NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS
Faculty of Economics
Department of Business Economics and Finance
Center of Financial Studies
Laboratory for Investment Applications
Internal Audit Program
Course: Managerial Economics and Financial
Management - Chapter 5
Instructor: Panayotis Alexakis
In cooperation with:
Under the aegis of:
Managerial Economics and
Financial Management
Chapter 5: Price Determination in Practice
Contents of presentation:
Product pricing in practice
The mark up pricing policy
Current price level and quality of the
Offer of products at low prices
Other pricing policies
Pricing of a product line
Interdependence of products with
product
respect to the
consumption
Interdependence of products in the production
process
2
Introduction

As shown in Chapter 4, the basic assumption in
the perfect competition model is that many
companies operate, their products are not
differentiated at all, while all market participants
are fully informed. Both enterprises and
consumers know where they can acquire low
price materials and low price products,
respectively. Prices are fixed for all companies
(price takers) formed by the market forces of
supply and demand, which in turn represent the
cumulative of company / personal behavior.
3
Introduction

In case demand exceeds supply, equilibrium
price will change to a higher level while, in
the opposite case, to a lower level. Under
this market model, firms that increase the
product price above the market level will
not be able to sell their products. Also, a
reduction in the price by a company is not
meaningful, given the company’s very small
size in comparison to the market size, as
the company can sell all its production at
the market price.
4
Introduction
In the other market models, the difference in the
basic assumption lies in the existence of many
differentiated products while information is
imperfect and characterizes consumer behavior in
product choice among competitive companies.
 Monopolistic competition entails many enterprises
which however provide differentiated products.
 Oligopoly is characterized by a relatively small
number of companies whose products are usually
significantly differentiated, through a combination of
product design, promotion policies and sale points.
Monopoly is characterized by one seller while no
substitutes exist for the product which therefore is
highly differentiated from the products sold by
other companies.

5
Introduction
In contrast to perfect competition, companies
active in other market models have the ability
to affect market prices (price makers), either
upwards or downwards, on the basis of their
business objectives.
 Therefore, the ability of a company to
determine the price of its product is linked to
its ability to actually differentiate it. Every
company can increase its product price up to a
certain degree without losing its customers,
provided that the customers believe that this
product deserves this price.

6
Introduction


The purpose of managerial economics (in
contrast to microeconomic theory) is to deal
with the issue of price determination, aiming to
answer the following question,
“Which is the price level that a firm has
to choose in order to achieve its business
objectives”?

Consequently, it is the model of price
determination that should be examined
rather than theoretically accepting that
prices are given under perfect competition.

In practice, a company can face conditions
which resemble all market forms.
7
Introduction
In all examples mentioned which assume certainty
conditions, the firm knows both the cost and
demand characteristics for its products, accurately.
In the same context, if the company’s objective is
profit maximization, the price is determined at the
point where marginal cost equals marginal
revenue.
 In practice, though, all conditions that were
considered as given are not valid for the
enterprises. The company has to collect and
follow the market data, systematically, both with
respect to cost and demand in order to approach
the marginal cost and marginal revenue curves and
determine the price that satisfies its objectives in
the best possible way, under an environment of
uncertainty and imperfect information
8

.
Product pricing in practice
 Business
decisions are not taken
autonomously but instead they usually take
into account a series of variables which are
interdependent, as, for example, the current
price of a product, the technology utilised
and the organizational structure adopted
for the support of production and the sale
of a product. The interdependence of the
variables which support business decisions
creates complex issues to the company.
9
Product pricing in practice


However, for the determination of the price at
the level where the business objectives are
attained, the need is for systematic search
for information with respect to demand
and cost, elasticities, possible reactions
by the competitors, and marker shares,
among others, which, usually, are unavailable or
particularly expensive to be retrieved.
Therefore, pricing becomes a difficult and
complex task. What economic theory does, is
to try and facilitate it by underlying the basic
principles of pricing.
10
Product pricing in practice
However, theory may not always provide practical
solutions to pricing problems. Those responsible for
the formation of the firm’s pricing policy face the
difficult task of selecting market data and analysing
them in order to proceed and plan the appropriate
methods and pricing mechanisms.
 The collection of appropriate market data is a
particularly cumbersome task, both in terms of time
and cost, which explains why, frequently, the pricing
methods adopted by the companies are not
conducive to the price optimization models
suggested by theory. This does not necessarily mean,
though, that pricing is not directed by economic
theory.
11

The mark up pricing policy
The mark up pricing policy, according to the
analyses of Truett and Truett (1992), Douglas
(1987) and Thomson (1985) maintains that a
margin is added to the average cost, aiming at
covering general expenses and a certain profit.
 Therefore,
the basic variable for the
determination of the mark up percentage, refers
to the average cost (AC).

P  AC  AC  (1   )AC
(1)
12
The mark up pricing policy

This pricing method is very frequently met in
practice. In order for a company to estimate its
average cost, it has to calculate both the average
variable cost and the average fixed cost. However,
since cost is a function of the quantity
produced, the company must determine the
quantity to be produced. In practice, the
determination of the production level is set
according to the expected production capacity of
the firm, subject to small diversions due to changes
to the level of demand. In the following diagram,
this cost plus method is presented.
13
The mark up pricing policy
The method of mark up pricing
14
The mark up pricing policy
Note:
 It should be stressed though that, irrespective of
the market structure, setting a high product price
tends to reduce product demand. Therefore,
pricing on the basis of the cost plus
method should take into account, not only
the cost but also the price elasticity of
demand for a product.
 Also, it should be pointed out that, under this
pricing, in case a company produces more than
one products, it has been observed that the mark
up differs from one product to the other.
15
The mark up pricing policy

This means that, even if the production cost
is linked to the products produced, the
company selects different mark up
percentages for its products by taking into
account the particular demand and cost
conditions as well as the competition that
characterizes the flow of each product.
16
The mark up pricing policy
In this process, the company in calculating the mark
up percentage, takes into account the demand
conditions, indirectly. However, this “cost plus”
practice does not integrate the prevailing demand
conditions explicitly, as the case is in marginal
analysis where the equality condition between
marginal revenue and marginal cost is utilised.
 Therefore, the price determined at the mark up
pricing model is differentiated from the price
derived through the equalization of marginal
revenue with marginal cost. It is only incidentally
that they can coincide, to the extent that the mark
up percentage is such that leads to the same price
with the one that maximizes profits through the
marginal approach.

17
The mark up pricing policy

However, under certain conditions, the “cost plus”
technique provides for the ability to approach the
price derived by the marginal analysis: According to
microeconomic theory MR (marginal revenues) is
related to the price elasticity of demand (ε).
1
MR  P (1  )


(2)
Profit is maximized when MR = MC. Therefore,
through substitution.
1
MC  P (1  )

(3)
18
The mark up pricing policy

In practice, average cost is not differentiated
according to the production level, as, usually, steady
scale economies prevail and a horizontal average
cost curve. So, when the average cost takes the form
of a horizontal line, average cost equals marginal
cost. In this case relation (3) becomes:
1
AC  P (1  )

And,
AC  P[(
(  1)

(4)
)] (5)
19
The mark up pricing policy

Therefore,
P  AC[(


(  1)
)]
(6)
Relation (6) is the same with relation (1) of the
“cost plus” technique.
P  (1   )AC

From (6), it follows that:
1 α 

 1
(7)
20
The mark up pricing policy
And
 [
And since,

(  1)
] 1

1
 1
,
(  1)
(  1)
1
 
(  1)
then
(8)
21
The mark up pricing policy

Therefore, it is derived that the mark up
percentage equals the (negative)
inverse of one plus the value of the
price demand elasticity. So, an inversely
proportional relation holds between
the mark up percentage and the price
demand elasticity. It comes that, for each
product, when the price demand elasticity
(ε) is high, the mark up percentage is low,
and the reverse.
22
The mark up pricing policy
Based on this conclusion, a product
characterised by a significant number of
substitutes, and therefore a high price
elasticity of demand, will be related to a low
mark up percentage, as is the case for paper
products. On the other hand low price
demand elasticity products, such as various
kinds of gifts, tend to have high mark up
percentages.
 For a product with a price elasticity of
demand of -4, the mark up percentage is
33,3% . If ε=-5, then α=25%.

23
The mark up pricing policy
Consequently, when accepting that the
average cost is not varying with the
production level, the case could be that the
“cost plus” price formation coincides with
that stemming from profit maximization
analysis. (Seo 1991, Keat and Young, 1992
 The mark up percentage changes in the
course of time, following, largely, the changes
taking place in the demand and cost
conditions. The new price formed under the
new mark up percentage should also satisfy
the business objectives of the firm.

24
The mark up pricing policy

So, given that that profit maximization forms
the main company objective, this
methodology of successive readjustments
of the mark up percentage can finally
approach the same result derived with
the use of marginal analysis, as the
company makes use of the relation existing
between ε and α, readjusting (α) whenever it
realizes that (ε) has changed.
25
The mark up pricing policy
1
 As it was shown in (8),   
(  1)
From (1), it holds that,
P  AC   (AC)
 Therefore,

(P - AC)

, and
AC
1
(P - AC)


, so
(  1)
AC
- AC

1
(P - AC)
(9)
26
The mark up pricing policy
Relationship (9) is useful as it demonstrates the
required value of the price demand elasticity
in order for an existing mark up percentage to
maximize profits.
Example:
 A company producing writing pads, sells them at 2.5
euros, each package of 5 writing pads, 39% above
the average cost, which remains steady at 1.8 euros
per package. Which elasticity has to be obtained for
the mark up percentage to be the one that
maximises profits?

1.8
1.8
 
 1    1  2.57  1  3.57
(2.5  1.8)
0.7
27
The mark up pricing policy
Therefore the demand elasticity with
respect to price must be – 3.57 times, in
order for the 39% mark up to maximize
profits.
 The company could subsequently analyse
whether the mark up percentage is low or
high. If it lowers price say, by 10%, it can be
seen whether sales increase by 35,7%. If this
does not happen and sales increase by a
lower rate, say 25%, then the mark up
percentage is low and the company will
further increase price in order to approach
maximum profit.

28
The mark up pricing policy

In case that companies within a sector
follow this practice in product pricing, they
can impose the same mark up percentages
so that prices change by the same
percentage, and no price differentiation is
observed. Under these conditions, it is
possible, with a great approximation of
reality, to foresee, the reactions of the
competitor companies following changes in
costs and prices.
29
Other pricing policies

The pricing policy analysed above is
determined on the basis of the production
cost. Companies, though, under the effect of
uncertainty, can also adopt other pricing
policies, in practice, in the context of their
business strategy and objectives. The pricing
policy under uncertainty, beyond the
production cost, can also take into account
demand, market share and existing
competition (Douglas, 1987, Mussa and
Rosen, 1978, Lambert, 1980).
30
Current price level and quality of
the product
In the context of a production sector, the current
price level is formed as a result of the actions of the
participating companies. So, the leading companies
can set the price of their product, while they follow
the changes in the market and the price elasticity of
demand.
 For the other companies, the current price level
forms the basis for the determination of the price
of their own product, for which they believe that it
is differentiated on certain characteristics, compared
to the other products of the sector, and therefore
the price that they shall set differs, either higher or
lower, from the price of the other products.

31
Current price level and quality of
the product
A significant role in this price formation is played by
the consumers’ perception with respect to the
existence or not of desired characteristics
incorporated to the product.
 For example, in the television market, one can find
many types with different characteristics, such as a
flat screen, plasma and LCD, among others. The
adding of characteristics provides room for the
price margin to move higher for each company.
 However, when the quality level is similar, prices
cannot be differentiated and are expected to
approach each other, among the competing
companies. As it is obvious, pricing takes into
account the quality of the product.

32
Current price level and quality of
the product
Companies endeavour to link in the general picture
for their product the existence of uniqueness,
aiming, through a higher price, to “convince” the
consumer that the product they offer is of high
quality. They believe that by setting the price at a
higher than the normal level, consumers will realize
that the product has a higher quality, as compared
to other competitive products, increasing in this
way their sales and profits in relation to the case of
setting a lower price.
 In case the consumers cannot easily realize the
quality of the product, this policy may prove to be
ineffective for a company.

33
Current price level and quality of
the product
On the contrary, when they do realize the
quality, they are willing to pay more.
 For example, for products such as those
of high technology, the price reflects
consumer evaluation of the quality of the
product, as well as for drugs, branded
cosmetics, specially designed branded
clothes, for which certain consumers are
willing to pay a high price.

34
Offer of products at low prices
Another way of sales promotion, especially for
products of elastic demand, refers to the policy that
is followed in practice, where price is set at a
lower level than the market price, for a given
time period. So, a company could aim at increasing
its sales and attract new consumers, whose demand
will spillover to other products of the company.
 That is, the formation of a low price for a product
from the total product line offered by a company,
leads not only to the increase of demand for this
product, but also to the rise of demand for all
products of the product line, resulting to the
35
increase of total sales and to company profits.

Offer of products at low prices

Durable consumer goods, domestic
appliances and similar products, for which
repetitive purchases are made, fall into this
category. Factors such as the behavior of
competitive enterprises and the perception
of the consumers on the quality of the
product, form significant variables which
determine the demand for the product
when the price changes.
36
Other policies


Frequently, a pricing policy is adopted aiming to be
linked with a specific business objective of a
company, such as the faster repayment of the
investment cost and the improvement of the cash
flow of a company. The pricing level which succeeds
to the attainment of this objective is then adopted
and assists the company to face a poor cash flow,
especially when frequent market changes take place
affecting the demand for the product.
For the formation of this price, certain factors are
also taken into account, such as the price demand
elasticity, the competition facing the product and the
maturity of the market, as well as the expected
changes in demand.
37
Other policies


Douglas (1987) asserts that this policy of
price differentiation where the bigger is the
“size” of a product the smaller is the price per
unit of product paid by the consumer, is
effective only if the company has the ability
to offer the product at a bigger size and
to increase its consumer base, since, for the
consumer, the additional cost is smaller
compared to the additional quantity that he is
to acquire.
This policy is usually implemented for
consumer products, such as food, drinks and
cleaning products.
38
Other policies

Another policy implemented, refers to the
offers made by companies in the form of
coupons, in this way intervening to the
market in order to revitalize the demand for
a product, to smooth out seasonal variations
in demand, or face the accumulation of high
stocks.
39
Other policies
The choice of the skimming price
 The skimming price refers to the choice of a
relatively high price for a newcoming
product to the market, aiming at achieving the
higher possible short term profit. In this case,
demand is restricted to those buyers who are
able and willing to pay a relatively high price. If
the time horizon of a company is not very
long, then the skimming price maximizes
profits.
 The following diagram presents the price
which maximizes company profits.
40
Other policies
The skimming price for short-term profit
maximization
41
Other policies
Although
this diagram refers to the case of
monopoly, it is repeated for stressing two
significant points:

Firstly, the innovating company functions in
practice as a monopoly in the market of the
new product, since there is no other company
with similar product, at least in the beginning.
In the following periods, the entry of
competitors with similar products will turn the
market into oligopoly, unless this development
stops through entry barriers, such as patents
owed by the company, lack of resources on the
side of the potential competitors, or lack of
technology.
42
Other policies
Also, the skimming price is frequently chosen
when the demand for a product is considered
as a short – term one and then the consumer is
to turn to other products.
 Secondly, the production capacity of a
company could be small in relation to market
demand. Since the risk of producing failed
products is high, the company may be skeptical
in committing resources to construct a bigger
production unit or it may not be in a position
to proceed to that until the demand size is
definitely shown. In this case the company
produces beyond the production level that
minimizes average cost.

43
Other policies
In the long term, the company can advance
to the construction of a bigger unit and the
skimming price could facilitate this
expansion.
 The choice of the skimming price is also
appropriate when the company aims at
profit maximization in the long run,
particularly when important obstacles and
costs do not favour the entry of competitor
companies, or when the company’s strategy
refers to linking the price with the quality of
the product.

44
Other policies
The penetration price
 The penetration price refers to the practice where
a company sets the price of a product at a
relatively low level in the current period in
order to achieve a broader penetration to the
market and secure, subsequently, a bigger market
share. Certainly, the maximum penetration can be
achieved by selling the product at a price which is
linked to a minimum percentage of profitability for
the company.
 In practice, the penetration price is linked to a low
mark up percentage which leads to the
penetration of the product to the market, and
refers to short term sales maximization subject to
the achievement of a minimum level of profit.
45
Other policies
Usefulness:
The penetration price is adopted when the
company is concerned with the entry of
other companies to the sector, with
products that are considered as substitutes.
 Therefore, it discourages competitors from
entering the market with substitute
products. It is also useful for companies
whose time horizon extends beyond the
short-term period.

46
Other policies
Sales maximization subject to the attainment of a
minimum profit level must not be considered as
incompatible with the maximization of the expected
present value of the long term profits. More sales in
the short-term, particularly for price elastic demand
products, lead to more profits in the long-term, due
to larger repetitive sales, larger sales of
complementary products and lower probability of
entry of other companies, as a result of the lower
price.
 The determination of prices in practice is not
exhausted with the cases referred above, as in reality
there are many other methods. The continuous
adjustment of the price of a product, throughout its
life cycle and the entry price of a new product, form
also pricing methods (Alexakis – Xydeas, 1998).

47
Pricing of a product line
The operation model of a company is differentiated
when it comes closer to a modern company,
producing a series of products – a product line – in
order for the profit maximization objective to be
achieved.
 In the case of a company producing more than one
products, these products can be independent
among them, that is both the cost and demand for
a product are not affected by the other products.
Therefore, according to economic theory each
product can be produced at the level where its
marginal revenue equals its marginal cost.
 If, however, there is dependence between the
products, then the determination of the quantity
and the price must take into account specific
48
interdependences, for profit maximization.

Pricing of a product line
Thompson (1985) has determined certain
significant cases of product interdependence.
a) Product interdependence with respect
to
demand
consumption,
for
complementary or substitute products, as
for example is the case of a certain type of
television and its spare parts in the first
case and various beverages in the second
case.

49
Pricing of a product line
b)
Product interdependence with respect
to the production cost. This holds, firstly,
for products co-produced in constant
proportions with the use of common
resources, that is, when, a fixed quantity of
resources produces more than one products
in constant proportions, and, secondly, when
the products are co-produced competing for
the limited available quantities of resources,
since the production of one product takes
place at the expense of the quantity of the
remaining products.
50
Pricing of a product line


Companies have various reasons for
producing more than one products. When
they are complementary, such as the camera
and the film, they are used together and
frequently purchased together. The company
aims at determining prices at the levels that
achieve profit maximization.
When the products are substitutes, the
companies proceed to their production in
order to gain the biggest possible market
share and also create, in this way, difficulties to
their competitors in entering the market.
51
Pricing of a product line

In general, the production of a number of
different products which, however, share
certain common features, forms a preferable
policy on the part of the companies to
compete one another, mainly in oligopolistic
markets.
52
Pricing of a product line
In particular, for the case of Product
interdependence
with
respect
to
consumption, on the basis of the mark up
pricing practice, the price of each product is
chosen using the product’s position in
the product line as a criterion and the
competition it faces in the market,
while the value of the price elasticity of
demand is also taken into account.
 The latter depends on the existence of
substitute and complementary products.

53
Pricing of a product line
When the products of the line are complementary,
companies usually determine a low mark up for the
basic good, in order to achieve a broad penetration
to the market and an increase in the sales of the
complementary products.
b) When the products are substitutes, firstly, the price
for the lower quality product of the line is
determined in relation to the prices of the products
of the competitors in the market. Then, the price for
the next product of the line is determined based on
the additional qualitative characteristics that it
possesses, and on the prices of the competitor
54
companies for almost the same product.
a)
Pricing of a product line
This process continues along the production
line, successively, while higher mark ups are
determined for products of higher income
elasticity of demand.
 Frequently, the lower quality product is
priced at a very low price, in order for the
customers to be attracted and become
convinced for the advantages of the high
quality substitute product of the line. This
happens for many durable consumer goods.

55
Pricing of a product line
A policy frequently met, contributing significantly to
sales promotion, refers to the sale of a group or
package of two or more products together,
as for example a modern television system, the
home cinema.
 However, in order for this policy to be the best
possible for the company, it should provide the
ability to also offer these products, separately, since
certain consumers would wish to pay only for one,
say, of these products. It is obvious, though, that the
price of each of these products, when sold
separately, is higher to that of a group sale, and
therefore the value of the group of the products is
lower than the cumulative of the separate values of
all products.
56

Questions
1.
2.
3.
In practice, the assumptions that are
considered to hold in market models for
price determination of a product, are rather
not valid. The company by following the
market conditions aims at determining the
price that satisfies its objectives, in the best
possible way. Express your views on these
comments.
Pricing on a mark up basis takes also into
account the price demand elasticity of the
product. Comment.
How is the pricing policy determined for a
company under conditions of uncertainty?
57
Questions
4.
5.
6.
Under what conditions the skimming price
is appropriate for company profit
maximization?
When is the choice of the penetration
price the appropriate policy for a
company?
Describe cases of interdependence
between products produced for the case
of pricing a product line.
58
Exercises
A company selling female clothes buys a quantity
of female dresses from a wholesaler by paying 30
euros per dress, irrespective of the quantity of
the dresses. These dresses have a mark up of
33,33%, above cost. The objective of the
company is to determine the price at a level that
achieves the maximum in both covering costs
and obtaining profits. The company management
is faced with the question, whether the 33,33%
markup is the one that maximizes profits.
 Which is the elasticity of demand that should hold
in order for the used mark up to be the optimum
one?
1.
59
Exercises
2.
A company introduced a new product to the
market in the first month of the year, which was
supported by the relevant advertising campaign
and presented a steady rise during the next
months. The initial price was set at a level 30%
above cost. The objective of the company is to
cover its general expenses and maximize profits.
Therefore, it examines whether the price of 7.5
euros is the optimum one. Through continuous
sales growth, the company undertook market
research and derived a price demand elasticity of
-3. The sales (tones) and the cost (thousand
euros) for the next 3 months, are estimated as
follows:
60
Exercises
January
February
March
Sales (volume)
2,250
2,500
2,750
Raw materials
1,400
1,550
1,700
Labour
3,350
4,050
4,950
Other Industrial Cost
3,000
3,075
3,150
Management Costs
2,150
2,150
2,150
Electricity – Heating
450
475
300
2,200
2,200
2,200
Other general expenses
61
Exercises
a)
b)
c)
Assuming that the price can be changing,
estimate the price per month.
What is the mark up percentage derived
for each month?
What other possible issues may have to
be taken into account, beyond the
decision on the price and the sales?
62
Exercises
3.
A company introduces a new product which
depicts unique characteristics. The production
director estimated the following average cost
(euros) for the product, for the first year and for
the other two years.
Production level
2,000
4,000
6,000
8,000
10,000
1st year
12.50
11.75
11.50
11.7
12.00
2nd year
10. 00
9.70
9.55
9.50
9.80
3rd year
9.10
9.00
8.80
8.75
8.85
63
Exercises

The introduction of the product was
accompanied by a large advertising campaign
which put emphasis on the unique
characteristics of the product. The time for the
determination of the price has arrived. The
market research undertaken depicted a price
demand elasticity of – 4 for the first year, - 3
for the second year and – 2 for the third year.
The indications from the market suggest that
the demand for the product will be increasing
during the first 3 years, and then the entry of
competitors with product substitutes will lead
to a shift of its demand curve towards the left.
64
Exercises

Pricing should take into account the
management objective for profit and return
maximization, in particular following the
increased amount spent on advertising and
promotion, by the company.
On the basis of the above information, which
is the price that maximizes profits for each of
the three years?
b) Under what conditions, would you suggest to
the company to adopt the policy of the
penetration price?
a)
65
Exercises
4.
a)
b)
Answer the following:
Derive the formula that provides for the
price elasticity for a given mark up rate to be
profit maximizing.
Suppose that body strengthening herbal
pills are sold for 1.20 euros per packet, 26%
above average variable cost which is at 95
cents per packet. Which is the price elasticity
that has to hold if this margin represents the
profit maximizing mark up? What does this
elasticity imply for this particular case?
66
Exercises
c)
If, due to a price decrease of say 10%
sales were to increase by 35%, what
would this imply for the above mark up
and the price of the product, for profit
maximization?
67
Solutions to Exercises
68
Exercise 1

AC = € 30/ per dress

The company, using a mark up percentage
a=33,33%, maximizes profits.

P = AC + a*AC  mark up policy

P=30 + 0.3333*30  P ≈ 40
a = -1 / (ε+1)
 The mark up percentage equals negative inverse of
one plus the price demand elasticity (ε).

69
Exercise 1
When ε is high, then the mark up percentage
is low, and the inverse.

a = -1 / (ε+1)

P = AC + a (AC)

a = (P-AC) / AC
 Then, -1/(ε+1) = (P-AC) / AC
 ε = [ -AC / (P-AC)] -1 = [-30/(40-30)] – 1
= -4
 Meaning: An increase in price by 1%, leads
to a reduction to the quantity demanded by
4%.

70
Exercise 2
 εP = -3
 Formula: AC = Expenses / Sales
 Expenses (January) = 1,400 + 3,350
2,150 + 450 + 2,250 = 12,600
 Expenses (February) = 13,500
 Expenses (March) = 14,450
 For January:ACJ = 12,600 / 2,250
 ACJ= 5.6
 For February:ACF = 13,500 / 2,500
+ 3,000 +
 ACF = 5.4

For March:ACM = 14,450 / 2,750
 ACM = 5.25
71
Exercise 2
From the elasticity formula 
 εp = [-AC/(P-AC)] – 1, we derive the price
per month:
 PJ = 8.4
 PF = 8.1
 PM = 7.87

72
Exercise 2
b)
P = AC + a*AC or a=-1 / (ε+1)

January: 8.4 = 5.6 + a*5.6  …  a=50%

February: 8.1 = 5.4 + a*5.4  …  a=50%

March: 7.87 = 5.25 + a*5.25  … 
a=50%
73
Exercise 2
c)
Other issues: Elasticity with respect to
advertising, disposable income, reaction of
competitors (when the new products will
be launched), among others.
74
Exercise 3

Note1: Since it is not defined which
production level is to be chosen, alternative
combinations can take place. They assist in
deriving the most beneficial combination.

Note 2: P = (1+a)*AC
75
Exercise 3
 For the production level of 2,000 units:
 1st Year  a=-1 / (ε+1) = -1/(-4+1) = 0.33
Then , P = (1+0.33)*12.50 = 16.625 euros
 2nd Year
 a= -1 / (-3+1) = 0.5
Then, P = (1+0.5)*10.00 = 15 euros
 3rd Year
 a= -1 / (-2+1) = 1
Then, P = (1+1)* 9.10 = 18.2 euros

The same process is followed for the
remaining production levels.
76




Exercise 3
b) Penetration Pricing 
A relative low product price during the current
period, aiming at a wide penetration of the
market and securing, subsequently, a bigger
market share.
In practice, it is related to a low mark up
percentage  short term sales maximization,
subject to attaining a minimum level of
profitability.
It is adopted when the entry of other companies
to the sector is taking place, with products which
are considered as substitutes. (εPa > 0)
77
Exercise 3
It discourages competitors to enter the
market with substitute products
 It is useful for enterprises whose time
horizon extends beyond the short-term
period.

78
Exercise 4
a)
 AC

1
p  AC
Therefore,
b)
 0.95

1.20  0.95
1
and
  4.8
The price elasticity that has to hold is -4.8 .
It implies that a, say decline by 10% in the
product’s price leads to a rise in demand by
48%.
79
Exercise 4
c)
When, however, a 10% decrease in price
leads to a sales increase by 35%, it
implies that ε=-3.5 times. Therefore,
both the mark-up and the price have to
change, to be increased.
a
1
1

 0.40
  1  2.5
or 40%.
80