Advanced Pricing Techniques
© Dr Prabha Bhola, RMSoEE, IIT Kharagpur
Advanced Pricing Techniques
• Price discrimination
• Multiple products
• Cost-plus pricing
Capturing Consumer Surplus
• Uniform pricing
– Charging the same price for every unit of the
product
• Price discrimination
– More profitable alternative to uniform pricing
– Market conditions must allow this practice to be
profitably executed
– Technique of charging different prices for the same
product at different quantities; different time; to
different customers; or in different markets when
these price differences are not justified by cost
differences
– Used to capture consumer surplus (turning
consumer surplus into profit)
• Examples:
– Power (electrical and gas) cos. Charging lower
prices to commercial than to residential users
– Telecom cos.
– Medical and Legal professions
– Entertainment cos.
– Service industries
– Hotels
The Trouble with Uniform Pricing
Price Discrimination
• Exists when the price-to-marginal cost ratio
differs between two products:
PA
PB
≠
MC A MCB
Price Discrimination
Three conditions necessary to practice
price discrimination profitably:
1) Firm must possess some degree of market power
(imperfect competitor)
2) A cost-effective means of preventing resale
between lower- and higher-price buyers
(consumer arbitrage) must be implemented
3) Price elasticities must differ between individual
buyers or groups of buyers
First-Degree (Perfect) Price Discrimination
• Every unit is sold for the maximum price each
consumer is willing to pay
– Allows the firm to capture entire consumer surplus
• Difficulties
– Requires precise knowledge about every buyer’s
demand for the good
– Seller must negotiate a different price for every
unit sold to every buyer
First-Degree (Perfect) Price Discrimination
Second-Degree Price Discrimination
• Lower prices are offered for larger
quantities and buyers can self-select the
price by choosing how much to buy
• When the same consumer buys more than
one unit of a good or service at a time, the
marginal value placed on additional units
declines as more units are consumed
Second-Degree Price Discrimination
• Two-part pricing
– Charges buyers a fixed access charge (A) to purchase as
many units as they wish for a constant fee (f) per unit
– Total expenditure (TE) for q units is:
TE = A + fq
Average price ( p) is:
TE A + fq
=
q
q
A
= + f
q
p=
Second-Degree Price Discrimination
• When consumers have identical demands,
entire consumer surplus can be captured
by:
– Setting f = MC
– Setting A = consumer surplus (CS)
• Optimal usage fee when two groups of
buyers have identical demands is the level
for which MRf = MCf
Inverse Demand Curve for Each of 100 Identical
Senior Golfers
Suppose you are the manager of Golf
Club catering exclusively to retired
senior citizens. The club’s membership is
composed of 100 seniors, all of whom
possess identical demand curves for
playing rounds of golf. You know that the
annual (inverse) demand equation for
each one of the identical gofers is Psr.
Club incurs both fixed and variable
costs. The club spend total of $1 million
annually on fixed costs, no matter how
many rounds of golf are played each
year. The AVC per round is constant &
equal to $10 per round of golf. Since,
AVC is constant, thus AVC = SMC = $10.
The owner recently fired previous
manager for making losses, who
practiced uniform pricing by charging a
price of $67.50 for every round of golf.
• From the figure, each one of the 100 identical senior members chooses to
play 115 rounds of golf annually, so the revenue generated from uniform
pricing = $67.50 x 115 = $7,762.50 annually per member. So TR for 100
members = $7,762.50 x 100 = $776,250
• TVC = 115 x 100 x $10 = $115,000; TC = TVC + TFC = $115,000 + $1,000,000
• Hence, previous manager incurred annual losses of - $338,750 (=$776,250 $115,000 - $1,000,000)
• You can successfully practice price discrimination, but unfortunately, firstdegree price discrimination requires haggling for every round of golf sold.
• You decide to undertake all haggling to implement perfect price
discrimination.
• To obtain the highest fee for every round played, you are aware that
MRsr curve coincides with its demand curve (Dsr). Thus, you find it
optimal to sell additional rounds until every player buys 230 rounds per
year at point e where MRsr = SMC.
• Now from every golfer you can collect $15,525 [=230 x ($125 + $10)/2]
which is the shaded area of trapezoid 0cef in the figure.
• With 100 identical golfers, annual total revenue is $1,552,500 thus
increasing annual profit to $322,500 (=$1,552,500 - $230,000 - $1,000,000)
• You wish there was a way to avoid haggling with senior citizens over fees
for every one of the 23,000 rounds played.
• You realize that actually same amount of profit can be earned by optimally
designing a two-part pricing plan.
• You set a “low” green fee f = $10 (=MC) for playing each round of golf and
they must also pay “high” annual club membership charge (A) of $13,225
per year as the golfer enjoys annual consumer surplus of $13,225 = 0.5 x
230 x $115 i.e. the area of triangle ace.
• Under two-part pricing annual total revenue is $1,552,500 which is the
sum of total annual membership charges of $1,322,500 (=$13,225 x 100)
and total green fee of $230,000 (=$10 x 230 x 100)
• The profit generated is equal to $322,500
• Thus, f* = SMC and A* = CS
• In this example, all golfers are assumed to be identical so they all choose
to play 230 rounds per year.
Second-Degree Price Discrimination
• Declining block pricing
– Offers quantity discounts over successive
discrete blocks of quantities purchased
Block Pricing with Five Blocks
Third-Degree Price Discrimination
• If a firm sells in two markets, 1 & 2
– Allocate output (sales) so MR1 = MR2
– Optimal total output is that for which MRT =
MC
• For profit-maximization, allocate sales of
total output so that
MRT = MC = MR1 = MR2
Third-Degree Price Discrimination
• Equal-marginal-revenue principle
– Allocating output (sales) so MR1 = MR2 which
will maximize total revenue for the firm (TR1 +
TR2)
– More elastic market gets lower price
– Less elastic market gets higher price
Allocating Sales Between Markets
Suppose Manager wishes to
sell a total of 500 units in the
two markets
How should the manager
allocate sales between the
two markets to maximize
TR from the sale of 500
units?
1
𝑀𝑀𝑀𝑀 = 𝑃𝑃 (1 +
)
𝐸𝐸 𝑝𝑝
First consider an equal
allocation of 250 units in
each market (w & w’) but
MR1 < MR2 (10 < 30)
Units allocated in Market 1 is
decreased and increased in
Market 2 unless MR1 = MR2
(v & v’ at 20) equalmarginal-revenue principle
Constructing the Marginal Revenue Curve
Profit-Maximization Under Third-Degree Price
Discrimination
Multiple Products
• Related in consumption
– For two products, X & Y, produce & sell levels
of output for which
MRX = MCX and MRY = MCY
– MRX is a function not only of QX but also of
QY (as is MRY) -- conditions must be satisfied
simultaneously
Multiple Products
• Related in production as substitutes
– For two products, X & Y, allocate production
facility so that
MRPX = MRPY
– Optimal level of facility usage in the long run is
where MRPT = MC
– For profit-maximization:
MRPT = MC = MRPX = MRPY
Multiple Products
• Related in production as complements
– To maximize profit, set joint marginal revenue
equal to marginal cost:
MRJ = MC
– If profit-maximizing level of joint production
exceeds output where MRJ kinks, units beyond
zero MR are disposed of rather than sold
– Profit-maximizing prices are found using demand
functions for the two goods
VARIOUS PRICING STRATEGIES
Adopted by Firms
Cost-Plus Pricing
• Common technique for pricing when firms do
not wish to estimate demand & cost
conditions to apply the MR = MC rule for
profit-maximization
• Price charged represents a markup (margin)
over average cost:
P = (1 + m)ATC
Where m is the markup on unit cost
Cost-Plus or Mark up Pricing
• Does not generally produce profit-maximizing price
– Fails to incorporate information on demand & marginal
revenue
– Uses average, not marginal, cost
• It is not suitable when competition is tough or when a new (or
existing) firm is trying to enter a new market
• For a long time Indian companies used this method because it
was essentially a seller’s market; however with the onset of
economic reforms and entry of MNCs, no firm can continue
with cost plus pricing
Marginal Cost Pricing
• Price of the product is the sum of variable cost plus a profit
margin
– When Demand is slack, market is highly competitive then full cost
pricing may not be the right alternative. Thus, price on the basis of
variable cost is fixed.
• This method is very useful to beat competitor’s and is also
used by firms to enter a new market
• Useful in case of public utility (or social justice) where
profitability is not the objective
• The only limitation is it cannot be adopted as a long term
strategy as it ignores the element of fixed cost
• Hence, it is used as a short term strategy
An Arithmetic Reconciliation of Cost-Plus and Marginal Pricing
• It can be shown mathematically that under certain circumstances, cost-plus
pricing can be consistent with profit maximization (i.e., MR = MC).
• Mathematical relationship among price, marginal revenue, and demand
elasticity is as follows:
𝟏𝟏
𝑴𝑴𝑴𝑴 = 𝑷𝑷 𝟏𝟏 +
𝑬𝑬 𝒑𝒑
• As profit is maximized when MR = MC, we can rewrite the equation as:
𝟏𝟏
𝑴𝑴𝑴𝑴 = 𝑷𝑷 𝟏𝟏 +
𝑬𝑬 𝒑𝒑
• Further, under certain conditions, marginal cost will equal average cost.
𝟏𝟏
𝑨𝑨𝑨𝑨 = 𝑷𝑷 𝟏𝟏 +
𝑬𝑬 𝒑𝒑
𝑬𝑬 𝒑𝒑 + 𝟏𝟏
𝒐𝒐𝒐𝒐 𝑨𝑨𝑨𝑨 = 𝑷𝑷
𝑬𝑬 𝒑𝒑
• To show how price is based on average cost, we can rearrange the equation as:
𝑬𝑬 𝒑𝒑
𝑷𝑷 = 𝑨𝑨𝑨𝑨
𝑬𝑬 𝒑𝒑 + 𝟏𝟏
• Under conditions of cost-plus pricing,
P = (1 + M)AC
• On comparing two equations,
𝑬𝑬 𝒑𝒑
𝟏𝟏 + 𝑴𝑴 =
𝑬𝑬 𝒑𝒑 + 𝟏𝟏
• It can be shown that there is an inverse relationship between markup and demand
elasticity.
For example, if Ep = −2, then (1 + M) = −2/−1 = 2 and M is therefore 100
percent. If, however, Ep = −5, then (1 + M) = −5/−4 = 1.25, and markup is
only 25 percent. This result is quite reasonable; it indicates that the less
elastic the demand curve, the larger will be the markup.
• Thus, under the not infrequent conditions where the average cost curve is constant
in the relevant range of production, cost-plus pricing may give results identical to
those that would be obtained if managers were pursuing profit maximization.
Target Return Pricing
• A producer rationally (not arbitrarily) decides the minimum
rate of return that the product must earn
• Margin is decided on the basis of target rate of return
determined on the company’s experience, consumers’ paying
capacity, risk involved and similar other factors
The three methods can be understood with the
help of an example illustrated:
Let the dema nd function of shampoos by Herby Shampoos Pvt.
Ltd. be P = 20 - 2Q. The ma nager estimates the total cost per
month of production t o be C = 5 + 16Q - Q2 where Q is bottles of
sha mpoos in thousa nds.
i.
Find the output at wh ich the firm would maxi m ise profit.
Find the corresponding price level
rr
= R (Q)
- C(Q)
= 4Q
5
Q2
-
For maximum profit, First order condition: d rr =O
dQ
2
Second order condition: d
=- 2 <0
dQ
-7 Q = 2, P = 16
ii. Alternatively if the firm aims at maximizati on of sales (i.e.,
revenue) instea d of profit, then it w i ll consider ma rginal cost
TR (R) =20Q - 2Q2
On differentiating , we get Q = 5, P = 10.
It ca n be summa rised that price is higher {16) for cost plus
pricing and lower {10) for margina l costing
PRICING STRATEGIES
Based on Firms’ Objectives
• Firm may aim at maximizing profit or sale or
growth or managerial function
– Profit maximization: naturally consider total cost
of production and hence will adopt mark up
pricing
– Sales Maximization: such firms would have to
adopt competitive pricing like marginal costing as
it will be able to sell maximum output
Competition Based Pricing
• Degree of competition largely depends upon entry
and exit barriers
• Pricing strategies adopted for entering a new market,
& creating hurdles for others in competitive markets
1. Penetration Pricing: When a firm plans to enter a new
market which is dominated by existing players, its only
option is to charge a low price, even lower than the
ongoing price. This price is called penetration price.
Ex. Reliance telecom, Nirma, Air Deccan, etc.
– The principle of marginal costing may be used
– Also short term in perspective
– Success largely depends upon the price elasticity of demand of the
product as in long run factors other than price may become important
2. Entry Deterring Pricing: Price is
kept low thus making the market
unattractive for other players. If the
prevailing price is already very low,
new entrants with high fixed costs will
not be able to enter the market at a
price lower than the prevailing price.
On the other hand, existing small
players may not be able to survive at
this price due to higher average costs.
It is also known as Limit Pricing.
3. Going Rate Pricing: Most
of the players do not
indulge in separate pricing
but prefer to follow the
prevailing market price.
Normally price is fixed by
the dominating frim &
other firms accepts its
leadership & follow that
price
• Success of this strategy
depends on the fact that the
firm earns economies of scale
(mean reduction in costs of
production by way of
producing in bulk) and hence
afford low price
• Success depends on the fact that most
of the firms do not want to enter into a
price war
• Small or new firms may not be sure of
shifts in demand by charging a price
different from prevailing market price
• Products sold are very close substitutes
hence their cross elasticity is very high
Product Life Cycle Based Pricing
1.Price Skimming: Charge a very high
price in the beginning to skim the market
& earn super margins on sales for early
adopters with very low price elasticity of
demand. In the Introduction stage mark
up on cost is very high. Once the product
is established & approaches maturity
sellers charge lower price to attract large
no. of consumers.
– This is price discrimination of first degree
where entire consumer surplus is taken
away by the sellers.
2.Product Bundling or Packaging: Two or more products are bundled together
for a single price. It is used for propagating a new product as well as for selling a
product in its decline stage. It may be adopted during growth & maturity.
Advantages are:
Customer satisfaction of additional good at no extra cost; adopted during maturity stage when
demand starts falling & helps regain customers
3.Perceived Value Pricing: Value of goods for different consumers
depends upon their perception of utility of the good. It is also termed as
Psychological Pricing. This is adopted during growth & maturity stage so
as to differentiate the product from that of competitors & retain the
quality conscious customers. Hence, price of the good is not at all
governed by cost of production.
4.Value Pricing: Sellers try to create a high value of the product and
charge a low price. Thus seller allows some consumer surplus to the
buyer. This strategy is suitable for maturity & saturation stage when
demand can be maintained by keeping focus on higher quality & lower
cost. Eg. Koutons: price tag high then allow heavy discounts.
5.Loss Leader Pricing: Multi product firms sell one product at a low price
and compensate the loss by other products. Success depends when goods
are complementary in nature. Firm charges low price for the good which is
durable & has high value like printer while charges high price for the
consumable & has low value like cartridge. Thus printer is the loss leader
while cartridge compensates for the loss. Loss not necessarily on cost of
production but may be in margin terms.
Cyclical Pricing
Attempts have been made to identify pricing strategies at each
phase i.e., expansion & recession of business or trade cycles
Rigid Pricing
• Suggests that firms should
follow a stable policy
irrespective of the phase of
the economies cycle
• Be it a recession or expansion,
if consumers can postpone
their purchase they would not
be affected by a fall or rise in
prices.
Flexible Pricing
• Firms keep their prices
flexible to meet the challenge
of change in demand
• During recession prices
should also be reduced in
view of declining income or
paying capacity of consumers
& vice-versa, especially for
FMCG and agricultural
products
Transfer Pricing
• Charges made when a company supplies goods, services or
financials to its subsidiary or sister concern
• Price determination of intermediate products sold by one
semiautonomous division of a large scale enterprise and
purchased by another semiautonomous division of the same
enterprise.
Peak Load Pricing
• Different prices are charged for the same facility used at
different points of time by the same consumers
• The time zone is divided into peak load and off peak load,
consumers using the product at peak load time pay a higher
price (say, mark up price) and users at off peak load pay a
lower price (say, incremental price)
THANK YOU...