plus pricing as the rule-ofthumb method for determining the profit-maximising prices.
The advantages of mark-up pricing are:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
by pinning the price to unit costs, sellers simplify their own pricing task considerably and
they do not have to make frequent adjustments as demand conditions change.
There is also generally less uncertainty about costs than about demand.
It requires less information and less precise data than in MC=MR case.
It results in stable prices when costs do not vary much.
It provides a justification for price increases when costs rise.
It is easy and simple to use (may be misleading since difficulty of projecting TVCs and
overheads allocation).
Limitations
(i)
Assumes firm’s resources are optimally allocated and the standard cost of production is
comparable with the average for the industry.
(ii)
Uses historical cost rather than current cost data- this may lead to underpricing under
increasing cost conditions and to overpricing under decreasing cost conditions.
(iii)
If VC fluctuates frequently and significantly, cost plus pricing may not be an appropriate
method of pricing.
(iv)
It is “alleged” that cost plus pricing ignores the demand side of the market and is solely
based on supply conditions (“alleged” because firms determine the markup on the basis
of what the market can bear.).
(b) Marginalist Pricing .There are three main ways of practicing marginalist pricing under
uncertainty:
(i) Given estimated demand and MC curves. MR has the same intercept value and
twice the slope value as compared with the demand curve and thus we can quickly
derive an estimate of MR. Setting the expression for MR equal to that of MC, we can
solve for the quantity level that preserves the equality. This method of price
8
determination involves inserting the result back into the demand curve to give us
the price that will maximize contribution and hence profit.
(ii) Given estimated price elasticity and MC- involves using the elasticity value and
the current price and output levels to find an expression for the demand curve and
then proceed to equate estimated marginal revenue and marginal cost.
(iii) Given estimates of incremental costs and revenues- is a marginalist approach
since it is concerned with changes in both total revenues and total costs. Where
demand contains indivisibilities or discontinuities we cannot construct the marginal
revenue function, since the total revenue curve is not continuous and therefore is
not differentiable. Instead we must compare the incremental costs and incremental
revenue at each price level and choose the price that allows the maximum
contribution to be made.
(c) Target Pricing- also cost oriented pricing approach in which the firm, tries to
determine the price that would give it a specified target rate of return on its total
costs at an estimated standard volume e.g. pricing of good X so as to achieve an
average rate of return of 15 to 20% on a firm’s investment. The breakeven chart can
be used to illustrate target pricing. The total cost curve (TC) and total revenue (TR)
curve have to be worked out. Target pricing has a major conceptual flaw- the
company uses an estimate of sales volume to derive the price but price is a factor
that influences the sales volume.
2. DEMAND ORIENTED PRICING STRATEGIES
This calls for setting a price based on consumer perceptions and demand intensity rather than
on cost.
(a) Perceived value pricing or prestige pricing-deliberately setting high prices to attract
prestige-oriented consumers (goods have a snob appeal. An increasing number of companies
are basing their price on the product’s perceived value. They see the buyers’ perception of
value as the key to pricing. Price is set to capture the perceived value. A company develops a
product for a particular target market with a particular market positioning in mind with respect
to price, quality and service. Market research has to be carried out to establish the market’s
perceptions.
(b) Demand Differential pricing- is another of demand oriented pricing. It is also called price
discrimination. It takes many forms (i) Customer basis- different customers pay different
amounts for same product/service. (ii) Product form basis- different versions of the product are
priced differently but not proportionately to their respective marginal costs. (iii) Place basisdifferent locations are priced differently although there is no difference in MC. (iv) Time basisdifferent prices charged seasonally by the day, by the hour, etc. For effectiveness the market
must be segmentable and have different demand elasticities, no resale to segment paying the
higher price. The cost of segmenting and policing the market should not exceed the extra
revenue derived from price discrimination the practice should not breed customer resentment
and turning away.
Price discrimination types
There are three types
9
First degree Discrimination – involves charging the maximum possible price for each unit of output.
It involves making the price per unit of output depend on the identity of the purchaser and on the
number of units purchased. Thus the consumer who attaches the greatest value to the product is
identified and charged a price of P1 (this being individual 1’s reservation price) Similarly, the
consumers willing to pay P2 for the second unit (this being individual 2’s reservation price) and P3 for
the third are identified and required to pay P2 and P3 respectively. each customer is being charged
different prices. Each unit of product is charged separately. All consumer surplus is extracted.
First degree
P1---P2 ------P3-------------Pc
Second Degree
P1
P2
MC=AC
P3
D
Q1 Q2 Q3 QD
O
Q1
Q2
Q3
With first degree price discrimination , the profit maximising output rate is where the MC and
Demand curves intersect. Any sale in excess of QD would reduce profits because price would have
been less than MC. First degree Price discrimination is uncommon because it requires that the seller
have complete knowledge of the market demand curve and also of willingness of individuals to pay
for the product, In addition the market must be segmentable and also that resale is not possible.
Second degree price discrimination- this involves pricing based on the quantities of output
purchased by individual consumers.. That is it involves making the price per unit of output depend on
the number of units purchased. The monopolist designs a menu of prices and quantities (or use rates
of quantities purchased) such that each consumer chooses a price –quantity combination that allows
the monopolist to discriminate profitably between consumers. The price does not depend on the
identity of the purchaser. It involves charging uniform prices per unit for a specific quantity or block
of the product sold to each customer, a lower price per unit for an additional batch or block of the
product and so on.. This is easy where there are meters as in electricity and water. Another version
is discriminating among groups of buyers on a time or urgency basis. This probably applies to new
products. For example first 10 units at 15cents, next 20 units at 10 cents and all additional at 5cents
each. In other words blocks are charged at different prices. Examples include the charging of
electricity, whereby there is a two-part tariff, requiring the payment of a fixed fee if the consumer
wishes to make any purchases at all, plus an additional uniform price per unit purchased. It also
involves charging different prices in two or more different markets at the same point in time (until
MR of the last unit of product sold in each market equals the MC of producing the product). This
implies that MR1=MR2=MC. The market is segmentable e.g. student versus nonstudent.
Third Degree price discrimination - most common. The price per unit depends on the identity of the
purchaser. The price does not depend on the number of units purchased. Involves separating
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consumers or markets in terms of their price elasticity of demand. The monopolist charges a relatively
high price to consumers whose demand is price inelastic, and a relatively low price to consumers
whose demand is price elastic. Segmentation can be based on several factors e.g. geographical
location (selling of books outside US at lower prices), telephone users may be residential or
commercial (nature of use), usage of electricity ( industrial or residential) or during certain times),
can be according to age (personal characteristics).
Forms of price discrimination used in practice
These include:
 Intertemporal price discrimination, whereby the supplier segments the market by the point in
time at which the product is purchased.
 Branding, whereby different prices are charged for similar or identical goods differentiated
solely by a brand label.
 Loyalty discounts for regular customers.
 Coupons that provide price discounts discriminate between consumers on the basis of
willingness to make the effort to claim the discount.
 Stock clearance sales involving successive price reductions are a form of intertermporal price
discrimination.
 Free-on-board pricing involving the producer or distributor absorbing transport costs, and
representing a form of price discrimination favouring buyers in locations where transport
costs are higher.
3. COMPETITION ORIENTED PRICING
This is when a company sets its price chiefly on the basis of what its competitors are charging. It is
not necessary to charge the same price as the competition. The firm may seek to keep its prices
lower or higher than the competition by a certain percentage. The distinguishing characteristic is
that it does not seek to maintain a rigid relation between its price and its own costs or demand.
Conversely the same firm will change its price when competitors change theirs, even if its costs or
demand have remained constant.
Going rate pricing- the firm tries to keep its price at the average level charged by the industry. The
pricing primarily characterizes pricing practice in homogeneous product markets, although the
market structure itself may vary from pure competition to pure oligopoly.
Bidding
Sealed Bid pricing- also called competitive tendering or competitive bidding. In this there is only one
buyer in the market whose requirements are individual to himself. In other words a number of
sellers compete for the business of a single buyer. Confronting him is a number of suppliers each of
whom is capable of doing the work e.g. building a ship, an office block, or building a nuclear power
station. The buyer, wishing to secure the benefits of competition, puts his contract up for tender. It
may be open to all comers or may be restricted to a select group which the buyer judges to have the
competence and resources to undertake the work successfully. Normally the contract will go to the
bidder quoting the lowest price but, with a view to protecting his own interest, the buyer will usually
reserve the right to accept any tender – or none. Competitive bids may also occur where Services of
a product may not be identical hence combination of price and quality also matter. Examples are in
the service sector. all bidders have to submit their bid in a sealed envelope at the same time. The most
striking difference with open auction is that you do not learn about the private information of the other
bidders during the auction process. In sealed bid auctions, the private valuations of all players remain
11
unobservable. In situations of uncertainty regarding the true value of the auctioned object, all private
valuations must be based on estimates.
Normally buyer has budgeted expenditure whilst bidders do not know of it. Too low a price leads to
loss or loss of tender. Too high a price may be rejected If you are the winner, there may be good news
and bad news in the outcome. The good news is that you have got the deal. The bad news may be that
you have based your calculations on the most optimistic calculations of all competitors. This is called
the winner’s curse in game theory. A firm can thus win a tender but may incur losses due to rising
costs- and end up with the ‘winner’s curse’.
Types of sealed Bids
There are three types of bids
(1) Fixed price bids.
(2) Cost plus fee bids.
(3) Incentive bids.
Fixed Price Bids
This is when suppliers tender for a price bid regardless of variation of costs. Supplier tenders a bid
price or price quote and undertakes to complete the job for that price regardless of any variation of
costs from expected levels.
Pb   t  Ct where Pb is the bid price;  t is target profit and C t is supplier’s target cost. The
actual profit  a =  t + ( C a  Ct ) where C a is actual cost. (NB. If Ct > Ca  a falls)
Cost Plus Fee Bids
In these the entire risk is borne by the buyer who agrees to meet the actual cost plus what supplier
stated was their profit.
Pb  Ca   t   a   t where Pb is the bid price. (NB.  t is the fee)The buyer expects to audit
the costs. The contract is unfair to the buyer because of the problems of conducting the audit.
Incentive BidsThese are also called risk sharing bids. The buyer and seller (supplier) agree before hand on a bid
price but agree to share any deviation from expected costs level in a given way.
More formally mathematically if  = supplier’s share of cost variation where 0<  <1 then
For the buyer Pb  Ct   t  (1   )(Ca  Ct )...............................(1)
Pb is the bid price , C t is supplier’s target cost,  t is target profit.
For the Seller  a =  t +  ( C a  Ct ).
If  =1 then Pb  Ct   t and this becomes fixed price bids. All risk goes to the seller.
 a =  t + C a  Ct .
On the other hand if  =0, Pb   t  C a . In this case the buyer is bearing the burden.
 a =  t . This is the cost plus fee bid. All risk goes to the buyer.
Auctions
There are four basic auction formats.
1. English Auction- also called the ascending bid auction and involves the price being set
initially at a very low level which many bidders would be prepared to pay, and then raised
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successively until a level is reached which only one bidder is willing to pay. The last
remaining bidder secures the item at the final price and the auction stops.
2. The Dutch auction- also known as the descending bid auction, is the exact opposite of the
English. Price is set initially at a very high level which no bidder would be prepared to pay,
and is then lowered successively until a level is reached which one bidder is prepared to pay.
The first bidder who is prepared to match the current price secures the item at that price, and
the auction stops.. normally used to sell agricultural produce.
3. First price sealed bid auction- each bidder independently submits a single bid, without seeing
the bids submitted by other bidders. The highest bidder secures the item, and pays a price
equal to his or her winning bid. This has been used by governments to sell drilling rights for
gas and oil, and the rights to extract minerals from state owned land.
4. The second price sealed bid auction- sometimes known as a Vickrey auction after the seminal
paper on auction theory by Vickrey in 1961. The bidding process works in the same manner
as a first price sealed bid auction: Each bidder independently and privately submits a single
bid. Again the highest bidder secures the item, but pays a price equal to the second-highest
submitted bid. Has been used occasionally in practice.
There is a Sealed bid auction and an open auction
Open Bid- the bids of all parties are observable. In an ‘increasing bid’ competition the optimal
strategy for the individual bidder is to remain in the bidding competition until the price rises to his
own valuation of the item. If all bidders are rational and execute this strategy, the item, the item will
be transferred to the buyer with the highest private valuation of the item. As the bidding process
unfolds one is able to observe the private valuations by noticing who remains in the competition and
who drops out. The bidding process forces the players to reveal their preferences. In the ‘Dutch
auction’ instead of an increasing bid competition, the auctioneer starts off from a very high price. The
auctioneer cries out loudly prices which slowly decrease.
4 PRICING WITHOUT COMPETITION
Cases exist where there may be only one source of supply in the market, for example, in the
provision of defence equipment. If there is only one source of supply but an exact specification can
be laid down- as where the same equipment has been supplied before- the supplier can be asked to
quote a firm price on the basis of which the order can be placed. The fairness of the price quoted
can be judged in the light of previous experience. Thus contracts under such circumstances are
stated “price to be agreed”. Such prices are to be agreed contracts based on costs. They may be
based on estimates of costs made either before or during production. Alternatively they may be
founded on actual costs which are ascertained after production has finished.
PRICING A NEW PRODUCT – SKIMMING AND PENETRATION
The term new product has many meanings. It may refer to a product of distinctive novelty- the first
TV set or the first ball point pen. On the other hand it may be a product new to the market in the
sense of a new brand of detergent or beer where guidelines to price already exist in the form of
established brands.
The producer of a pioneering product is faced is faced with a dynamic competitive situation – at first
he enjoys a degree of freedom because he is alone in the market- he may have protection of a
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patent, and if rewards look high enough, ways can usually be found to evade the patent without
infringing his legal rights. At the outset he has a choice between a skimming price and a penetration
price.
Price Skimming- It involves setting a relatively high initial price for a new product when it is first
introduced, to capture customers with high purchasing power, with the intent of getting as much
profit from the product as possible. This is a short term intent. This may be similar to first degree
price discrimination and can somewhat be compared to prestige pricing. Here the product pioneer
takes advantage of any price insensitivity which exists at the early stages of marketing and charges a
high “monopoly” price. In this way he secures a relatively high cash flow at an early stage which
helps to minimize his losses if, in the end, the product fails to “take off”. If however demand builds
up according to his hopes and expectations then he will be seen to be earning high returns. The
conditions to encourage competitors to try to enter the market are strongly established. As
competition builds up, he reduces his price in an attempt to check their (competitors) inroads on his
market. He may get credit for pioneering price reductions. The firm may also lower its price to draw
in the more price elastic elements of the market.
Rationale for price skimming
(1) it is difficult to know the demand curve when entering a market, which market is unknown.
Demand elasticity is unknown.
(2) Production of the new product is at small scale. Low plant size will limit output. Maximize
revenue through higher prices which will generate high initial cashflows.
(3) High R and D to be recouped as quickly as possible.
(4) Skimming may also enable firm to identify different market segments for the product, each
prepared to pay progressively lower prices. If there is product differentiation it may be
possible to continue to sell at higher prices to some market segments.
(5) There is presently a sufficient number of buyers having high current demand.
(6) The high price creates an impression of a superior product.
(7) The high initial price will not attract more competitors.
Skimming can also be maintained by :
(1) barriers.
(2) Quality of product. Demand is expected to be maintained.
Penetration Pricing
This is the opposite strategy to price skimming strategy and has the aim of discouraging competition.
This type of policy is likely to be followed when the producer is likely to be followed when the
producer is of the opinion that the period of exclusive occupation of the market is likely to be of
short duration. Competition will arise quickly and his aim is to try to make this as unattractive as
possible by setting a low price and a fine margin of profit. The motive for so doing will be
strengthened if the market is one which is not easily segmented and where it is considered that the
sales volume of the product will be very sensitive to price even when it is first introduced. An added
inducement in support of such a policy is to be found in those cases where an increased volume of
output is subject to marked economies of scale. The policy requires faith in the speedy realization of
a high volume of sales and will almost certainly need to be associated with a considerable sales
promotion effort.
Circumstances favouring this strategy
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(1) wish to discourage rivals from entering.
(2) Firm wishes to shorten initial period of PLC in order to enter growth and maturity stages
quickly.
(3) Significant economies of scale to be realized from large output may build larger capacity and
then reduce prices further.
Other Pricing Practices
These include:
Price lining-this refers to the setting of a price target by a firm and then developing a product that
would allow the firm to maximise total profits at that price. Thus instead of deciding first on the type
of product to produce and then on the price to charge so as to maximise the firm’s total profits (as
usual), the order is reversed with price lining. (Cart before horse strategy).
Value Pricing- refers to the selling of quality goods at much lower prices than previously. The
manufacturers are also redesigning the product to keep or enhance quality while lowering costs so
as to still earn a profit.
Ramsey Pricing
No product should be supplied by a firm unless its incremental revenues are expected to exceed its
incremental cost. If there are common costs managers must decide which products will be priced
above incremental cost and how much above. According to the Ramsey pricing, for an enterprise to
cover its total cost at least one of its two goods must be priced above its marginal cost. In its simplest
form, Ramsey pricing requires that price deviations from marginal costs be inversely related to the
elasticity of demand. That is, for goods with very elastic demand, the price should be set close to
marginal cost. Conversely for goods with relatively inelastic demand, the price should deviate more
from marginal cost. The rationale for Ramsey rule is that if demand is elastic, increasing the price
causes a substantial reduction in quantity demanded. . But if demand is highly inelastic , large changes
in price will result in little change in the quantity demanded. In the extreme, if demand were totally
inelastic (a vertical demand curve), there would be no change in quantity demanded as price
increased. Hence , if deviations from marginal cost pricing are greatest for those goods with inelastic
demand, the resource misallocation will be minimized.
Ramsey pricing
P’y
P’x
Px
MCx
Py
MCy
Dx
Q’x
Dy
Q’y Qy
Qx
Good X
Good Y
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Prices charged for X and Y are respectively P’x and P’y.
PRODUCT LIFE CYCLE (PLC)
The product life cycle concept draws an analogy between biological life cycles and the pattern of
sales growth exhibited by successful products. In doing so it distinguishes four basic stages in the life
of a product- introduction, growth, maturity and decline. The concept in other words derives from a
biological metaphor namely that all “living things” go through a cycle of birth, growth, maturity and
inevitable decline and death. Product forms, product classes and brands are likened to living things
in this context.
Product Life Cycle
Product
Sales
Growth or
Expansion
Maturity
Decline
Introduction
Stage 1
Stage 2
Stage 3
Stage 4
Time
Stage 1 Introduction Stage or introductory stage- this is the most hazardous stage of all, when the
product has to prove its value and find a market. Preproduction costs are also high at this stage.
Pursuing the life cycle analogy, infant mortality is very high and most products do not survive this
stage. The initial price will be relatively high compared with later stages in the life cycle. The aim is to
recover development costs as quickly as possible. Some consumer goods may be sold at an
introductory price offer which is withdrawn when the selling momentum picks up.
Stage 2 Expansion, growth, or breakthrough period. The product receives general acceptability, rapid
growth as more cautious buyers enter the market. Other firms are joining in. Production costs are
likely to fall. Prices are also likely to fall.
Stage 3 Maturity stage- the product is now well established, existing in a variety of forms to suit
different needs and different markets. The uniqueness of the product (characteristic of stage 1) has
gone and the rapid period growth of stage 2 has disappeared. The original firm may be on the point
of withdrawing. Costs including advertising and promotional costs are likely to fall as the momentum
of sales gathers strength.
Stage 4 Decline- this marks the old age and virtual death of the product in its original form. There are
many causes of decline but two main ones are (1) Change in fashion. (2) a technical breakthrough
may render the original product obsolete.
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PRICE POSITIONING
Price setting is a very challenging task because reaction of consumers and competitors is very
difficult to ascertain. Apart from cost considerations other factors, particularly in the consumer fields
ought to be considered as they play an important role.
(i)
Possible existence of a traditional price range for the product. Unless the product
embodies something entirely new most consumers and producers know instinctively
what a “reasonable” price ought to be and a decision to move outside this band involves
not merely finding a new market segment but possibly also a new marketing strategy.
(ii)
Prevailing attitude of mind of the customers towards switching. If there is a strong brand
loyalty, the situation is particularly difficult for the newcomer. In this situation a
dramatic break with the existing price structure, either a substantially cheaper product
or improved mark ups for the distributors, may be required.
In established product markets, firms can be classified as price makers or price takers, that is, they
are either price leaders of followers. Price leaders normally choose the price that they feel best
fulfils their objectives, perhaps subject to the constraint that the chosen price must lie within a range
that is acceptable to the price followers.
In established product markets, the general price level may be regarded as being historically
determined, in the sense that it has gravitated to a specific level (in real terms) over a prolonged
period of time , and to the general satisfaction or acquiescence of the firms involved. The firm must
therefore position its price correctly in relation to its competitors.
Product Line Price Strategy
Almost all firms have more than one product in their line of production. These multiple models or
sizes of a product produced by the same company may be considered as different products or
perfect substitutes for each other. Each has different AR and MR curves. The pricing under these
conditions is known as multiproduct pricing or product line pricing.
A frequent procedure is to apply a common mark up percentage to the per unit variable costs of
each item in the product line. This is not optimal pricing since some products have relatively smaller
price elasticities while others have relatively higher price elasticities. Higher price elasticities result
from a product’s having a variety of substitutes and / or being relatively expensive. There are 3 basic
decisions to be made in product line pricing:
(1) Choose the price of the basic or bottom of the line item. The “loss leader” considerations must be
weighed against connotations of lower quality that may be attached to lower prices, in order to
achieve maximum contribution from the entire production line.
(2) Choose the price of the top of the line item with an eye to the impact of that price on sales of the
whole line. A high mark up prestige item at the top of the line may confer status and quality
connotations on all other items in the line. Alternatively a price too high could give the impression
that other items are overpriced as well and could cause total sales and contribution to be reduced.
(3) Choose the price intervals for the remaining items in the line. These price differentials should
reflect the presence, absence, or degree of perceived attributes and should be chosen after
observation of rival firms’ chosen differentials.
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