Pricing Strategy

Pricing Strategies

INTRODUCTION

In this research we deal with pricing strategies of firms that have some market power:

firms in monopoly, oligopoly and monopolistic competition. Firms in perfect competition

are price takers and they don’t have a pricing strategy of their own. This research goes as

far as providing practical advice on implementing pricing strategies for those firms with

market power, typically using information that is readily available to managers, including

publicly available information such as the price elasticity of demand.

The optimal pricing strategies for firms with market power vary depending on the

underlying market structure and the instruments (e.g., advertising) available & the nature

of product whether it has elastic or inelastic demand (i.e. whether it is luxury or necessary

good). To account for that, this research presents some sophisticated pricing strategies

that enable a manger to extract greater profits from the consumers.

BASIC PRICING STRATEGIES

We will first look at the very basic pricing strategy which relies on single or uniform

pricing. This strategy uses the profit-maximizing rule: MR=MC to derive the optimal

price. This rule is then mathematically manipulated to provide a rule of thumb that makes

use of the markup to arrive at the price.

Review of the Basic Rule of Profit Maximization

Firms with market power can restrict output to charge a higher price; thus they have a

downward-sloping demand curve. In this case the price is different from marginal

revenue. The profit-maximizing rule for firms with market power is given by

MR = MC.

This rule is first solved for the equilibrium output which in turn is substituted in the

inverse demand equation to solve for the optimal or equilibrium price. Managers of large

firms may have research department that have economists who can estimate demand and

cost functions and apply this rule and to solve for optimal price and output

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Demonstration 1:

Suppose the inverse demand equation is given by

P=10−2Q(downward sloping demand=market)

and the cost function is

C (Q )=2Q

Determine the profit-maximizing output and price.

Answer: Recall MR has twice the slope of the price in this case.

Then

MR=10−4 Q

Set MR=M C

10−4Q¿=2

Solve for Q*. Then Q* = 2 units. Plug Q* into the inverse demand equation

P¿=10−2Q¿=$ 6

A Simple Pricing Rule for Monopoly and Monopolistic Competition

Some small firms such as retail clothing stores do not hire economists to estimate their

demand and cost functions. They can, however, rely on publicly available information

such as information on price elasticity of demand. We can derive a rule of thumb from

the profit-maximization rule and estimate the price with minimal or crude information

and still be consistent with profit-maximization.

Formula: Marginal Revenue for a firm with Market Power (Monopoly and Monopolistic

Competition):

MR=P[ (1+ Ef )E f

]where E f=%∆ Q%∆ P

=(∆ Q

∆ P )∗P

Q

where Ef is the firm’s own direct price elasticity of demand. Substitute this in the profit-

maximization rule

P[ (1+ Ef )E f

]=MC

Solve for the price:

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P=[ (1+E f )E f

]MC

or

P=(K )MC

where K=[ E f

(1+E f ) ]can be viewed as the profit maximization (optimal factor)

markup factor.

Example: The clothing store’s best estimate of elasticity is -4.1 and this is known. Thus,

the optimal markup is

K = -4.1/(1- 4.1) = 1.32.

Then the optimal price

P = (K)MC = 1.32*MC

(That is, 1.32 times marginal cost).

The manger should note two things about this price elasticity: First, the more

elastic the price is, the lower the markup factor and the price (if Ef = -infinity, then K= 1

and P = MC as is the case in perfect competition); the lower MC is, lower the price.

Demonstration 2:

Suppose the manger of a convenience store competes in a monopolistically competitive

market and buys Soda at a price of $1.25 per liter. The price elasticity of demand for the

typical grocery is -3.8. The manger of this convenience store believes that demand is

slightly more elastic than -3.8. Let the price elasticity of the convenience store is -4. What

is the profit maximizing price for this store?

P = [-4/(1-4)]MC = 1.3 MC

A Simple Pricing Rule for Cournot Oligopoly

Strategic interaction is an important issue in Cournot oligopoly. Each firm maximizes

profit taking into account of the output of the rival firms in the industry. It believes that

the output of the rivals will stay constant. The maximization rule is the same as in the

monopoly case,

MR = MC.

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But under Cournot monopoly, MR depends on the firm’s output and on the rivals’ output

as well. Each oligopolistic firm uses this rule to derive its interaction functions in which

its own output depends on the rivals’ outputs. Then the interaction functions are used to

determine the profit-maximizing outputs (Q1*, Q2*)

Fortunately and similar to monopoly, a simple markup pricing rule can be used in

Cournot oligopoly when the oligopolistic firms have identical cost structures and

producing similar products. Suppose the industry consists of N firms with each firm

having identical cost structures and produces similar products. In this case we can use

the markup pricing rule for monopoly and monopolistic competition to derive a pricing

formula for a firm in a Cournot Oligopoly. First, it can be shown that if products are

similar then

Ef = N*EM

Where Ef is the price elasticity of demand for the typical firm, EM is the industry’s price

elasticity of demand and N is the number of firms in the industry. Recall that the markup

pricing rule under monopoly and monopolistic competition is given by

P = [Ef /(1+Ef)]MC

where MC is the individual firm’s marginal cost. Upon substitution for Ef from above, the

profit maximizing price for a firm under Cournot is given by:

P = [NEM /(1+NEM)]*MC (rule of thumb pricing under Cournot)

Demonstration 3:

Suppose a Cournot industry has three firms, with market elasticity Em equal -2 and the

individual firm’s MC is $50. What is the firm’s profit maximizing price under Cournot

oligopoly

P = {(3)(-2)/[1+(3)(-2)] }*$50 = $60

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STRATGIES THAT YIELD EVEN GREATER PROFITS

These are strategies that can be implemented under monopoly, monopolistic competition

and oligopoly by which the manager can earn a profit greater that it can get using the

single pricing rule (MR = MC) whether directly or through a pricing formula. These

strategies which include: price discrimination, two–part pricing, block pricing and

commodity bundling, are appropriate for firms with various cost structures and degrees of

market interdependence.

Extracting Surplus from Consumers

All the above four strategies aim at extracting consumer surplus and turn it into profit for

the producers.

I. Price Discrimination

Price discrimination is the practice of charging different prices to different consumers for

the same good or service sold. There are three types of discrimination; each requires that

the manager have different types of information about consumers.

First- degree price discrimination (perfect price discrimination)

This type of prices discrimination amounts to charging each customer the maximum price

it is willing and able to pay. This price is called the reservation price.

Definition: Reservation Price: The maximum price the customer is willing to pay (e.g. P1

and P2 ), which is greater than or equal to the actual price.

Actual P

P

Q

D

P1

P2

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If monopoly single pricing strategy is used and the monopoly price is P*M, then

consumer surplus (CS) in the graph below is the yellow triangle above the P*M-

line and below the D-curve.

If 1st degree price discrimination is practiced then: Consumer surplus (rectangle area) =

0, (because the price is the maximum price the consumer is willing to pay).

Fig. 11-1a below shows the firms’ total (operating) profit (CS + PS) when the firm

charges the maximum price. It is the area below the demand curve and above the MC

curve up to Q*M. Note that the area below the MC curve and below the price line P*M up

to the quantity Q*M is the producer surplus (PS).

First-degree price discrimination is also called perfect price discrimination because it

requires identifying the reservation price for each consumer under alternative quantities.

This is not possible in the real world.

CS

PC

MC

P*M

Q*MMR

M

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Fig. 1 First and Second Degree Price Discrimination

Second Degree Price Discrimination (discrimination based on quantity)

This type of price discrimination leaves the consumer with some consumer surplus. Thus

relative to the first degree price discrimination, the total profit under the second degree is

lower. This discrimination practice is based on giving discount for buying extra quantities

of the good.

In Fig. 1b, the firm charges the consumers $8 a unit for the first two units. In this case it

extracts [1/2*(8-5)*2= $3] of the consumer surplus which would have gone to the

consumers under single pricing. It also extracts some more by charging $5 per unit of on

the units from 2 to 4. This is an additional extraction of CS. The firms cannot extract all

consumer surpluses; some consumer surplus will be left to the consumers under the 2nd

degree-price discrimination.

Example: Electric companies: it works by charging different prices for different

quantities or blocks of the same good or service (KWH). This is the case of natural

monopoly (economies of scale) where both AV and MC curves are declining all the way.

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Graph: Natural monopoly with second-degree price discrimination.

Fig. 1(b) above shows how much of the consumer surplus is extracted by the firm when

the second-degree practice is used.

Third-Degree Price Discrimination

Customers are divided into few groups with a separate demand curves or elasticities for

each group. This is the most prevalent form of price discrimination.

Example: Airline fares: Airline passenger tickets are divided into groups 1st class fare,

regular unrestricted economy fare, and restricted economy fare.

How are customers divided into groups?

Some characteristic is used to divide consumers’ into distinct groups: willingness to pay,

Identity can be readily established (ID ….etc)

What price to charge each group?

Given whatever total output is produced, this total output is allocated among the groups

based on the profit maximization rule 1.

Q3Q1

P3

P2

PM*

P1

MR D

MC

Q2QM*

1st block 2nd block 3rd block

AC

Break even

EM

Natural Monopoly: MR = MCBreakeven: P = AC or TR = TC

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1. MR1 = MR2 = --- = MRN

That is, prices should be designed as a result of equating MRS and read off their

corresponding demand curves.

If for example MR1 > MR2 output should be shifted from group 2 to group 1 (because the

first group is adding more to total revenue), this will lower P1 and increase P2 until that

MR1 = MR2

2. Determination of total output (Q*) is by equating MRT = MCT

Where MRT is the horizontal sum of all groups MRi , i = 1,…, n. That is, fix MRi at a

certain level then add up the corresponding quantities Q1, Q2,. ..,Qn. Then repeat this

process by fixing MRi at a different level and so on. You will get MRT.

Then equate MR1 = MR2 = --- = MRN = MCT to divide the total output among the n

customer groups.

Where MCT is the marginal cost of total output.

If MRi > MCT for all groups i, then profit will increase by increasing total output and

lowering prices.

MRi < MCT then profit will increase by decreasing total output and increasing prices.

This continues until MRi = MCT for all groups i = 1,…., n.

Suppose there are two groups

Group

1Group 2 Total output

Q1 Q2

QT = Q1 + Q2

P1 P2

Total cost function C = C (QT)

TR1 = P1Q1

TR2 = P2 Q2

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π = P1Q1 + P2Q2 – C(QT) (profit)

Q1 will increase until incremental profit ∆π / ∆Q1= 0

∆π /∆Q1 = ∆ (P1Q1) / ∆Q1 – ∆C / ∆Q1 = 0 which means

MR1 – MC = 0

this implies that

MR1 = MC

Similarly Q2 will increase until incremental profit ∆π / ∆Q2 = 0

MR2 = MC

Putting these relationships together

MR1 = MR2 = MC (which is the condition allocating total output Q* among the two

groups).

This is the condition for profit maximization under third degree monopoly.

Monopolists practicing this price discrimination may find it easier to think in terms of

the relative prices that should be charged to each group and to relate these prices to

elasticity.

Recall MR1 = P1 + P1(1 / EP1D1) = P1(1+1/EP1

D1)

Recall MR2 = P2 + P2(1 / EP2D2) = P2(1+1/EP2

D2)

Note that Ep11 /(1+Ep1

D1) = ( 1 +1/EP1D1)

This can be rewritten as

P1[(1+E1)/E1] = MC

P2[(1+E2)/E2] = MC

Therefore from 1st profit max ruler under 3rd price discrimination:

MR1 = MR2

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P1(1+1/EP1D1) = P2(1+1/EP2

D2)

P1 = [1+(1/EP2D2 )]

P2 [1+(1/EP1D1)]

The higher price will go to the consumers with the lower elasticity.

Example: EP1D1

= - 2 (lower elasticity)

EP2D2

= - 4 (higher elasticity).

P1 / P2 = (1-1/4) / (1-1/2) = 1.5

Or P1 = 1.5P2

Demonstration 4:

Local monopoly is near campus. Let MC =$6 per pizza.

During the day only students eat there, while at night faculty members eat. If student’s

elasticity of demand is -4 and of faculty is -2, what should be the pricing policy be to

maximize profit?

Answer:

The faculty has more elastic demand

P1[(1+E1)/E1] = MC

P2[(1+E2)/E2] = MC

Let L =lunch or day pizza, and D = Dinner pizza.

PL[(1-4)/-4] = $6

PD [(1-2)/-2] = $6

Then PL =$8 (more elastic )and PD =$12 (less elastic)

II. Two-Tier (Part) Pricing

With two-part pricing, the firm charges a fixed fee for the right to purchase its goods,

plus a per-unit charge for each unit purchased. This pricing policy is commonly used by

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athletic and night clubs. As is the case with price discrimination, the purpose of this

policy is to enhance the seller’s profit by extracting consumer surplus from consumers.

Similar to the first-degree price discrimination, this two-part pricing strategy allows firms

to extract the entire consumer surplus. To address this pricing strategy, we first present

the case of profit maximization by a firm with market power (say monopoly) and

estimate its profit based on using a single pricing policy. Then we use the two-part

pricing policy and estimate the profit for this policy. In this example, we will show how

the two-part pricing gives higher profit.

Fig. 2: Comparison of Standard Monopoly Pricing and Two-Part Pricing

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Fig. 2(a) gives the profit maximization for a firm with market power using single pricing

which based on the rule:

MR =MC.

Suppose that the demand curve is given by

Q = 10- P.

Then the inverse demand is given by

P = 10 –Q

And, thus,

MR = 10 – 2Q.

Suppose that the total cost function is given by:

C(Q) = 2Q,

Which implies that MC = 2 (in this case MC = AC and constant).

The firm’s equilibrium output and price based on single pricing are determined by

10 -2Q = 2.

Then Q* = 8/2= 4 units and P* = $6.

Total profit = (P – MC)*MC = (6 – 2)*4 = $16

Consumer surplus = (1/2)*(10 -6)* 4 = $8

Now let us use the two-part pricing strategy. Suppose the demand function in Fig. 11-2

(a) be for a single consumer. The firm can use the following two-part pricing strategy: the

fixed initiation fee for the right to purchase units $32 and that the price per unit is $2.

This situation is depicted in Fig. 11-2(b).With a price of $2 per unit, the consumer will

purchase

Q = 10 – P = 10 -2 = 8 units.

The consumer surplus with 8 units is

CS = (1/2)*(10 - 2)*8 = $32.

To implement this pricing strategy, the firm can charge a fixed initiation fee (whether as

membership fee or an entrance fee) of $32. This fee will extract the entire consumer

surplus.

Note that at $ 2/ unit, revenue will equal cost (net of fixed cost). That is,

(Variable) Profit = (P – MC)*Q = (2-2)*8 = $0.

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But the firm receives $32 as a fixed payment which is greater than the $18 profit which

receives by charging a single price

Demonstration 5:

Suppose the total demand for golf services is Q = 20 – P and MC =$1. The total demand

function is based on individual demands of 10 golfers. What is the optimal two part

pricing strategy for this golf services firm? How much profit will the firm earn?

Answer:

The optimal per unit charge is marginal cost. At this price, 20-1 = 19 rounds of golf will

be played each month. The total consumer surplus received by all 10 golfers at this price

is thus: ½[(20-1)19] = $180.50

Since this is the total consumer surplus enjoyed by all 10 consumers, the optimal fixed

fee is the consumer surplus enjoyed by an individual golfer ($180.50/10 = $18.05 per

month). Thus, the optimal two part pricing strategy is for the firm to charge a monthly fee

to each golfer of $18.05, plus greens fee of $1 per round. The total profits of the firm thus

are $180.05 per month, minus the firm’s fixed costs.

III. Block Pricing

Here the seller packs units of the same product and sells them as one package. The

consumer is faced with buying either the whole package or none of it. An example of this

practice is selling eight rolls of toilet paper or 12–pack of soda. The seller will assign a

value to the package that covers the cost as well as the consumer surplus.

Example: Suppose an individual consumer’s demand is given by

Q = 10 – P

The inverse demand is expressed as

P = 10 – Q

Let the cost be C(Q) = 2Q.

Then P = MC

10 – Q = $2

Q = 8 units.

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In this case, the firm will sell eight units. (see Fig. 11 – 3; Block pricing).

The cost of buying the eight consumer is $16 and the CS = ½ (10-2)*8 = $32

Total value of the eight units = 16+32 = $48

Fig. 11-3: Block pricing

Then the profit maximizing price for the package of eight units = $48

Demonstration 6:

Suppose a consumer’s (inverse) demand for gum produced by a firm with market power

is given by

P = 0.2 – 0.04 Q

And the marginal cost is zero. What price should the firm charge for a package

containing five pieces of gum?

Answer

When Q = 5, P = 0.2 – 0.04 * (5) = 0

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When Q = 0, P = $0.2 . The linear demand is graphed in Fig. 11-4 (optimal Block Total

Pricing with zero marginal cost)

Value of the five units = C5

= ½ ($0.2 - $0) * 5 = $ 0.50

The firm extracts all consumer surplus and charges a price if $0.50 for a package of five

pieces.

IV. Commodity Bundling

Travel bundle may include “airfare, hotel, car rental, meals”. A computer bundle may

include “computer, printer, scanner, software …”. This pricing practice is different from

block pricing because under bundle pricing the goods or the services are not the same,

while they are identical under price discrimination because under bundling the sellers

know that for different consumers, price the components of the bundle differently but

cannot identify them into groups. Because of this lack of information the profit under

bundling is usually less than under price discrimination.

Suppose the manager of a computer firm knows there are two groups of consumers who

value its computers and monitors differently. Table 11-1 shows the maximum prices the

two groups would pay for a computer and a monitor.

Table 1: Commodity Bundling

Consumer Valuation of Computer Valuation of Monitor

1 $2000 $200

2 $1,500 $300

The manager does not know the identity of those two groups, and thus cannot practice

price discrimination. Suppose the cost is constant and equals to zero to simplify matters.

The manager can separately sell one computer and total profit equals

TR – TC = 2,000 – 0 = $2,000

If it sells it at $1,500, then

TP = 3,000 – 0 =3,000

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Moreover, it can also sell monitors separately. At $300 it can sell one. At $200, it can sell

two and then total profit equals

= $3,000 + 2 * $200 = $3,400

If the manager bundles the computers and the monitors and sell them at $1,800 a bundle

then

Total profits = 2 * $1,800 = 3,600

which $200 more than selling the computers and the monitors separately. Thus

commodity bundling can hence profit.

Demonstration 7:

Suppose there are three purchasers of a new car that has the following valuations of two

options: air conditioner and power brakes.

Consume

rAir Conditioner Power brakes

1 $1000 $500

2 $800 $300

3 $100 $800

Suppose the costs are zero

1. If the manager knows the valuations and consumer identities what is the optimal

pricing strategy?

Profit from consumer 1 = 1,000 + 500 = 1,500

Profit from consumer 2 = 800 + 300 = 1,100

Profit from consumer 3= 100 + 800 = 900

Total Profit = $3,500

2. Suppose the manager does not know the identities of the buyers. Hoe much will the

firm make if the manager sells brakes and air conditioners for $800 each but offers a

special options, package (power brakes and an air conditioner) for $1,100.

Consumer 1 and 2 will buy the bundle

Profit = 2 * $1,100

Consumer 2 will buy power brakes at $800

Total Profit = $3,000

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