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 3
Instructor: Panayotis Alexakis
In cooperation with:
Under the aegis of:
Managerial Economics and
Financial Management
Chapter 3: Cost Concepts for Decision Making
Contents of presentation:





The economic cost as an opportunity cost
Forms of costs and management rules
Cost and the choice of the size of the
production unit
Breakeven analysis and operational leverage
Economies of scale, learning and combining
Introduction
Every business decision takes place following the
comparison between the benefits, that is the revenues
to be obtained, and the costs related to it. Benefits
should exceed costs. The measurement of cost related
to a business decision must be accurate, which is not an
easy case for two main reasons:
1. The economic cost for the production of a good may
differ from the expenditures occurred for the
production of this good.
2. The use of fixed assets do not become obsolete after
the production of a certain quantity of the good, but
instead remain and are used for the production of
more product units in the course of time.

3
The economic cost as an
opportunity cost
As microeconomic theory indicates, the
correct measurement of cost is the one that
takes place under the concept of the
opportunity cost.
 The opportunity cost of a production factor is
determined by its value in its best possible use.
The prices prevailing in the market for a
production factor are considered as a
satisfactory indicator of the opportunity cost.
 This is justified by the understanding that
market prices express the amounts that the
various users of this factor are willing to pay
for the acquisition of this production factor.

4
The economic cost as an
opportunity cost
Example:
 Let us suppose that a raw material, say
aluminum, is used for the production of goods
by various factories.
 The prevailing market price represents the
value that the marginal user places for its use.
 The acquisition of a unit of raw material by
another user deprives this unit from the
marginal buyer and prevents him to produce a
value that is equal to the raw material value
that he is willing to pay.
5
The economic cost as an
opportunity cost
An alternative way to comprehend OC:
 Let us suppose that a firm possesses a quantity
of raw material in its warehouse.
 In order for the company to estimate correctly
whether the use of the raw material is to its
benefit, the company could consider the price
prevailing in the market.
 This price is the opportunity cost because the
alternative use for the company would be to
dispose it to the market and obtain revenues
at the market price.
6
The economic cost as an
opportunity cost
The previous example of the warehouse raw material is
sufficient in order to shed light on the important
difference between accounting and economic cost.
Differences:
 The accounting cost has to do with the recording of
the expenditures that were realised for the production
of a unit of a product. The economic cost represents
the opportunity cost.
 The accounting cost implements the reporting of
expenditures that were undertaken. The economic cost
takes into account the alternative uses of resources and
forms the appropriate calculation for proper
management decisions.
 Under certain conditions, both coincide while under
other conditions they differ.

7
The economic cost as an
opportunity cost
Example:
 Suppose that company A undertakes the
production of aluminum frames and has for this
reason acquired and keeps in its warehouse 10
tons of aluminum, at the price of € 1,000.00 per
ton. Three months later, it is getting prepared to
use this quantity to the production of aluminum
frames. However, within these three months
international aluminum demand has suddenly
increased due to needs of the aerospace industry,
resulting a rise in the price to € 1,100.00 per ton
8
The economic cost as an
opportunity cost
If A has the ability to sell this raw material stock
to the market at the price of € 1,100.00 per ton,
this new price is the opportunity cost of the use
of aluminum for the production of frames.
 The initially purchased price € 1,000.00 per ton,
has however been recorded in the company
books and presents the accounting cost.
 If the aluminum price remains steady during the
quarter between the purchase and the use of the
raw material, then both the accounting and the
economic cost would coincide.
 If, however, the price had been reduced in the
meantime, then the economic cost would be
lower as compared to the accounting cost.

9
The economic cost as an
opportunity cost
However:
 The prices prevailing in the market are not sufficient for
all cases for the determination of the opportunity cost.
This happens, mainly, for the cases that certain
production factors are so specialized in the production
of a company that their alternative uses outside the
company are rare or absent.
 The cases where this happens relate mainly to
machinery. The source of this problem can be
understood, as contrary to the raw material which is
offered for many uses, specialized machinery has a very
different acquisition price and sale price, subsequently.
Usually, the second price is lower than the first. For this
reason, the opportunity cost of a machinery, before its
use by the company, equals the market price, while
following its acquisition, equals the sale price.
10
The economic cost as an
opportunity cost
A last dimension of the opportunity cost of
particular importance for the case of equipment,
has to do with its multiple use inside a company.
Example:
 A machine can be used for the production of
product I and also of product G. Its use for
product I, represents an opportunity cost equal to
the income that would be achieved from its
alternative use for the production of G.
 It becomes evident that, in this case, an
intracompany comparison of alternative uses is
taking place, which depends not on the value of the
machine but on the profitability it generates to the
various activities of the company.

11
Forms of costs and management
rules




The identification of the cost connected to
each entrepreneurial decision is assisted if one
takes into account the various forms of cost
appearing in practice.
One first dimension assisting towards this
direction is the distinction between explicit
and implicit cost.
Explicit cost is easily calculated as it is
composed of expenditures directly related
with the activity.
The calculation of implicit cost is more
troublesome as it has to be perceived as an
opportunity cost.
12
Forms of costs and management
rules
Example:
 Let us suppose a unit producing pairs of stockings,
and requires the purchase of fixed assets of 100,000
euros, annual labour cost (in full capacity) of 15,000
euros, and cost of raw materials and energy of
10,000 euros. The last two categories of costs are to
be covered by the sales. The cost of fixed assets
should be covered immediately. Two businessmen, A
and B, separately, consider the undertaking of this
activity. A already possesses 100,000 euros through
savings. B must borrow at 15% borrowing rate and
therefore has to bear an additional annual amount
of 15,000 euros.
13
Forms of costs and management
rules
It can be seen that the explicit cost is higher for B
(15,000 + 10,000 + 15,000 = 40,000 euros) as
compared to A (15,000 + 10,000 = 25,000 euros).
 However, it would be a mistake to conclude that
the production of stockings is more profitable for
A, as he is subject to the implicit cost of 15,000
euros. This means that the 100,000 euros that he
possesses imply an opportunity cost, as he could
lend this amount at an interest of 15%, instead of
using it for the purchase of the fixed assets.
 Therefore, the total annual cost is the same for
both A and B.
14

Forms of costs and management
rules
A second distinction is the one between
incremental and disbursed cost.
 The incremental cost of a business decision
equals the total outflow that is exclusively
related to this decision.
 On the contrary, the disbursed cost is
composed of outflows that have already
taken place which do not change due to
the undertaking of the business activity
under study.

15
Forms of costs and management
rules
Example:

Company ABC spends 50,000 euros for the
construction of a warehouse with freeze
compartments, especially designed for the
maintenance of dairy products. Unfortunately, the
processing of dairy products that was planned was
cancelled due to environmental problems threatening
milk contamination. Since that time the warehouse
remained unutilized and the freeze compartments
were subjected to destruction. Now ABC plans to
use the warehouse and its equipment for meat
maintenance. The repairs and adjustments that have
to be undertaken require expenses of 23,000 euros,
while the new activity is estimated to bring revenues
(before the warehouse costs) of 32,000 euros.
16
Forms of costs and management
rules
The question is whether this activity should be
undertaken.
 The incremental cost of this activity is to
generate a profit of 9,000 euros and
therefore it is beneficial and is recommended
for realization. The initial warehouse and
equipment cost should not be taken into
account as it is an already disbursed amount
and this expenditure exists, independently of
whether the new activity is undertaken or
not.
17
Forms of costs and management
rules
The third cost dimension, is already known
from economic theory and distinguishes
between fixed and variable cost.
 While in the previous two cases, the analysis is
related to a business activity in total, this last
distinction refers to the way that the
production cost changes as the quantity
produced changes, too.
 The fixed cost is the size which does not
depend on the change of the production
quantity

18
Forms of costs and management
rules
Fixed cost is related to fixed expenses
(buildings, equipment, installations, managerial
operation), which are required for the
fulfillment of the production activity and
remain steady irrespective of the production
scale (of course, within limits).
Example:
 The expenses for space rental, the interest
paid on company loans for the acquisition of
equipment, the salaries of top executives,
refer to sizes which do not depend on the
upward or downward changes of the
production level.

19
Forms of costs and management
rules
The variable cost depends on the
number of units produced.
 It originates from expenses on production
factors which are incorporated in each
production unit (e.g. a raw materials,
energy, labour cost). These expenses,
obviously, depend on the production cost.

20
Forms of costs and management
rules
Having in mind the characteristics which,
respectively, determine the fixed and the
variable cost, it can be easily deducted that
their relative sizes depend on the
production function that is used.
 A production procedure that is highly
capital intensive brings forth a high fixed
cost, while a production procedure of low
capital intensity is related to a relatively
higher variable cost.

21
Forms of costs and management
rules
Cost sizes
Quantity Total
Fixed
Variable Average Average Average Marginal
Cost
Cost
Cost
Total
Fixed
Variable Cost
(TC)
(FC)
(VC)
Cost
Cost
Cost
(ATC)
(AFC)
(AVC)
(MC)
1
120
100
20
120.0
100.0
20.0
20
2
138
100
38
69.0
50.0
19.0
18
3
151
100
51
50.3
33.3
17.0
13
4
162
100
62
40.5
25.0
15.5
11
5
175
100
75
35.0
20.0
15.0
13
6
190
100
90
31.7
16.7
15.0
15
7
210
100
110
30.0
14.3
15.7
20
8
234
100
134
29.3
12.5
16.8
24
9
263
100
163
29.2
11.1
18.1
29
10
300
100
200
30.0
10.0
20.0
37
22
Forms of costs and management
rules
Costs per product unit
23
Forms of costs and management
rules
The table and diagram above incorporate three worth
observable points:
a)
The effect of the fixed cost in the formation of the cost per
unit of output is continuously falling. Therefore, on the side of
fixed cost, it is to the benefit of the company to achieve the
maximum possible increase of production.
b) The effect of the variable cost in the formation of the cost
per unit of output is initially falling. However, after the 6 units
produced it becomes rising. For this reason, the maximum
possible increase in production may not necessarily be the
most beneficial from the side of total cost. In the above
examples, the minimum total cost per unit of output is
achieved at 9 units produced.
c)
The marginal production cost does not coincide with the
average cost, as it presents the change in total cost. This
change is due to the variable cost change as production
increases by one unit, given that fixed cost remains
unchanged.

24
Forms of costs and management
rules
Note:
 The distinction between fixed and variable cost
requires special attention on the part of decision
making, as it is valid only within certain limits.
 The production factors which determine fixed cost
have always a maximum use limit and they can
support the production process up to a given scale.
For example, the capacity utilization of a factory, the
capacity of a warehouse, the capacity of a
management team to offer services, they all have a
natural limit. Within this limit, the distinction
between fixed and variable cost is valid. Beyond this
limit, it is not valid as the increase of production at a
higher scale requires the additional capacity of the
factory, new warehouse spaces, or more executives.
25
Forms of costs and management
rules
Using the example of the above table, suppose also
that the production limit is at 10 product units. The
11th unit requires new installation leading to the
change of fixed cost from 100 to 200. The same can
be repeated for the 21st unit and so on. Therefore,
in order for production to be increased to a bigger
scale, the fixed cost is transformed to variable, too.
 However, since the big changes in the production
scale occur usually (not always) in long time periods,
economics considers the presentation of the above
table as representing the short term behavior of
cost, while it considers that when adopting a long
term perspective all cost kinds are variable.

26
Forms of costs and management
rules
From the company side, the decision
makers must consider as short term the
least period required for the change of the
production factors which affect (feed in)
the fixed cost.
 For example, if the change in the
production capacity of a factory requires
construction works for a year, the short
term behavior of cost applies for a period
less than a year.

27
Inventory management as cost
factor


Managing the company’s supply chain and
logistics, the sources of its raw materials and
inputs and the handlers of the outcome
(outputs), forms one of the essential direct
cost factors which contribute to pricing.
A company carries inventories because of
the difficulty to predict, quantities and also
the timing and location of demand (or
supply). Minimizing cost (so minimize one of
the pricing factors), is essential in this case
by finding the optimal inventory level.
28
Inventory management as cost factor
The most significant factors are:
a. Ordering costs which are fixed costs of placing an
order - independent of the amount of units
ordered, and
b. Carrying costs (known as holding costs), which
may be, rents, taxes, lying and demurrage charges,
depreciation (or obsolesce), and opportunity cost,
among others. Carrying costs are reduced by
minimizing the inventory level.
 Also other non-operating factors, such as theft, or
waste can play their role. In order to avoid
troubles and risk stock-outs and shrinkages, safety
stock must always be present.

29
Theoretical model
The challenge is to find the spot where total
costs of inventory are minimum (given the
total cost and the order quantity). The
intersection of the carrying costs with the
ordering costs curve is represented by the
following formula.
 EOQ=[(2ad/K)] 1/2, which
 a= variable cost per order (or production
setup)
 d= Demand (periodical) in units
 K= Carrying cost (unit periodic)

30
Theoretical model
31
Theoretical model

This formula indicates that EOQ varies
directly with demand and order (setup)
costs, and varies inversely with carrying
costs. The average level of inventory is
always the ½ of the EOQ. The model has
its limitations relating to its restrictive
assumptions on these 3 variables, which
remain constant throughout the period.
Also, stock-out costs here are zero and
no safety stock is held.
32
Practical models (methods)
ABC Inventory Management

ABC method focuses on cost-reducing
tactics and leads managerial control by
often and regularly reviewing the
inventory on A Group, less often in B
Group and not so often on C Group
(because it consists, from lesser value
inventory items).
33
Cost and the choice of the size of
the production unit
So, the size of a production unit, a factory
for example, determines the limits and the
relative magnitudes of fixed and variable
cost. Under a different size of a factory the
short term cost curves will differ, too.
 The following diagram presents three cases
of factory scales A, B, C, where A is the
smallest and C is the largest scale.

34
Cost and the choice of the size of
the production unit
Q1
Q*
Q2
35
Cost and the choice of the size of
the production unit
Size of Production Unit and Variations in Production and Sales
36
Cost and the choice of the size of
the production unit
As it can be seen from the diagram, the
lower cost per unit of output is achieved
when the production scale B is selected,
with Q* being the quantity produced.
 This, however, does not imply that the
company will, at all cases, select this
production scale. If it expects that
production will exceed Q2, then production
scale C forms the best choice. Production
scale B is more appropriate for production
levels which are between Q1 and Q2.

37
Cost and the choice of the size of
the production unit


Another, but equally essential, dimension in
the choice of the size of a production unit
refers to the flexibility in large variations of
the quantity of production. Diagram (a)
depicts a typical presentation of this
characteristic. It can be observed that the
production unit A achieves a very low cost
per unit of output at the level of 5,000 units,
while unit B depicts a higher cost, at the same
level.
Unit A depicts a very large cost increase as
production moves away from the level of
5,000 units.
38
Cost and the choice of the size of
the production unit


On the contrary, unit B presents a small cost
increase only for production levels above
5,000 units. From the cost side, unit A is a
specialised factory achieving very high return,
for a specific production scale, while unit B is
very flexible to changes in production.
Furthermore, selecting the type of unit A is
not the best business decision, always. The
right choice depends on the degree of
variation of production and this in turn is
determined by the variation in sales.
39
Cost and the choice of the size of
the production unit
Diagram (b) on production size and variations in
production and sales, presents two probability
distributions of sales. Both present an expected
sales level of 5,000 units.
 However D depicts a relatively smaller variation
around the expected level of 5,000 production units,
while E has a significant variation.
 If the probability distribution D presents the sales
behavior correctly, then the choice of type A
production unit is favoured.
 If on the other hand distribution E presents the
right sales behavior, then production unit B is
favoured.

40
Break even analysis and operational
leverage


The formation of the production cost leads to
the right business decision only if it is
combined with the revenues from the sales of
the product.
One known way for the analysis of this
combination is the break even analysis. The
break even point of a company refers to the
quantity of production where revenues are
exactly offset by the production cost, and it is
estimated with the use of the production cost.
41
Break even analysis and operational
leverage
The break even point is calculated as follows:
Suppose that:

P, is the price per unit of product
 Q, is the quantity of the product, produced and sold
 FC, is the fixed cost
 AVC, is the variable cost per unit of product
 QB, is the break even quantity produced and sold.


The break even point requires that revenues equal costs:
(1)
PxQB  FC  (QB xAVC)
42
Break even analysis and operational
leverage

which derives:
FC
QB 
P  AVC
(2)
Example:
 Suppose that a publishing company V plans
the publication of a book on the medical
science. The cost of publication is as
follows:
43
Break even analysis and operational
leverage
Fixed cost
€
 Correction texts 1,700
 Pictures
2,700
 Composition
5,600
 Total fixed cost
Variable cost per book
 Paper, printing, binding
 Bookshop fee
 Writer rights
 General Sales Expenses
 Total variable cost p.b.
Sale price per book
10,000
€
1.21
0.80
0.34
0.85
3.20
4.00
44
Break even analysis and operational
leverage

Then by formula (2) above:
10,000
QB 
 12,500books
4  3.2

It is derived that for the company to
produce profits, it has to sell more than
12.500 books. If the estimations from the
market suggest that a lower number of
books will be absorbed, then this
publication does not have profit prospects.
45
Break even analysis and operational
leverage
However, before the publication is abandoned, two
other solutions could be analysed.
 One solution is to raise price to € 4.50 per book, as in
this case the break even point is at 7,962 books.
 The other solution lies on cost cutting. If by using a
simpler set of pictures reducing fixed cost by 1,000
units, a different quality of paper and simplifications on
binding reducing average variable cost by 0.5 euros per
book, then the break even point is at 6,923 books sold.
 Certainly, the company could combine the reduction in
cost with the rise in the price per book

46
Break even analysis and operational
leverage
However, it should be stressed that there
are limits on these maneuvers. The rise in
price is not always possible, when
competitors offer lower prices, while cost
reduction reduces the quality of the
product leading to a lower sales price.
 Finally, the increase in price could lead
certain cost elements upwards, such as
writer rights, bookshop fees, which are
estimated as a percentage of sales.

47
Break even analysis and operational
leverage
An alternative presentation of the break even
analysis refers to the calculation of the quantity of
production and sales which leads to the minimum
profit. Many companies consider that an activity
should be undertaken only if it brings forth a
minimum level of profit.
 By defining MI as the minimum profit and
QMI
the quantity that secures this minimum profit,
then:
(3)

PxQMI  FC  QMI xAVC  MI
48
Break even analysis and operational
leverage
And,
QMI
FC  MI

P  AVC
(4)
By comparing (4) and (2), it can be seen that
always:
QMI  QB , When QMI is positive
 By using the example of the publishing company,
let us assume that the publication is to proceed
only if it brings forth a minimum profit of 1.000
euros. Then,

49
Break even analysis and operational
leverage
QMI

10,000  1,000

 13,750books
4  3.2
So, while a publication of 12,500 books
realised zero profit, when 13,750 books are
produced and sold, a profit of 1,000 euros
is secured. Based on formula (4), one can
search various choices relating to cost and
price adjustments.
50
Break even analysis and operational
leverage
Break even analysis or analysis of the minimum
profit quantity, provides information on the
minimum production levels without losses or with
a minimum profit.
 Frequently, in reality the production and sales size is
not steady but varies according to the market
situation, the evolution of incomes and seasonal
factors, among others. For this reason, a sensitivity
measure is needed on the level of profits to the
variation of sales.
 This measurement is achieved with the use of the
Degree of Operational Leverage (DOL).

51
Break even analysis and operational
leverage

It practically measures the elasticity of
profits with respect to the product
quantity:
dI Q
DOL 
x
dQ I
(5)
when dI is the marginal change of profit and
dQ is the marginal change of the quantity.
52
Break even analysis and operational
leverage

From the above, profit is defined as follows:
I=(PxQ)-(AVCxQ)-FC (6)

The size dI / dQ is the derivative of profit
with respect to quantity:
(7)
dI
 P  AVC
dQ
while, I / Q is derived from (6) as follows:
(8)
I
FC
 P  AVC 
Q
Q
53
Break even analysis and operational
leverage

DOL is produced when dividing (7) with (8):
Qx ( P  AVC )(10)
DOL 
Qx ( P  AVC )  FC
Formula (9) can be understood in a simple way, given
that the nominator and the denominator differ only due
to the deduction of FC in the denominator. By defining
(P - AVC) as the operational profit margin per unit
of output, then DOL can be determined by the
relative sizes of the operational profit and the fixed
cost.
 The bigger the operational profit in relation to fixed
cost the smaller the DOL, and the reverse.

54
Break even analysis and operational
leverage
That is, when the company has a relatively large
operational profit and a smaller fixed cost, (labour
intensive company), the sensitivity of profit on the
variation of sales is being reduced.
Example:
 Let us suppose two companies A and B produce
exactly the same product but with a different
technology. The sales price per product unit is 20
euros. A uses simple equipment but a large quantity
of labour, while B (capital intensive) uses a
complicated equipment of high automaticity and
very small labour quantity. The formation of cost
appears in the following table.

55
Break even analysis and operational
leverage
Cost formation, revenues and breakeven point
Company A Company B
FC
200,000
600,000
AVC
15
10
P
20
20
56
Break even analysis and operational
leverage
Quantity Revenues Cost
Profit Revenues Cost
Profit
(000
(000
(000
(000
(000
(000
euros)
euros) euros) euros)
euros)
euros)
20,000
400
500
-100
400
800
-400
40,000
800
800
0
800
1000
-200
60,000
1200
1100
100
1200
1200
0
80,000
1600
1400
200
1600
1400
200
100,000
2000
1700
300
2000
1600
400
120,000
2400
2000
400
2400
1800
600
140,000
2800
2300
500
2800
2000
800
160,000
3200
2600
600
3200
2200
1000
57
Break even analysis and operational
leverage
From the sizes of this table it can be seen that:
 Firstly, A has a lower break even point than B
(40,000 and 60,000, respectively). Therefore, by
increasing production, it achieves profits at an
earlier stage, than B.
 Secondly, by increasing production beyond the
breakeven point, B achieves a much faster increase
of profits, than A.
 Thirdly, the profits of B appear to have a higher
sensitivity to the variation of production. This is
also derived from the calculation of DOL for the
two enterprises in various production levels.
58
Break even analysis and operational
leverage
For example:
 At the level of production of 80,000 units:
80,000 x(20  15)
DOL ( A) 
2
80,000 x(20  15)  200,000
120,000 x(20  15)
DOL ( B) 
4
120,000 x(20  15)  600,000
59
Break even analysis and operational
leverage

At the level of production of 120,000 units:
120,000 x(20  15)
DOL ( A) 
 1.5
120,000 x(20  15)  200,000
120,000 x(20  15)
DOL ( B) 
2
120,000 x(20  15)  600,000
Note:
 DOL is always bigger for company B.
60
Break even analysis and operational
leverage
A «critique» of DOL

1.
2.
The use of DOL and the break even analysis is certainly very
informative for business decision making. However, there
seem to be two restrictions that should be taken into
account in the analysis:
It assumes that the sales price is constant and independent
from the production and sale levels. If the sale price varies,
then a demand function has to be incorporated to the
analysis which links the change in prices with the change in
quantity.
It assumes an average variable cost which is also given and
independent from the production level. This assumption
too can diverge from reality. In this case one has to
incorporate an estimation of the cost function to the
analysis.
61
Economies of Scale, Learning and
Combining
 The purpose?
 When it comes
to business initiatives of long term
prospects and growth of the production activity, the
cost estimation must be undertaken on the basis of
projections of its size, when the company is at a
future advanced stage of development, as compared to
the present. Along the growth of a company and
production, three frequent phenomena are taking place
which are conducive to the reduction of cost. These are
the economies of scale, the economies of
learning and the economies of combining.
 Certainly, all three have to be estimated for each
particular case so that their presence is verified, as well
as the size of their effect.
62
Economies of Scale, Learning and
Combining
1.
Economies of scale

The economies of scale describe the case where for long
periods of production increases, the reaction of the quantity
produced is that it increases at a rate which is bigger than the
proportional rise of the production factors used towards this
purpose.
For example the doubling of the production scale requires
less than double increase of production factors, which implies
that as production increases the average cost per unit of
product is being reduced.
Therefore, economies of scale are achieved as the cost per
additional product unit is being reduced during the increase of
production, which is explained by reasons of operational
efficiency in the production process.


63
Economies of Scale, Learning and
Combining
Why is that happen?
 Due both to the fact that the fixed cost is being
absorbed by the rising volume of production, as well as
to the fact that the bigger production, the
standardization of the product and the labour
specialization are combined for the production and
contribute to the reduction of the variable cost.
 More specifically, the existence of economies of scale,
is related to certain significant determinants. So,
indivisibilities on the use of certain production factors,
in combination to the abilities of large production units,
frequently drive the production increase at faster rates
as compared to the rate of increase of production
factors.
64
Economies of Scale, Learning and
Combining
Bigger production units entail a more efficient
utilization and specialization of the labour force and
therefore its effectiveness, as well as a higher
effectiveness of the total production process.
 Also, technology acts as a catalyst to the
achievement of this phenomenon, as it frequently
leads to the complete utilization of large scale
equipment and / or to improvement of the quality
of the final product. The large production units are
the ones which utilize the most efficient production
methods.

65
Economies of Scale, Learning and
Combining
2.



Economies of learning
The economies of learning describe the phenomenon
where the accumulation of production experience
allows for improvements in the production process
which in turn lead to the reduction of the production
cost.
This phenomenon is particularly linked to the
production of complex products, in which other
simpler products can be incorporated, where the
coordination of quality, quantity and the attainment of
outmost accuracy form a complex venture which is
smoothed out along the practice, repetition and
learning.
The production of airplanes and computers form
typical examples of this case.
66
Economies of Scale, Learning and
Combining
3.
Economies of combining

The economies of combining describe the phenomenon where
the production of a product favours the production of another
product, so that their coproduction cost is smaller than the
addition of the costs, if the production of each product were to
take place separately.
A baker, for example, can expand his production in a profitable
way to pastry products because his knowledge and equipment
are offered for this activity. The expansion of the companies of
electronic computers to telecommunications explains also the
emergence of this phenomenon.
The economies of combining force the company to analyse, not
only the profitability of a product, but also the profitability of
activities which can be combined.


67
Questions
1. Describe, how cost affects the choice of size of a
production unit.
2. Explain the relationship between the average cost
curve and the marginal cost curve.
3. Define the difference between disbursed and
incremental cost and utilize an example in order to
make this distinction clearer.
4. Define the difference between accounting and
economic cost. What are the consequences of this
distinction on business decision making?
5. Describe the procedure of the break even analysis.
6. Distinguish between economies of scale, learning
and combining.
68
Questions
7. Under what conditions can a business expansion be
a combination of all the above economies?
8. The degree of operational leverage forms a
significant factor for business decision making,
particularly those related to the structure of the
production unit and the proportional use of the
production factors. Express your views on that.
9. How does depreciation affect a company’s break
even analysis?
10. In the choice of the size of a production unit, an
important factor that should be taken into account
refers to the flexibility in large variations in
production quantity. Do you agree or disagree?
Express your opinion on that.
69
Exercises
1.
DANUBE S.A. deals with the trade of
legumes. It purchases in advance 1000 tones
annually at pre-agreed prices, paying the
producers 20% in cash and the rest in
promissory notes which are redeemed
following the sale of the product. This year
the total purchase value is 30,000 euros. The
warehousing for the product costs 3,000
euros and is prepaid by DANUBE S.A. The
company faces three choices for the sale of
the product.
70
Exercises
Sale of the product at the domestic market
with a guaranteed price of 24 euros per ton.
b) Sale of the product at the European market
where the price can range (with equal
probability) to 24 euros or 36 euros per ton,
on the basis of current expectations.
c) Sale to the Asian market, where the price
can range with equal probability to 12 euros
or 50 euros per ton, on the basis of current
expectations.
a)
71
Exercises
DANUBE S.A. has to settle, now, the
transportation of the product which is to be
sold to only one of the above markets.
 Which choice should the company adopt?
 Which choice should the legume producers
prefer?
 Which choice should the company prefer, if it
was wholly owned by one shareholder only
with a total worth of 60,000 euros?
•
72
Exercises
2.
Two total cost functions are given:
TC1  2,000,000  150Q  0.02Q 2
TC2  2,250,000  200Q  0.01Q
a)
b)
c)
2
Derive the marginal and average cost
function for each case.
Determine the production limit where
scale economies are exhausted for each
cost function.
Compare the two cost functions.
73
Exercises
3.
Three postgraduate students of business
economics at Munich University, plan their
summer work. One possibility for them is to
work for a local bank with a total three
month salary of 8,000 euros for each one of
them. The other is to organise a summer
canteen for the sale of ice cream in a zoo. A
kiosk and its full equipment is rented at the
zoo, for 16,000 euros for a three month
period. An additional cost of 2,000 euros is
needed for the insurance of the installation
and 0.80 euros per ice cream.
74
Exercises
a)
b)
c)
Derive the cost function.
Which is the opportunity cost of the
canteen business?
Which is the break even quantity point?
75
Exercises
Two companies A and B, plan the
production of the same product by using
different technologies. The sale price is 20
euros and the production capabilities
range from 20,000 to 160,000 units per
company. The cost data is:
 Company A: FC = 200,000, AVC = 15
 Company B: FC = 600,000, AVC = 10
4.
76
Exercises
a)
b)
c)
Derive the break even quantity for each
company.
Estimate DOL for 80,000 and 120,000
units for A and B.
Assume that the product price changes
according to the demand function P = 30 0.00025Q. How are the previous
calculations adjusted (Assume that each
company ignores the existence of the
other).
77
Exercises
5.
a)
b)
The price function for the product that a
company produces is: P = 40 - 0.000006Q,
while the cost function is TC = 1,562,500
+20Q + 0.000004Q2.
Which is the profit maximizing quantity?
Which is the price and the cost per unit
in the above quantity?
78
Exercises
6.
The Agricultural Cooperative of Chania
(ASX) has asked for a bid of offers for the
transportation of 100 tones of products
to Thessaloniki, in September. This
transportation is taking place with lorries.
The minimum time for loading, travel,
unloading and return is 48 hours. Two
types of lorries are offered, as follows:
79
Exercises
Type

Capacity
Travel costs
Loading costs
A
2 tons
73,000 euros
8,000 euros
B
5 tons
101,000 euros
20,000 euros
Two transport companies are preparing their offers
setting a price equivalent to cost plus 20% profit.
Company DEF plans to rent lorries. The monthly rent
equals 150,000 euros for type A and 400,000 euros for
type B. Company XYZ owes lorries of type A, which
the company intends to use. As the possibility of
damages or delays exists in sea transport, each
company foresees a spare a capacity of at least 20% in
its offer. Which is the most economic offer of each
company?
80
Exercises
7.
OLYMPUS S.A. produces two products A
and B for which relevant data for the past
month, are as follows:
Sales (units)
Price per unit (€)
Materials cost (€)
Labour cost (€)
Overheads (€)
A
420,000
2.50
193,200
264,600
283,946.5
B
110,000
4.25
52,800
138,600
148,733.5
81
Exercises

OLYMPUS is operating at full capacity but is
unable to meet the demand for product A,
which is half a million units per month. One
way to meet demand for A is to reduce the
output of product B and shift these
resources to the production of A. For each
unit reduction in B, OLYMPUS produces two
units of A. Note that the average variable
costs are constant in both production
processes.
82
Exercises


Alternatively, OLYMPUS could contract out
to have product A manufactured by another
firm in the same industry and sold as if this
product were from OLYMPUS plant.
KENTAVROS S.A. which has excess capacity
is willing to supply 80,000 units of A at a
price of €2.25 per unit.
How should OLYMPUS resolve this
problem? Support your answer with the
discussion of the various issues involved.
83
Exercises
8. The following table depicts combinations
of inflows for the production of 100, 200
and 300 units of a product.
Method
A
B
C
D
E
F
Inflow 1: capital
9
14
16
20
21
26
Inflow 2: labour
15
13
20
16
25
22
Product
100
100
200
200
300
300
84
Exercises
a)
b)
If the remuneration for each unit of
labour is €10.00 and for each unit of the
capital €5.00, which is the combination
with the lowest possible cost for the
production of each production level?
Does the company opt for techniques of
more or less capital intensity? Please,
explain.
85
Exercises
9. Explain why the degree of operational
leverage (DOL) forms a basic factor in
business decision making, particularly for
those decisions which are linked to the
structure of the production unit and the
proportion of the production factors
used. Furthermore, are there any
disadvantages in the use of DOL?
86
Exercises
10. A company functions inside a
competitive sector facing a fixed cost of 4
thousand euros and a variable cost
presented below (in 000 euros).
Production quantity (q)
Variable cost (VC)
1
22
2
27
3
31
4
38
5
48
6
56
7
68
8
81
87
Exercises
a)
b)
Estimate, TC, AVC, AFC, ATC and MC.
Given that the company’s supply curve is
formed as the part of the MC curve that
is above the AVC curve, determine the
supply curve of the company (the pricequantity combination).
88
Solutions to Exercises
Exercise 1
The company pays in advance: 20% x 30,000 = € 6,000
 The remaining amount (€30,000 - €6,000) = € 24,000 forms an
obligation
 Warehouse cost: €3,000







Choice A (Full Certainty)
DANUBE S.A.
Revenues: 24 x 1,000 = €24,000
Payment: - 24,000
Net Return: 0
Average Return: 0
Suppliers
 +24,000

90
Exercise 1








Choice B (Low Risk and Return)
DANUBE S.A
Revenues: 24 x 1,000 = 24,000
36 x 1,000 = 36,000
Payment: - 24,000
Net Return: 0
12,000
Average Return: 0 + 12,000 / 2 = 6,000
Suppliers
+ 24,000
91
Exercise 1
Choice C (Low Risk and Return)
DANUBE S.A
Revenues: 12,000
50,000
 Payment: 12,000
24,000
 Net Return: 0
26,000
 Average Return: (0 + 26,000) / 2 = 13,000




Suppliers 12,000
24,000
92
Exercise 1
Decision

The company opts for C. (The company is an S.A.
where the owners’ responsibility reaches the amount
of their contribution to the share capital. Therefore, a
possible loss may not shut the company down,
immediately, as part of it can be undertaken by the
shareholders.


The suppliers opt for A or B.
The only owner would opt for B.

Note: It is clear that, the behavior of the investor
towards risk should be taken into account, each time.
93
a)
Exercise 2
AC1 = TC1/Q = 2,000,000/Q + 150 + 0.02 Q
 AC2 = TC2/Q = 2,250,000/Q + 200 + 0.01 Q

MC1 = dTC1/dQ = 150 + 0.04Q
 MC2 = dTC2/dQ = 200 + 0.02Q

b)

Each function encompasses economies of scale up to the point
of AC minimization.
dAC1/dQ= -2,000,000/Q2+0.02=0 => Q1=10,000
 dAC2/dQ= -2,250,000/Q2+0.01=0 => Q2=15,000


The 2nd function encompasses economies of scale at a larger
94
production limit.
Exercise 2
c)
 At the two minimization points, we have:
AC1
AC2
Quantity
10,000
550
525
Quantity
15,000
583.33
500
Observation
 At the range [10,000, 15,000], the second is
the most effective function, as it presents the
smaller AC and therefore it is more preferable.
95
Exercise 3
a,b)

TC = FC + VC
TC = (16,000 + 2,000 + 24,000 = fixed cost + opportunity
cost) + 0.80Q

TC = 42,000 + 0.80Q

c)

Q* = TC / (P-AVC) = 42,000 / (2-0.80) = 42,000 / 1.20 =
35,000 ice creams

Therefore, 35,000 ice creams must be sold in order to
cover the total cost of the canteen.
96
Exercise 4
a)

Q1* = 200,000 / (20-15) = 40,000 units

Q2* = 600,000 / (20-10) = 60,000 units
Labour Intensive
 Capital intensive

97
Exercise 4
b)
DOLa (at 80,000) = [Q*(P-AVC)] /[Q*(P-AVC) –
FC] = 2
 DOLb (at 80,000) = 4


(keep in mind, FCa < FCb)


DOLa (at 120,000) = 1,5
DOLb (at 120,000) = 2

Note: DOL is always higher for higher capital
intensive techniques.
98
Exercise 4
c)

K = P x Q – AVC x Q – FC = (30-O.00025Q) x Q – AVC x Q
– FC
And DOL now is,

DOL = [ dK / dQ ] x [Q/K]

DOL = [ Q* x (P-AVC] / [Q*(P-AVC)-FC]

By proceeding with the appropriate substitutions,
DOLa (Q=80,000)=…
DOLa (Q=120,000)=…
DOLb (Q=80,000)=…
DOLb (Q=120,000)=…




or
99
Exercise 5
a)




K= (40-0.000006Q)xQ-1,562,500-20Q0.000004Q2
K= 20Q+0.00001Q2-1,562,500
Proceeding to the derivative of this function
with respect to Q and equalizing to 0, we
have:
d K /d Q = 0  Q * = 1,000,000 units
100
Exercise 5
b)

Hence, the price P* = 40 – 0.000006Q =
€34

AC=TC/Q= € 25.56
101
Exercise 6

Type A (2T capacity)  15 routes (maximum number
within a month)  transports 30 tones. The 4 Type A
transport 120 tones (20% of spare capacity).

Type B (5T capacity)  15 routes (maximum number
within 1 month)  transports 75 tones. The 2 Type B
transport150 tones (20% spare capacity).

Monthly rent: 150,000
Minimum time for loading, route, unloading and return: 2
days (48 hours).


Then, we estimate the cost for each combination of
lorries (it should be noted that many such combinations
can take place, keeping in mind the spare capacity of each
lorry).
102
Exercise 6

For the 4 As:
Number of Routes
100 tons / 2 = 50
routes
Rent
4 x 150,000 =
600,000
Route – Loading
50 x (73,000 + 8,000)
= 50 x 81,000 =
4,050,000

Total cost for As: 4,050,000 + 600,000 = 4,650,000

For the 2 Bs:
Number of Routes
100 tons / 5 = 20
routes

Rent
2 x 400,000 =
800,000
Route – Loading
20 x (101,000 +
20,000) = 20 x
(121,000) =
2,420,000
Total cost for Bs: 2,420,000 + 800,000 = 3,220,000
103
Exercise 6
Offer of XYZ: (It possesses four owned type A
lorries):
 4,650,000 x 1.20 = 5,580,000


Note: we include the rental cost, despite the lorries
being owned by XYZ, as it forms the opportunity
cost, as the fact remains that it could (potentially)
rent them. In other words, it is a lost opportunity
cost.

One case could be, that XYZ does not include the
600,000 and therefore the offer would be stand at
4,050,000 x 1.20 = 4,860,000
104
Exercise 6
Offer by DEF. (It does not possess owned lorries).
 3,220,000 x 1.20 = 3,864,000


It is therefore the lowest offer and could be selected, as this choice
dominates.

This forms a threat for XYZ, which would rather not stay stand
still. It could rent the four Type A lorries (for some use) and follow,
too, the selection of 2B, or proceed to an even better offer.
Another combination could be lorries of both Type A and B:
 1B + 2A (=75+60=135 tons) with a 35 % spare capacity.
 Solution 2B is more competitive even from 1B + 2A (proceed to
the necessary calculations).

105
Exercise 7
Need to purchase 80,000 units of A. Therefore,
A. Reduce B by 40,000 units
Then:
•
Reduction in materials cost of B by
(52,800/ 110,000)*40,000=
0.48*40,000=19,200
•
Reduction in labor cost of B by
(138,600/ 110,000)*40,000= =1.260*40,000= 50,400
•
Reduction in revenues of B by
40,000*4.25= 170,000
•
Reduction in overheads by
(148,773.3/110,000)*40,000= 1.352*40,000= 54,085

106
Exercise 7
Net result of B:
19,200+ 50,400+ 54,085- 170,000=
= -46,315
• Increase in materials cost of A by
(193,200/ 420,000)*80,000= =0.46*80,000= 36,800
• Increase in labor cost of A by
(264,600/420,000)*80,000= =0.63*80,000= 50,400
• Increase in revenues of A by
80,000*2.5= 200,000
• Increase in overheads by
(283,946.5/ 420,000)* 80,000=
=0.676* 80,000= 54,085

107
Exercise 7
Net result of A:
200,000- 50,400-36,800-54,085=59,115
• Net overall result: 59,115- 46,315= =12,800

B.
Cost: 80,000*2.25 = 180,000
Revenues: 80,000x2.50 = 200,000
Net result: 200,000-180,000 = 20,000
Suggestion: Buy rather than make.
108
Exercise 8
a)
Method
A
B
C
D
E
F
Quantity
of K
9
14
16
20
21
26
Value of
K
45
70
80
100
105
130
Quantity
of L
15
13
20
16
25
22
Value of
L
150
130
200
160
250
220
Product
(units)
100
100
200
200
300
300
TC
AC
195
200
280
260
355
360
1.95
2.00
1.40
1.30
1.18
1.17
109
Exercise 8
Therefore,
• for production level of 100 units A is preferable.
• for production level of 200 units D is preferable.
• for production level of 300 units F is preferable.
b) Along the rise of the product volume, AC is
being reduced implying capital intensive
techniques, and economies of scale.

110
Exercise 9

Useful in deciding on labour intensive
versus capital intensive techniques. Also,
comment on possible disadvantages of
DOL.
111
Exercise 10
a)
Firstly, TC (=FC+VC) is estimated and
them follow other cost elements:
q
0
1
2
3
4
5
6
7
8
FC
4
4
4
4
4
4
4
4
4
VC
0
22
27
31
38
46
56
68
81
TC
4
26
31
35
42
50
60
72
85
AFC
4
2
1.3
1.0
0.8
0.7
0.6
0.5
AVC
22
13.5
10.3
9.5
9.2
9.3
9.7
10.1
ATC
26
15.5
11.6
10.5
10
10
10.3
10.6
MC
22
5
4
7
8
10
12
13
112
Exercise 10
TC=FC+VC, AFC=FC/q, AVC=VC/q
 ATC=AFC+AVC, MC=TC(q)-TC(q-1)
b) The supply curve of the company is
determined as the part of the MC curve
which is above the AVC curve.
Therefore, the supply curve is composed
of the following points:

q
P
6
10
7
12
8
13
113