THE COPPERBELT UNIVERSITY
SCHOOL OF GRADUATE STUDIES
THE NATURE OF MANAGERIAL ECONOMICS
Managerial Economics is a discipline that shows how economic analysis can be used in
formulating company or firm level policies. It thus departs from the mainstream
economics or the simple theory of the firm. This is because the theory of the firm is
simple in the assumptions it makes but complicated in its logical development to be
managerially useful. Some examples worth giving of simple assumptions are:
a)
b)
c)
Perfect knowledge
Free entry and exist into the market
Many buyers and many sellers.
These assumptions are given to easy analysis, and enable us to construct theory. In
practice however, it may not be possible to attain perfect knowledge, free entry and exist
(as if this has no costs) and even having a ready market. The reality is that the firm faces
problems of information; it is stuck in the Industry once it is set up and markets are major
constraints to its development. Managerial economics though, tends to use economic
thought to analyze business situations.
According to Bringham and Pappas, Managerial economics is “the application of
economic theory and methodology to business administration practice. It bridges the gap
between economic theory and real business practice. It does this in two ways:
a)
It provides tools and techniques which enable Managers become more competent
in decision making.
b)
It also shows the various ways in which the business firm is integrated in its
environment.
We can therefore state with confidence that Managerial economics is the interaction of
Economic Theory and Business Management.
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Economic
Theory
Business
Manager
MANAGERIAL ECONOMICS
Managerial economics may be defined as a body of knowledge, techniques and practices
which give substance to those economic concepts which are useful in deciding the
business strategy. Thus Managerial economics helps improve managerial functions of
Planning, Motivation, Co-ordination and Control.
Managerial economics is also practiced in a very dynamic environment. In this
environment a number of factors keep on impacting on the firm. These include inflation,
resource limitations activities involving regulation, the setting up of fiscal and monetary
policies also impact on the firm.
Scope of Managerial economics
Managerial economics derives from economic theory. So many ask what the
fundamental difference is between economic theory and managerial economics. One
distinguishing factor is that Managerial economics is more empirical than economic
theory. Managerial economics provides Management with a strategic planning tool that
can be used to understand the following:
a)
b)
the operational or internal issues of the firm
the environmental and external issues affecting the firm.
Under the operational and internal issues of the firm, managerial economics focuses on
the most profitable use of scarce resources rather than on the achievement of equilibrium
quantities and prices dealt with in traditional micro-economics.
Secondly, under the environmental and external issues impacting on the firm, managerial
economics helps firms make decisions in situations of incomplete information or
uncertainty while traditional economics assumes complete market information.
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What then are these operational and environmental issues?
1.
Operational or Internal issues affecting the firm
Operational issues are normally internal to the firm and can be controlled by
Management. They involve problems of what to produce, when to produce and
how to produce for which category of customers. The other internal issues
involve management of profit, capital and inventory management (stocks). The
firm needs to understand the following:
a)
b)
c)
d)
e)
The theory of demand and demand focasting - This is important because
the firm needs to know how much to produce and when. Demand analysis
also exposes the market influences on the firms products and factors
influencing demand
Pricing and competitive strategy – The firm needs to have a proper pricing
strategy if it has to survive. It also needs to know the competitors
responses to the firms strategies regarding pricing, advertising and
marketing
Cost analysis - cost estimates are essential in managerial decision making.
A firm needs to know its cost structure without which it will be difficulty
to maximize profits. Cost analysis requires an understanding of cost
concepts, cost-output relationships, economies of sale, analysis of
production functions etc
Resource allocation – If profits have to be maximized, resources must be
allocated well. Managerial economics makes use of techniques like linear
programming to help in resource allocation in order to optimize profits
Other internal issues involve profit analysis, capital and investment
analysis and strategic planning.
These are issues that are internal to the firm which, Management can act on in order to
maximize profit.
2)
Environmental and External issues
These refer to the general business environment in which the firm operates. These
include the general economic, social and political atmosphere within which the firm
operates.
A study of the economic environment should include:
a)
b)
c)
the type of economic systems in the country
the general trends in production, employment, incomes, prices, savings and
investment
trends in the working of financial institutions like banks, financial corporations
and insurance companies and other financial intermediaries
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d)
e)
f)
the pattern of foreign trade
trends in labor and capital markets
governments economic policies
The social environment refers to the social structure, Trade unions, cooperatives etc.
The Political Environment refers to the:
a)
b)
-
Nature of state activity – especially towards private business
Political stability – stable governments are always required. This also concerns
issuing redress statements
This may also take the form of the laws made by government – e.g Investment
Act, Competition Laws, Privatization Laws, Environmental laws etc.
Taking into consideration the social and political environment highlight the social
objectives of the firm. Thus private gains alone cannot be the goal. The firm does owe
some responsibility to society.
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What disciplines is Managerial Economics related to?
Managerial economics is related to many other disciplines. It is related to Economics,
Management Theory and Accounting, Mathematics and Statistics, Operations Research
and Computer Science.
Thus managerial economics uses many borrowed methods and techniques to enable firms
make proper decisions. The diagram below shows some of the relationships.
Business Administration
(Decision Problem)
Traditional Economics
Theory + Methodology
Decision
Sciences,
Tools and Techniques
Managerial Economics
(Application of theory and
Methodology and Techniques to
solve Business Problems)
Optimal
solution
Business Problem
a)
to
the
Relationship with Traditional Economics
Managerial economics depends upon a branch of economics called positive
economics. This deals with description and explanation of economic behavior of
individuals and firms. Infact the theory of the firm and consumer behavior which
Managerial economics depends on comes from this branch of economics. This
branch of economics is also referred to as microeconomics. Managerial
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economics used many micro-economic concepts such as marginal cost, marginal
revenue, elasticity of demand and market structures to name but a few.
It also relates to macroeconomics in the sense that the firm depends on this as its
external environment. Macroeconomics deals with the economy as a whole. It
deals with the analysis of National Income, the level of employment, the general
price level, consumption and investment and even matters of International Trade
and public finance. Recall that demand forecasting for firms depends very much
on national income forecasting as business sales are affected by business cycles.
b)
Relationship with Management Theory and Accounting
Accounting refers to the recording of preliminary (monetary) transactions of the
firm in certain books – A proper knowledge of Accounting is essential for the
success of the profit maximization objective of the firm.
Accounting provides proper costs and revenue information. Therefore a student
of Managerial economics should be familiar with the generation, interpretation
and use of accounting data.
It is accounting data, which is important for the firm’s decision making
Accounting data helps understand the past and present help in the protection of
the future
c)
-
d)
Managerial Economics and Mathematics
The use of mathematics is significant for managerial economics.
The major objectives of the firm is cost minimization and profit maximization
Mathematical concepts are widely used in economic logic to solve problems of
minimization and maximization
Managerial economics relies very heavily on algebra, calculus and geometry in its
logic.
Managerial Economics and Statistics
Statistics helps very much in estimation of demand. A managerial economist
should be able to analyze the impact of variations in tastes, fashion and changes in
income on demand. Only then can he adjust the output. Managerial economics
also makes use of correlations and multiple regressions to relate variables like
price and demand to estimate the extent of depending of one variable on another.
The theory of probability is also useful in problems involving uncertainty.
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e)
Managerial Economics and Operations Research
Operations research assist Managerial economist in the field of product
development, materials management, inventory control, quality control marketing
and demand analysis. It provides models to manage these aspects of business.
In this area the linear programming technique is used in studying transportation
costs and allocation of purchases among different suppliers. Input-output analysis
can also be used by firms for planning, coordination and mobilization of resources
in various departments. Other tools used are queuing theory and game theory.
Queuing theory is used to find ways of reducing the waiting period in meeting
demand while game theory is useful in explaining or predicting the behavior of
competitors. These tools have brought more accuracy to decision making.
f)
Managerial economics and other sciences. Managerial economics is also related
with other sciences. The theory of decision-making is one such a discipline. It
has been developed to explain multiplicity of goals and uncertainty. Traditionally
most economic themes try to explain single goals. Computer Science is also
being used in data storage. It has increased the speed with which decisions are
made.
The Methodology of Managerial Economics.
Managerial economics. Managerial economics as a branch of economics depends very
much on the methodologies of economics. These include:
a)
b)
c)
a)
The scientific method
Case study method
Historical method
Scientific method
i)
ii)
iii)
This involves making observations about a phenomenon.
Since
experiments cannot be conducted regularly, observations are a quick
method of identifying problems in a firm
The deductive method – This helps in making conclusions on the basis of
assumptions. One has to make assumptions about the world and then
conclude from there. This is common in economics and that is why the
“ceteris paribus” clause is often used
Inductive methods – This is required to verify the conclusions and
theories. These two methods require carrying out a survey. At times they
have been referred to as the survey method.
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b)
Case study method
This involves carrying out detailed empirical studies of some firms. It requires
digging into the history of the firm to analyze its strengths and weaknesses and
the forecast the future course of action for the firm. The case study method
normally employs the historical method.
Usefulness of managerial economics
1.
It enables the use of economic logic in business administration.
2.
Helps focus on the most profitable uses of scarce resources.
3.
Ensures that firms work within the confines of their corporate strategy.
4.
It helps in decision-making.
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2. THE FIRM IN MANAGERIAL ECONOMICS
The firm is a system of relationships which come into existence when the direction of
resources is dependent on the entrepreneur.
Firms can take three major forms. A firm can be operated by a single person. This single
person is the entrepreneur. In this case the entrepreneur is the sole proprietor. A firm can
also be owned by a group of entrepreneurs who form another business organization called
a partnership. Further, many entrepreneurs or investors may form a joint stock company.
This is modern terms may be referred to as a corporation. thus we have:
a)
b)
c)
the Sole proprietorship
the Partnership and
the Corporation (Private or Public (Plc)
a)
The Sole Proprietorship
Characteristics – one person or a family usually owns it.
It has unlimited liability because there is no distinction between the
company and the owner as an individual
Before the law the business and the owner are the same
Advantages
a)
b)
c)
d)
There is a direct relationship between the effort put in and the out put. So it is
easy to get motivated and boost output.
Decision making is easy (after all you are alone).
There is personal attention to issues.
Legal procedures including paper work are simplified.
Disadvantages
c)
d)
There are limitations in acquiring finance e.g. loans – because of no security
Unlimited liability – serious draw back in the event of closure – liability extends
to personal assets
Proper accounts may not be kept
Loose expert opinion on issues.
b)
The Partnership
a)
b)
-
Two or more individuals owning a business characterize this
Partnerships are common among Lawyers, Surveyors and Architects
It consists of two (2) but less than (20) twenty individuals
It must have a written agreement in which the following must be specified:
a)
How to share profits
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b)
c)
Succession in case of death
Extent of liability (e.g. if the company gets a loan from a bank A
might be required to pay 70% and B 30%.
Advantages
i)
ii)
There is increased financial strength
There is a pooling of managerial talent.
Disadvantages
i)
ii)
iii)
Personal differences might develop
Joint – liability – before the law each Partner is equally liable for any misdeed
regardless of whether you have lesser shares
Limited life span – if one partner dies, that partnership is dissolved.
c) Corporations
Characteristics
These are organizations which are legally allowed to produce and trade and are
regarded as legal persons before the law. They can enter into contracts as legal
persons.
They pay tax just like an individual does. This tax is referred to as company or
corporation tax, which is deducted from gross profits. he tax liability however is
separate from that of its owners.
Its life is not related to the life of the shareholders
The corporations can lease/own/rent land and buildings
Ownership of a company is divided among shareholders. A shareholder who
holds more shares is called majority shareholders. Shareholders can also be legal
persons. Meaning that they can be other companies (corporations) which may be
private, public or institutional. Corporations more especially public corporation
raise funds by selling shares mainly at the stock exchange.
Types of corporations
a)
b)
c)
There are basically three types of corporations
Those, which are wholly owned by the state (e.g. former Indeco etc)
Those, which are owned by private individuals and raise money privately
Public companies or corporations – These raise money by selling shares on the
stock exchange. Shares can be sold on the stock exchange by anyone prepared to
pay the going price. The trading on the stock exchange is reported in the daily
papers. This is primarily the Sale and Resale of existing shares in public
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companies. However, additional new shares can also be issued to raise new funds
for the business.
-
Shareholders Return
Shareholders get their return in two ways:
a)
By waiting for a dividend. (From Profit on business)
b)
By capital gains (Profit on Sale of Shares)
Running of Organizations or Firms
-
A Board of Directors normally runs the corporations
These are either the actual owners of the shares or their representatives or a proxy
They make decisions on how the firm should be managed
The board reports to the shareholders
The shareholders elect the Board
There are two types of shareholders:
a)
Preferred shareholders
-
b)
These are given preference on all claims if the company shuts up
Preferred shares – have a cumulative feature. If the company makes profit
but does not declare a dividend, their claim will still hold
They however do not vote
These shares can also be converted to common shares.
Common shareholders
They are the owners of the company.
Structure
Shareholders
Board of Directors
Management
Operatives
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Advantages
a)
It has limited Liability
b)
Ownership is easily transferred through buying and selling of shares
c)
The corporation has a continuous life span
d)
It has diverse and specialized Management as the diagram below shows.
Board of Directors
Managing Director
Manager
Finance
e)
Manager
Marketing
Manager
Personnel
Manager
Production
It has easy access to capital (Banks) and can also raise funds easily on the stock
exchange. Can also raise funds easily on the stock exchange.
Disadvantages
a)
b)
c)
It lacks personal involvement like in the sole Proprietorship
It has increased Bureaucracy and complexity (signing of contracts, which
complicate matters)
There is limited flexibility in decision-making.
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3. THE PLACE OF A FIRM IN THE ECONOMY AND GOALS OF A BUSINESS
FIRM
i) PLACE OF A FIRM IN AN ECONOMY
The earliest economic models of a firm were developed as part of a wider analysis of the
allocation of resources in a market system.
The basic questions asked in the economic models were:
a. What goals and services will be produced by the system
b. How would the production process be determined
c. How will the final output be distributed among consumers
EXPENDITURE ON
GOODS
SELL OF GOODS TO
HOUSEHOLDS
AS CONSUMERS
HOUSEHOLDS
SELLER OF LABOR
PRODUCE OF GOODS
FIRMS
REQUIRED INPUTS
PAYMENT OF
FACTOR INCOMES
SELL OF LABOR
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This model of the market firmly places and defines the role of a firm in an economy.
a) It is a supplier of goods to households.
b) It pays for factor use (wages/rent etc.)
c) It employs factors (land, labor and capital
d) It receives money from households
e) It creates value in the economy.
Within the framework of the economic model, the firm’s objective is assumed to be
profit maximization. Why? This is because the proceeds from the sale of the firm’s
production must exceed the cost of the factors which the firm paid for. Thus
Sales Revenue > Cost of production
Thus from the economic model, we might assume that the most important objective of
the firm is Profit Maximization.
 The economic model also assumes a highly competitive market structure.
 Secondly , the economic model assumes the existence of the Entrepreneur – (the
owner/manager)
However it must be understood that when this model was conceptualized, there was at the
time a preponderance of family – owned businesses operating in competitive markets.
 It must also be understood that the model was designed to help explain the broad
operations of the market system rather than the operations of some specific
category of firms.
 In essence, the owner/manager or entrepreneurs reacted to the signals in the
market to reduce or increase output in order to maximize profit.
 With the growth of large firms/ and the growth of the divide between ownership
and management of firms, there has been a gradual shift from the conception of a
firm as a profit maximizer to the managerial theories of the firm.
There is a lot of controversy in the literature now as to what the objectives of a firm
should be. Traditionally, a firm is regarded as an economic institution or unit and
consequently only economic objectives are taken into consideration.
Because of the contributions, which firms can make to the well being of society, in terms
of employment and increased incomes and their outputs, firms contribute directly to
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economic growth. From this understanding, the traditional objective of the firm is to
maximize profits.
As ownership and management of firms became separated (especially in corporation or
joint stock companies), the goals of the firm also changed slightly. The shift is to
maximization of a function of a firm. This means that the firm can have as its objectives
any of the following:
(a)
Maximization of sales revenue;
(b)
Maximization of growth of the firm (in terms of asset holdings).
Firms can then concentrate on maximizing one or two functions or several at any one
time. The other objective of the firm is related to “satisfying objectives”; that firms do not
aim at maximizing profits but also at achieving satisfactory levels of profit. The latter
will then take into consideration employ and society needs if met by the firm as part of
the satisficing behaviour. Let us look at these in more detail.
ii) OBJECTIVES OF THE FIRM
We have already discussed the purpose of Managerial Economics and the disciplines it
relates to. We now pursue the objectives of the firm. Objectives provide the framework
necessary for analyzing a firm.
There are many objectives which firms pursue.
These can be categorized as (many perspectives).
a.
b.
c.
d.
(a)
Profit Maximization
Managerial theories of a firm
Behavioral models of a firm
Wealth or value maximization model of a firm
Profit Maximization
This is the traditional approach to understanding the firm. In this understanding the firm
aims at obtaining the maximum profit from its operations. Profit maximization means
obtaining the largest absolute amount of profit over a time period both in the short and
long-term. The short-term is a period in which a firm cannot adjust the factors of
production as well as the demand constraints. Both supply and demand conditions are
fixed for a period of time. The long run enables the firm to change conditions.
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Profit maximization depends on the market structure in which the firm is. If it is in
perfect competition, it cannot adjust the price. It will take the price. Thus the firm’s
option lies in reducing costs and increasing output. Through large sales volumes, it may
attain the highest profit levels.
If the firm is faced with an imperfect market structure such as oligopoly or monopoly, it
can adjust the price as well as its costs of production and output. Thus the firm can
manipulate these conditions in order to maximize profits.
It should be emphasized that the behavior of the firm will differ in oligopoly and in
monopoly. In oligopoly, price adjustment is difficult unless the firm is a leader in the
industry.
Profit is the difference between total revenue (TR) and Total Cost (TC).
Profit = TC – TR
The output, which yields the maximum profit, is the ideal to be achieved.
TC
Loss
TR
K1
Profit
K2
Loss
Quantity or Output
0
Q1
NB TC has an intercept >0. This represents the fixed costs.
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TR has an intercept = 0. This means that if there is no production, there will
be no revenue (e.g. Q  P  TR ) . If Q  0 , then TR  0 .
Profit is maximized at Q1 , where the gap between K1 and K 2 is the largest.
At K1 and K 2 the slopes of the TC curve and the TR curve are equal.
This is because these lines are parallel to each other.
The r The Rule arising from this is that as long as Marginal Revenue is greater than
Marginal Cost, the firm can continue increasing its output until it reaches a
point where Marginal Revenue is equal to Marginal Cost.
TC
Cost / Revenue
g
TR
a
f
b
c
d
e
Quantity or Output
0
Q
Q1
Q2
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From the diagram, one can see that the pattern of increase in costs and in revenue is as
follows: At the level of production Q to Q1, the marginal cost will be dc while the
marginal revenue will be ba and ba>dc. Moving from the output Q1 to Q2, the marginal
cost will be ef while the marginal revenue will be fg and fg<ef.
Marginal Revenue is the change in revenue, which comes from selling as additional unit
of output. Marginal Cost is the change in Cost, which results from producing an
additional unit of output (increasing quantities) as long as the Marginal Revenue is
greater than the Marginal Cost. This position can be illustrated in the following diagram:
MC
d
Q
P
AC
E
S
d
R
MR
0
In this diagram, the firm can continue producing outputs from 0 (origin along the x axis)
up to the point M . Up to this point MR  MC . At point E , the MR  MC and
quantities OM yield this point.
After point M , the Marginal Cost are higher than the Marginal Revenues. If a firm opts
to produce in this area, it will be operating at a loss and so conflict the profit
maximization rule.
Also note that the Price P , is a constant even if you produced one (1) unit of this good.
So to maximize revenue quantity must be multiplied by price (Q  P)  (OM  P) .
On the cost side, the cost of producing one (1) unit at the profit maximization point is
(S ) . So the cost of producing OM will be ( S  OM ) .
Thus:
TR  OM  P  OMQP
TC  OM  S  OMSR
TR  RC  P
OMQP  OMSR  SRQP
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Why should firms maximize profits?

It is natural that owners of the firm must get maximum returns.

This ensures survival of the firm. When there are many or a few firms as for
example in perfect competition or oligopoly respectively, the firm can survive.

Under monopoly, even though there is competition, it is the only way of the
owners rewarding themselves highly.
There are criticisms to the profit maximization principle:
o The goal has led to the separation of ownership and control of the firm.
Ownership is vested in shareholders while control is in the hands of managers.
Nobody knows whether this is what owners require.
o In conditions of uncertainty, it may not be possible to achieve this objective. So
the firm will adopt other objectives.

Profit may not be the best way of measuring profit since it can be
manipulated by changing the values of assets employed.
The approach neglects the social responsibility of the firm. A firm should be able to show
goodwill to the community, offer good high paying jobs. This goes beyond the objective of
profit maximization. All said, it is essential that firms maximize profits in order to survive.
b)
MANAGERIAL THEORIES OF A FIRM
i) THE SALES REVENUE MAXIMIZATION
Baumol (1967) developed a model of the firm in which sales revenue maximization was the
primary objective.
The model assumes an Oligopolistic Market structure in which the market is dominated by a few
sellers.
This also supports the power of management to pursue their own objectives. Managers do this
because;
a) Salaries and status may depend on the size of the firm, determined by the growth in
sales rather than profitability.
b) Growth in sales to be attractive to external finance.
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c) Distributors and retailers are more attracted to products with relatively highly sales
turn over. Even though the ability of the managers to influence objectives is clear, the
need to earn profits is not excluded.
d) However even though profits are included in the model, they represent a constraint to
the managers
e) Therefore, the managers operate with a minimum profit constraint which they think is
acceptable to the share holders.
f) This is represented as follows
TC
Cost
Revenue Rm
Profit Rp
T
R
Maxp
Pmin
output
O
Qp
Qm
quantity
Pr
Profit/loss curve
In this model, and following the sales maximization objective,
a) The firm will produce OQm goods
b) Achieve a sales volume of ORm while in the profit maximization objective the
firm would produce OQ p and achieve a sales volume of O Qp.
They will however do this if the minimum profit expected by the owners of the firm as P
min as opposed to P max.
Thus at the point of sales Maximization
a) Sales are at the highest
b) Profits though only satisfy the minimum profit constraint
c) Output for the firm is higher at OQm.
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Thus the firm depends on sales volume and sales volume depends on lower prices and
this leads to increased total Revenue for the firm.
Baumol further states in his theory that sakes volume is also dependent on sales
expenditure as shown below
Sales revenue
Sales expenditure curve
Marketing expenditure
The assumption underlying this relationship is that additional Marketing expenditure will
increase sales volume
ii) MANAGERIAL UTILITY MAXIMIZATION
The managerial utility model was developed by Oliver Williamson (1967)n and is based
on a more detailed analysis of the implications of managerial discretion in the context of
large corporations.
It makes the following assumptions
a) The shareholders are unable to exercise direct control over management
b) The firm is operating in a market structure which is not highly competitive
Williamson then examines the ways in which managers are able to pursue their own goals
subject to being able to maintain control of the firm.
The model is based on the maximization of a managerial utility function which depends
on
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a) Expenditure on staff
b) Managerial emoluments
c) Discretionary investment spending
Management has a positive preference for this
The model then is
Maximize U = U (S, M, I d)
Subject to: Pr >Pmin + Tax
S = Staffing expenditure (especially on special administrative staff)
M = Managerial emoluments (especially benefits in kind (car) with tax advantages,
Id = discretionary expenditure (allocation of profits above required for dividends just to
satisfy the shareholders
Pr = reported profits
T = Corporation Tax
In this model, the goals of management are placed within the context of profit.
Profit in this model has greater significance than in the sales maximization model.
In this model, managers are likely to increase potential profit (this is privy only to
management) and enjoy the benefits which go to management so that
Pr = (Pp – M) – T
Where:
Pr =Reported Profit
Pp = Potential Profit
M = Managerial Emoluments
T = tax
So it is in the interest of management to increase Pp (in order to disguise M properly)
iii) THE COPORATE GROWTH MODEL
Marris (1964) developed the corporate growth model of the firm in which Growth is the
key objective. Like Baumol and Williamson, Marris considers a firm where management
is separate from ownership. Secondly, the sales market is free from intense competition
(oligopoly). Further, managers correlate increased size of the firm with increased salaries
or emoluments and status.
Managers are also concerned with job security in the sense of keeping control of the firm.
(The potential threat being seen in a take-over raid by another company and the
replacement of management)
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 The motivation of the take – over raid arises from a depressed share valuation of
firm below its economic value as judged by the bidding firm.
 Marris assumes that the failure to pay attractive dividends to shareholders will
tend to depress the share valuation relative to other firms with a similar risk
profile
 If therefore, security alone were the determinants of managerial utility, dividends
would be maximized to support the share price and minimize the risk of take –
over.
 The primary goal of the managers however is to increase the size of the business
and this involves a trade – off with dividend payouts. On the reasonable
assumption that managers find retained earnings the most attractive source of
funds for expansion.
Thus management must find a fight balance in their dividend/retentions policy. From the
above assumptions we can state the model as follows:
Maximize U = U (g, v)
Subject to: v > v (min)
Where g = growth rate (percentage) of Net Assets
V = the valuation ratio = share price valuation
Accounting book valuation
V (min) = the minimum valuation ratio that management set to deter take –over raids.
In this model, if we assume that a take –over raid is likely when the share price valuation
is less than the accounting (book) valuation, then when the ratio is less than 1, this would
be a source of concern to management. V (min) is therefore unlikely to be below 1.
In this case, the valuation ratio is both a component of the managerial utility and the
constraint on management’s primary goal of growth because an aggressive retention
policy to finance growth will be at the expense of dividends and the valuation ratio. This
can be expressed in the diagram below.
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T
Vm
Un
U3
U2
M
U1
V(min)
Valuation curve
g1 g2
Growth Rate
In the diagram, the valuation ratio curve shows that there will be a trade- off between
growth and increased valuation where future dividends (Retention Policy) do not
compensate for the loss of current dividends
 The turning point in the relationship between growth and valuation is at point T
 The curves U, to Un are managerial Utility curves.
 The points on given utility curve represent a trade – off between g (growth) and v
(valuation) that would be accepted by management at a constant level of utility.
 Moving firm U, to Un represents the achievement of a higher level of utility
 Notice that the indifference (or utility) curves terminate at the valuation level ratio
V(min) Reflecting that management will not risk any further reduction because of
a take –over threat.
 The highest level of utility that can be achieved within the bounds of the valuation
curve is at point M, with the optimal values of growth and valuation being g2 and
Vm respectively
 As long as the utility function is negatively sloping, indicating that management
derive positive utility from both g and v, the optimal point will lie to the right of
point T, which equates with the value maximization of the firm
 The conclusion which emerges is that in the Marris model, the objectives of the
firm have a bias towards a growth rate greater than that sought by share Duners
who desire maximization of the valuation ratio g2 > g,
24
c) BEHAVIOURAL MODELS OF THE FIRM
The behavioral models reflect the concept of expressing corporate objectives as a
single function to be maximized. This also stems from the concept of “Satisfy icing”
behavior as developed by Simon (1957)
The basic argument in the behavioral model is that there is on the one hand
“economic man” who is complexly rational and the opposite of complete rational and
the opposite of complete irrationality.
Between the two extremes we get the situation of bounded rationality.
Zero
Rationality
Enjoyment
Bounded
Rationality
Many Contributions
Complete
Rationality
Economic
Profit
Because of the constraints imposed by the above factors by reality, the decision maker
sets a ‘satisfactory” goal and searches for possible courses of action that will satisfy this.
Satisfyicing is a dynamic concept in the sense that the goal can be revised in light of
experience (the failures and success in reality will affect goal setting).
THE MODEL
Building on the above foundations and understanding, Cyest and March (1963)
developed a general model of the firm from the perspective of organizational theorists.
The central theme was that, the process of decision making within a large firm is the key
factor determining the translation of information unto decisions. The emphasis is on the
mechanics of decision making and how this affects and changes the objectives of the
firm.
Cyert and March view the firm as a coalition of different interest groups including
managers, shareholders, employees, creditors, government etc. (STAKE HOLDERS)
Unlike other approaches, Cyert and March do not in their model see a single Universal
objective like profit maximization, sales volume maximization or managerial utility
maximization rather they see a sequential attention to different goals according to the
perceived importance of that individual or group to the coalition at that time (within the
constraints of bounded rationality.
The objectives of the coalition are determined by three factors.
1) The bargaining process by which the objectives of the coalition are fixed.
2) The process by which objectives are formulated (internally)
3) The process of adjusting to experience the coalition agreements.
25
The coalition is composed of different groups and those may pursue different objectives
and different interests.
These side payments are necessary to pacify groups whose objectives are not being met.
Management cannot easily be pacified by side payments and so they make sure they have
greater influence on the objectives of the firm.
If one group has more influence in the coalition the side payments may take the form of
some policy commitment (that is they will be written in the document for (conditions of
service.
It is important to note that even within management goals and objectives tend to differ. In
a production company you will find different sets of management objectives representing
a) Production goals
b) Sales goals
c) Inventory goals, and
d) General overall profit goals
Each of these goals is a prime concern of the sub- groups within the organization. This
reflects the – inherent goal conflict in an organization. Example – while marketing may
want higher production to increase sales volumes, the production department may think
that the goal may be technologically unattained because of conflicts in goals and
objectives, within the organization, there is a general tendency to reinforce “Satisfy icing
behavior”
Satisfying behavior is the tendency to meet the goals to satisfactory levels.
What are the strengths of this model?
a) It is much closer to reality. It does not see management as one entity
b) Because it accommodates conflict within the organization, the model offers
insight into the ways corporate objectives are formulated.
Limitations of this model
The model suffers from some limitations
It is not definite enough to have predictive qualities or capacity.
d) WEALTH OR VALUE MAXIMIZATION MODEL
The wealth or value maximization model takes the view that firms are basically economic
entities.
26
From this understanding it is assumed then that the primary objective of management is
to maximize economic value of the Net Assets under their control.
In the model, value is defined as “the present value of the firms expected future cash
flows” cash flows may now be equated to profit”
Therefore, the value of the firm today, its present value, is the value of its expected future
profits, discounted back to the present at an appropriate interest rate.
Thus
Value of the firm = PV of expected future profits.
PV =
+
+…
=
Where π = expected profit
t = year
i = interest rate
Recall that
Value== Sales Revenue – Costs.
Profit
This formula also gives responsibilities to the departments in an organization
Sales – are a responsibility of the sales Marketing Department.
Costs – Responsibility of Production Department and the General Management / Finance
Interest Rate – Concern of the Finance Department.
It should be pointed out however that all Departments are responsible for reducing costs
27
THE COPPERBELT UNIVERSITY
SCHOOL OF BUSINESS
POSTGRADUATE SUDIES DEPARTMENT
Managerial economics Units 3 and 4
OPTIMIZATION TECHNIQUES
Functional relationships can be represented in tables, graphs or equations. The Marginal
value of dependent variable is defined as the change in this variable associated with a
one-unit change in a particular independent variable. In tabular form this is calculated as
in the table below.
Summary of a Firms Maximum Profit.
1
2
3
Quantity Price Total
(Q)
(P)
Revenue
(TR)
0
200 0
1
180 180
2
160 320
3
140 420
4
120 480
5
100 500
6
80
480
7
60
420
8
40
320
4
Total
Cost
(TC)
145
175
200
220
250
300
370
460
570
5
Total
Profit
(TP)
-145
+5
+120
+200
+230
+200
+110
-40
-250
6
Marginal
Revenue
(MR)
0
+180
+140
+100
+60
+20
-20
-60
-100
7
Marginal
Cost
(MC)
+30
+25
+20
+30
+50
+70
+90
+110
MR>MC
MR<MC
It is easy to see that the Marginal Revenue (MR) and the Marginal Cost (MC) are
calculated using the formulae
MR = Change in Total Revenue
Change in Quantities
and:
MC= Change in Total Cost
Change in Quantities
In the above example profit is maximized at between 4 and five units. Notice that the
average of the MC ‘s and MR’s at four (40) units will be about 40
This information can also be presented in graph form. Let us try to put the same
information of a graph paper.
28
Marginal Analysis Using Calculus.
The dependent variable achieves a maximum when its marginal value shifts from positive
to negative. Thus, the derivative of Y with respect to X, denoted by dY, is the limit of
dx
the ratio ∆Y as ∆X approaches zero.
∆X
Geometrically, it is the slope of the curve showing Y (on the Vertical axis) and X on the
horizontal axis.
The diagram below shows this.
If y = ƒ(x) and if the limit
Lim
h
ƒ(x + h) – ƒ(x) exists, then
h

that limit is called the derivative of ƒ (x) at that point x = x1
Y
ƒ(x + h)
y = ƒ(x)
ƒ(x + h) – ƒ(x)
ƒ(x)
0
x
x+h
X
h
Let us first consider the X-axis .
If x1 represents quantities produced at some time period, (t) then xth are larger quantities
produced at time (t + 1). The change in quantities produced then will be
x+ h – x = h
Let us also consider that the price charged for these goods at time (t) is ƒ(x) and time
(t+1), it is ƒ(x + h), then the change in price will be:
ΔY = ƒ(x + h) – ƒ(x)
To find the slope of this curve then we use the normal rule of dividing the adjacent by the
horizontal change. Thus
29
ƒ(x + h) – ƒ(x) =  Y
h
x
Therefore, Lim ƒ(x + h) – ƒ(x) =
h
o
h
Lim
h
 Y
o x
Example
Supposing we have a function x2 – 4x, find ƒ(x) from first principles.
ƒ(x) = Lim
h
o
ƒ(x + h) – ƒ(x)
h
ƒ(x) = ƒ(x + h)2 – 4 (x + h) – (x2 – 4x)
h
Lim
H o
x2 + 2xh + h2 – 4x – 4h – x2 + 4x
h
Lim
H o
x2 + 2xh + h2 – 4x – 4h – x2 + 4x
h
Lim 2x – 4 + h
h
o
= 2x – 4
Example 2
Let ƒ(x) = 2x + 1. Find ƒ(x) using the Newton quotient.
Lim
h
o
ƒ(x + h) – ƒ(x)
h
Lim
h o
2(x + h) + 1 – (2x + 1)
h
Lim
h
o
2x + 2h + 1 – 2x + 1
h
Lim
h o
2h
h
30
ƒ(x)
=
2
The alternative method is to use the differentiation formula. Ideally, the use of the
Newton quotient and the differentiation formulae should yield the same result. There are
various rules to differentiate different types of functions. They are provided below For
our purposes we concentrate on the following:
Rule 1
Y = Cxn
dY = n.Cxn-1
dx
Example 3
Let y = x2 + 1
dy = 2.1.x2-1 + 0.1
dx
dY 2x + 0
dX
= 2x
Example 4
Let y = 2x + 1
dY = 2.1x1-1 + 0.10-1
dx
dY = 2 x0 + 0
dX
= 2 (since x0 = 1)
Rule 2
When y = C (and C = constants)
dY = 0
dX
This will apply to all constants.
31
Rule 3
If Y = U + V then
dy = du + dv
dx dx dx
Rule 4
Concerns the chain rule
If y = ƒ(u) and u = g(x)
dy
du
dX
dx
dY = dY. du
dX dx dx
Rule 5. The Product rule
If y = U(x). V(x) then
dy = Udv . Vdu
dx
dx
dx
Rule 6. The quotient rule
If y = U then
V
dY = Vdu – UdV
dx
dx
dx
V2
In using derivatives, we want to find the value of X that minimizes or maximizes Y. We
determine the value of X where dY equals zero.
dX
To find whether this is a minimum or maximum, we find the second derivative of Y with
respect to X, denoted by d2Y which is the derivative of dY
dX2
dX
If the second derivative is negative, we have found a maximum; if it is positive we have
found a minimum.
Example:
Y
= -40 + 20x – 2x2
32
dY = 20 – 4x
dX
d2Y = 4
dx
This is positive and it is a minimum.
It is important to note that a dependent variable often depends on a number of
independent variables not just one. To find the values of each of the independent
variables that maximizes the dependent variable, we determine the partial derivative of Y
with respect to each of the independent variables, denoted by dy and set it equal to zero.
dx
To obtain the partial derivative of Y with respect to X, we apply the rules for finding a
derivative; however, all independent variables other than X are treated as constants.
For example
The Lone Star Corporation makes two products, number and paper. The relationship
between  (profit) and its output of each good is:

= -100 + 80Q1 + 60Q2 – 10Q12 – 8Q22 – 5 Q1Q2
Where Q1 is the firms annual output for lumber (in tons). Find the output of each good
that the Lone Star Corporation should produce if it wants to maximize profit.
Solution:
d  = 80 – 20Q1 – 5Q2
dQ1
= 80 – 20 Q1 – 5Q2
d  = 60 – 16Q2 – 5Q1
dQ2
= 60 – 16Q2 – 5Q1
80 – 20Q1 – 5Q2 = 0
80 – 20Q1 = 5Q2
(divide throughout by 5)
=16 – 4Q1 = Q2
60 – 16Q2 – 5Q1 = 0
60 – 16 (16-4Q1) – 5Q1 = 0
60 – 256 + 64Q1 = 0
196 + 59Q1 = 0
-196 = -59Q1
33
3.32 = Q1
Q2 = 16 – 4Q1
= 16 – 4 X 3.32
16 – 13.28 = 2.72
Thus, the Lone Star Corporation should produce 3.32 tons of timber and 2.72 tons of
paper.
There are also some functions that can not be factorised easily.
Example 2.
 = -3000-2400Q + 350Q2 – 8.33Q3

d  = -2400 + 700Q – 24.99Q2
dQ
or –24.99Q2 + 700Q – 2400 = 0
To solve this equation we have to apply the following formula
-b 
b2 – 4ac
2a
For the equation –25Q2 + 700Q – 2400 = 0
a = -25
b = 700
c =-2400
Substitute these into the formula, we get
-700 
(700)2  4(25)(2400)
2 (-25)
= -700 
250,000
- 50
700  500
34
-50
=
200
50
=4
====
or 1200 = 24
50 ====
Marginal Analysis
In the Lectures on the goals of a firm, we did touch the concept of marginal analysis.
This enables us understand the contribution to profit or Sales (Total revenue) or Total
cost can be done from Total of each unit of a good produced. While this can be done
from Total revenue or cost figures, there are instances where the total revenue or cost is
expressed as an equation. The total revenue curve, the first derivative expresses the
marginal revenue curve.
On a graph the local maximum and local minimum are denoted by the letters B and C.
maximum
Y-axis
B
D
A
C
minimum
X-axis
From this one can see that the graphs for Total revenue will have a maximum while that
for Total cost will have a minimum.
In economics, we are used to dealing with Total revenue as Total cost functions. The
general rule is that :
Total revenue (TR) – Total Cost (TC) = Profit (  )
Thus,  = TR – TC
d  = d(TR) = d(TC) = 0
dQ
dQ
dQ
35
MR (Marginal Revenue) = d(TR) and marginal cost = d(TC)
dQ
dQ
So the above equation is equivalent to
MR – MC = 0
And so MR = MC as required.
From this it is true then to say
d  = MR – MC
dQ
If we differentiate again with respect to Q
d2  = d(MR) – d(MC)
dQ2
dQ
dQ
NB: If d2  < 0, then the profit is a maximum and this is so when
d(MR) < d(MC)
dQ
dQ
Recall the condition we reached when we introduced the Profit Maximisation objective
using the Total Revenue and cost curves.
PROBLEMS
1.
If Y = -30 + 20Y – 10X2, what is the value of X that maximizes Y?
2.
If Y = 40 – 5x + 10x2, what is the value that minimizes Y.
3.
In question 2 above, what is the value of d2Y that minimizes the value of Y.
dX2
4.
If Y = 100 + 2X – 3 X2 + X3, what values of dy equalizes the function to zero
2
3
If Y = 100 + 20X1 + 14X2-2X22
5
Find the values of dY and dY
dX1
dX2
6.
The Total cost function at the Tate Company is TC = 200 + 3Q + 7Q2, where TC
is total cost and Q is total output.
a)
b)
What is the Marginal cost when Q = 1
What is the Marginal cost when Q = 5
36
c)
What is the Marginal cost when Q = 10
For the Algonquin Company, the relationship between profit and output is as
follows:
Output
(Number of units per day)
0
1
2
3
4
5
6
7
8
a)
b)
c)
Profit
(Thousands of dollars per day)
-8
-4
0
4
8
11
13
12
11
What is the Marginal profit when output is between 4 and 5 units per day
At what output is profit a maximum?
At what output is average profit a maximum?
37
1. THEORY OF DEMAND
Demand refers to the willingness and ability to purchase a good. This definition
composes two parts: willingness and ability. Willingness refers to our desires and
portion to have the good. However and many times, we may not have the capability
to purchase that good. If that happens then we do not constitute demand. Ability
refers to the purchase power individuals may possess. This is what facilitates act of
purchasing. Therefore we can divide the concept of demand into two; ex-ante
demand and ex-post demand. Ex-ante demand refers to the willingness part, our
plans accompanied by actual ability to purchase. Willingness and ability then
constitute effective demand. The diagram below shows this:-
Ex-ante (Willingness, Plans, Desires)
Demand
Ex-post (Willingness, Plans, desires and ability)
Therefore Ex-post demand is actual demand or effective demand. Many times, when
economist talk about demand they refer to ex-post, actual of effective demand.
2. THE LAW OF DEMAND
The Law of demand shows the relationship between price and quantity demanded of a
commodity or a good in the market. The Law states that “the quantities of a good
demanded increase with every fall in the price of that very good. Conversely,
quantities demanded fall with rise in the price of good. We shall soon show that
there are exceptions to the Law of demand. For some good, this behaviour is
contradicted. To show how the Law works, let us consider an hypothetical
demand schedule.
38
DEMAND SCHEDULE
PRICE IN KWACHA
10
8
6
4
2
QUANTITY DEMANDED
1
2
3
4
5
This schedule shows that when the price is at K10 per unit of the good the quantity
demanded is only 1 unit of this good. As the price declines, more and more quantities are
demanded. Thus as the good becomes cheap (or its price lowers), the quantity demanded
increases.
This can be shown graphically as follows:Y-axis
Price
D

10

8

6

4
2

D
X-axis
0
1
2
3
4
5
Quantity
The result of joining all points of a demand schedule in a graph is the demand curve. It
shows an inverse relationship between price and quantity demanded. The resultant
demand curve is also down ward sloping.
3. THE MARKET DEMAND CURVE
The market demand curve is the sum of all individual demand curves. It is calculated by
adding the quantity demanded by each consumer at each level of price. Consider
the following market demand schedule.
39
MARKET DEMAND SCHEDULE
PRICE(K)
10
8
6
4
2
DEMAND BY CONSUMERS
B
C
2
0
3
1
4
2
5
3
6
4
A
1
2
3
4
5
MARKET DEMAND
D
0
0
1
2
3
3
6
10
14
18
It is possible to plot the demand curves for individuals A B C D. If their demand curves
are summoned up you can also plot the demand curve for the market. This will be called
the market demand curve.
d
Price
10 
8



Market demand curve
6

4

2

0


d
4
8
12
16
20
Quantity
What assumptions i.e. behind Market Demand Curve?
The following are the assumptions:(a) There is no change in consumer tastes or preferences.
(b) Incomes and prices are constant.
40
(c) It is also assumed that the good has no substitute, at least in the short run. However,
whatever the circumstances market demand or even individual demand is considered
at a point in time and it is not fixed for all times. In the long-run it will vary as
consumers change tastes, obtain higher incomes and as prices vary.
The demand curve, both individual and the market demand curve, slope downwards
because:(a) Individuals are assumed to be rational so that when the price is high, demand will be
low and when the price is low demand will be high. There are however exceptions to
this rule.
(b) The demand curve also slopes downwards because of the low of equimarginal utility. That consumers will arrange their purchases until the
ratios of marginal utility and prices of the various goods are equated.
Mu a Mu b Mu c Mu z


...
pa
Pb
PC
PZ
As stated earlier, there are exceptions of this rule. There are times when there is no
change in demand of a good even when price has fallen. In which case the demand will
be a stock.
d
P3
P2
P1
d
This is the case of goods such as salt. There are also times when the demand of a good
rises as prices rise. This is demonstrated below
41
Price
d
P2
P1
d
0
Q1
Q2
Quantity
What explains this behaviour;
(a) Giffen Good Paradox – the Giffen good or interior good is an exception to the law of
demand. When the price of an interior good falls, people will spend more on other
goods. For example, if the price of maize meal or rice falls, people would rather buy
other goods instead of increasing the quantities of maize meal or rice.
(b) The Demonstration or Veblen effectt
At times people buy goods for prestige reasons e.g. diamonds. So people will buy
expensive goods because they want to appear rich.
(c) Ignorance – sometimes people think that price represents quality so
that a higher price may mean higher quality.
(d) People may buy more because of speculative reasons e.g. that there
will be a shortage of a particular good.
CHANGES IN DEMAND
Demand can change because of a change in price. In this instance, the change will be
along a demand curve.
42
A

P1
 b
P2
0
Q1
Q2
A change from point A to point B demonstrates a movement along the demand curve.
Some changes however can result into shifts of the demand curve. These are normally
due to changes in income, in population and in taste. This is shown as follows:-
Price
d1
d
d2
4
4
d1
d
d2
0
Original demand curve
d1 d1, shows a movement outwards implying that people will demand more of the good.
A shift to d2 d2 implies that people will demand less of this good.
43
ELASTICITY OF DEMAND
From the foregoing, it is clear that the Law of demand explains the direction of the
change in demand. A fall in price will lead to a rise in quantity demanded of a good and
vice versa. What it does not tell us is the rate of change at which quantity demanded
changes with the change in price. This is what the elasticity of demand explains. The
elasticity of demand shows the extent of the change in quantity demanded due to a
change in price.
Demand can be elastic or inelastic. Elastic demand means that a small change in price
will lead to a great or large change in quantity demanded. Similarly, inelastic demand
means that a change in price will lead to a very small change in quantity demanded.
TYPES OF ELASTICITY OF DEMAND
There are three types of elasticity of demand.
a)
Price elasticity of demand
b)
Income elasticity of demand
c)
Cross elasticity of demand
Price Elasticity of Demand
This measures the changes in quantity demanded arising from a change in price.
Price elasticity (PE) = Proportionate (%) change in quantity demanded
Proportionate change in Price
PE = %  Qd
% P
Price elasticity can be (a) infinitely elastic, (b) perfectly inelastic (c) relatively elastic (d)
relatively inelastic (e) unit elasticity of demand.
44
a)
Perfectly elastic
Price
d
P
d
Quantity
This is the situation where at some price (P) any quantity of goods can be
demanded.
b)
Perfectly inelastic
Price
P1
d
P
d
O
Q1
Quantity
Here, Price changes have no effect on quantity demanded.
c)
Relatively elastic demand
d
P
P1
d
0
Q
Q1 Quantity
were demand changes more than proportionately to change in price. Thus  >1
d)
Relatively inelastic
d
P
d
O
Q
Q1
Quantity
45
Here demand changes less than proportionately to change in price.
e)
Unit elasticity of demand
P
P1
O
Q
Q1 Quantity
Here the changes in demand are exactly proportional to the change in Price  = 1.
Measurement of Elasticity.
Two major methods are used in measuring elasticity of demand. These are:
a)
the point method
b)
the Arc method
a)
The Point Method
The point method measures elasticity at a point. In this method, and depending
on the direction of the change in price, the solutions for the same point may differ
because of differences in the denominator
Price
P
A
B
P1
P2
C
Example
If the Price falls from P to P1 the elasticity of demand will be measured by the formula
PE = %  Qd =
% P
Q1 - Q
= Q
P1 - P
P
If on the other hand the initial point was B, a price rise from P1 to P2, the formula will be
46
Pe =
Q1 – Q
Q1
P1 – P1
P1
See that the denominators in both the numerator and the denominator have changed.
Thus for the same slope we obtain two different answers. That is why the Arc method is
preferred.
The Arc Method
Since the point method gives different answers for the same change, economists prefer
the Arc method. This sis also point elasticity but movements in Prices and qualities
either way are taken care of. The formula for Arc elasticity is:
Q1 – Q
Q1 + Q
2
Arc elasticity = _____________
or
Q
Q1 + Q
2
P
P1 – P
P1 + P2
P1 + P
2
2
The Arc method then allows us to obtain the same solution regardless of the direction of
the change.
Factors Affecting Elasticity of Demand
a)
Nature of the commodity
The nature of the commodity determines the elasticity of demand. If a good is a
necessity or a luxury is an important consideration. Normally, demand for
necessities of life such as maize-meal (or rice in some societies) salt etc are
inelastic. Demand for luxuries tend to be affected by changes in price.
b)
Availability of substitutes/compliments
The availability of a substitute good may also affect the demand of a good, so it is
for compliments.
c)
Variety of uses
If a commodity has many uses, demand is likely to be elastic. This factor
however holds only when new uses are found.
d)
Time
47
Time also determines demand. There are times when it takes too long to
consumers to know that the price of a good has fallen.
Importance of Elasticities of Demand
a)
Price fixation – each producer or seller must take into consideration price
elasticity’s before reducing or increasing prices. This is even more critical in
imperfect competition. Such as oligopoly or even monopoly. A firm can end up
loosing or increasing demand depending on the elasticity of the good in question.
b)
Production
Production is also affected by the elasticity of a good in production. If the good
has inelastic demand production levels must be maintained. If on the other hand
it has elastic demand, a slight reduction in price would entail producing more of
that good.
c)
The concept can also be used by government officers in fixing the levels of
taxation on some goods. Trade Unions can also use the same concept if they
know that the demand for a particular type of labour is inelastic. Conversely,
firms can also use the concept to reduce wage rates when labour supply is elastic.
Relationship between Elasticity of Demand and Revenue
It is important to recall that
Total Revenue = Total Quantity X Price
TR = Q x P
Average Revenue = Total Revenue Divided by Total Quantity
(average revenue is the price)
AR = TR
Q
Marginal Revenue =  TR
Q
This can be demonstrated by the following table.
Number
units sold
1
2
3
4
5
of Average
(AR)
(Price)
Revenue Total Revenue
TR
18
16
14
12
10
18
32
42
48
50
Marginal
Revenue
MR
18
14
10
6
2
48
6
7
8
6
48
42
-2
-6
From the table we can see the following:
a)
As long as average revenue (P) is falling, Marginal Revenue will be less than
average revenue.
b)
Total Revenue will be rising as long as Marginal revenue is rising.
c)
When Marginal Revenue (MR) is negative Total Revenue (TR) is falling.
d)
Total Revenue will be at a maximum where Marginal revenue is equal to zero.
Relationship with Elasticity
a)
Along the demand curve, when the price elasticity is greater than one, the
marginal revenue is positive and total revenue rises as the price falls.
b)
When the elasticity of demand is zero, total revenue will remain constant.
c)
When price elasticity of demand is less than one, the marginal revenue is negative
and total revenue falls.
RELATIONSHIP WITH MARGINAL REVENUE
It is important to know that elasticity has also got relationships with Average revenue and
Marginal revenue.
Average revenue
The relationship with average revenue is expressed by the following formula:
AR = MR x 
______
- 1
where  is the price elasticity of Demand
MR is Marginal Revenue
AR is the Average Revenue (=Price)
Thus for Marginal Revenue
MR = AR (  - 1)
e
49
- 1
or AR
e
or MR = P(  - 1) or P (1 – 1) or P (1 - 1)



where
MR = Marginal revenue
P = price
E = Price elasticity of Demand
OTHER TYPES OF ELASTICITIES
Other than the price elasticity of demand, there are two other types. These are:
a)
Income Elasticity of Demand
This shows the change in quantity demanded as a result of a change in income.
Income elasticity of demand is expressed as follows:

y = Proportionate change in quantity demanded
proportionate change in income
In a graph it is measured with income on the y-axis and quantities demanded on
the x-axis.
income
do
d
d1
P
P1
Depending on the slope of the demand curve the elasticity can be less negative in
the case of dodo, can be less negative in the case of dodo, can be zero in the case
dd and can be positive (   1 ) in the case of d1d1.
b)
Cross Elasticity of Demand
This comes about when the change in price of one commodity leads to a change
in quantity demanded of another commodity. This is expressed as follows:
50
Ec = Percentage (proportionate) change in quantity demanded of good x
Percentage (proportionate) change in the price of Y
Advertising and its relationship to Elasticity
Many times firms have to advertise in order to increase their sales revenues and volumes.
However it is important to know that even in advertising you can reach a saturation point.
Sales will initially increase with advertising up to the point where increases in the
advertising budged brings in less in sales volume. This is expressed as follows:
Sales
saturation point
0
Advertising outlay
The measurement of advertising elasticity is done using the following formula.
 a = Proportionate change in sales
Proportionate change in the advertising budget
or
Change in sales
Sales
 a = _________________________________________________________________________________________
change in advertising expenditure
original advertising expenditure
or
a =  S
s
=
S
S

A
x
or
S x A
A S
A
51
A
Advertising elasticity is affected by any of the following:
a)
Stage of development of the market for the product (whether it is a new product, a
product with a growing market or an established product).
b)
The extent of the competitors reaction to the company’s advertisement.
c) The influence of non-advertising determinants of demand like growth trends,
prices and incomes.
What does advertising depend on?
a)
It can be a fixed percentage of past expected sales. This is convenient but does
not tell us the cost of getting additional business.
b)
It can be based on profit. Meaning the higher the profit the more the advertising.
This is however dangerous because it does not follow that the higher the
advertising the higher the profits.
c)
It can also be based on the advertising expenditure of rival firms. This means that
advertising will be based on the firms market share. This avoids vicious
competition from rivals and helps maintain the firms share of the market.
Advertising can also have economic implications:
a)
b)
c)
d)
it informs customers about the product
it can help broaden the market
it encourages competition
it can also be wasteful as it deceives people that products are different when not.
d) in oligopoly, it can lead to market concentration. It can prevent small firms from
entering a market since small firms will find it too expensive to advertise.
52
Demand Forecasting and Estimation
One of the problems which we sited in our earlier lectures was uncertainty. Indeed no
one knows what the future holds. However, in Business, it is important to use tools that
help us predict what the future might be. While we apply such techniques, answers will
be obtained. These answers however may depart from the reality when we reach that
point. The prediction however may be within range of the reality. Most firms would like
to know the demand for their products in the future. For this we can only estimate or
forecast such future demand on the basis of current or time series data. Such estimates
will also help the firm in production planning as it is essential for the firm to produce the
required quantities at the right time.
Types of Demand Forecasting
Forecasting can be divided into short-term or long-term demand forecasting. The short
term demand forecasting is limited to relatively short periods of time normally less than
one year. It applies to forecasting prices for raw materials, expected sales etc.
Long term forecasting on the other hand considers the long-term demand for a product. It
may also involve planning a new plant or expanding an existing unit. However it should
be noted that long-term planning is prone to a high probability of error. For this quality
and competent forecasting is essential.
Tit should also be stated that to have good forecast it is important to know the objective
of the forecasts. It is also important that a good method of forecasting is selected. With
this, data analysis becomes relatively easy.
Methods of forecasting
Several methods are employed in estimating and forecasting demand. Estimation
involves determining demand at a point in time while forecasting involves determining
the levels of future demand in The methods can however be grouped under two broad
categories : the survey and statistical method. The chart below shows the two groupings.
53
Forecasting Methods
Survey
Method
Opinio
n
survey
Statistical Method
Exper
t
Surve
y
Complete
enumerat
or
Delphi
Method
Sample
Survey
Enduse
Method
Time
Series
Barometr
ic
technique
Regressio
n and
Correlati
on
Enduse
Method
Exponentia
l
smoothing
Moving
averages
You will note from the division in the methods that in some methods especially those
based on the survey method, you may end up using descriptive statistics in the analysis to
describe the state of things. While in the statistical methods, the future is being forecast.
Let us look at the Survey Method
The Survey method can be divided into four different types. There are opinion surveys,
expert opinion, the Delphi method and consumer interview method.
a)
Opinion Survey Method
This method has many names. It is referred to as the sales force composite
method or the collective opinion method. Under this method the firm may ask its
salesmen to submit estimates of the future sales in their respective territories. In
the case of Zambia you may ask the salesmen in the various provincial capitals to
estimate what the future sales will be. These salesmen may use or two techniques
to do this. However, salesmen tend to be too optimistic or pessimistic about the
54
general growth of sales. If paid a commission above a certain level of sales, they
are bound to be pessimistic so they can reach that target easily. If on the other
hand they are rewarded for aiming to achieve high targets, they may be over
optimistic.
These estimates are then consolidated reviewed and adjusted by management to
bring them to realistic levels. The estimates may be averaged to reach that
realistic forecast.
Advantages of the opinion survey
a)
It is simple and straight forward
b)
It is less costly
c)
It can be realistic as it is based on first hand information
Disadvantages
a)
It is extremely subjective. The forecast is just as biased as the people
estimating
b)
The method is useful only for short periods. It is less useful for longer
periods of time exceeding one year. In fact it is a better method for
monthly forecasts
c)
Sales people may not be the best to carryout forecasts.
b)
Expert Opinion
The expert opinion method is an advancement over the opinion survey method.
Other than the use of salesmen, experts from outside consumers and distributors
of the product may be used in forecasting. In the automobile industry, Dealers
may be used. There are various bureau’s in the world today who are engaged in
industry forecasts. These may also be used:
Advantages
a)
The method is quick and becomes more reliable by including others from
outside the firm.
b)
The method may be useful when introducing a new product. Only experts
may know the trends in the industry.
a)
b)
c)
Disadvantages
Opinions may still be subjective and so not very reliable
It is difficult to separate good and bad opinions.
The Delphi Method
The Delphi method is still an advancement of the survey method. In this method
both internal and external experts may be used except that they are kept apart
from each other. They express their opinions in an anonymous manner. The
method also employs a coordinator who acts as an intermediary. He prepares the
55
questionnaire and administers it to the panellists. At the end of each round of
questioning he/she prepares a summary report of the major outcomes.
The method has been employed in forecasting non-economic variables e.g
technological improvements.
d)
Consumer interview method
In this method consumers are contacted personally to know about their plans or
preferences regarding the consumption of a product. Each of these consumers
will be asked about how much they intend to buy of a particular product.
Advantages
a)
It gives first hand information about consumer preferences
b)
It is most likely to be correct if only it is corrected for levels of confidence
Disadvantages
a)
It can be expensive
b)
Customers may be hesitant to reveal their preferences
c)
Customers may also exaggerate their preferences to impress the
interviewer especially when the product is expensive and has social status
connotations.
The survey method can be undertaken by:
a)
b)
c)
Complete enumeration method, where all consumers are surveyed. This is
expensive and impractical
Sample survey method – This involves taking a representative sample of the
population at random or a stratified random sample. This is easy and less costly
but you need to know your customers well.
The end use method is applied by obtaining information from end users. Such as
industries, consumers, export and import companies etc. These will provide their
demand for your product. The industries may also product their input-output
coefficients for you to know just how much to supply. This may be very difficult
to do in practice.
56
STATISTICAL METHODS
Statistical methods are used for long-term forecasting. Normally these methods relies on
past historical data which are applied to forecast the future. Nearly all firms collect and
accumulate data over long periods of time. Some firms rarely use the data they have for
long term forecasts nor even just to establish the trends. The historical data can be
presented in tabular form or in a graph. The data may reveal some fluctuations.
TIME SERIES
A time series is defined as data classified chronologically. It is a set of observations over
a time period. The data may refer to sales of a firm or production overtime.
Two things are noticeable in a time series
(a) There is a steady growth in production or sales over a period of time.
(b) There can also be regular variations or fluctuations. The fluctuations may be due to
general tendencies. This is known as a secular or basic trend. This is a long-term
movement and it shows a steady growth. If on the other hand the fluctuations are due
to things like climate, temperature or weather conditions in general, they are referred
to as seasonal variations. These are variations from the trend. They generally occur
periodically, every quarter, week or month according to the nature of the data.
Changes arising from cyclical fluctuations like booms or slumps (depressions) are
called cyclical variations. These are Oscillatory movements super imposed on the
trend. In the case of economic and industrial time series they will correspond to
movements of the trade cycle. Other anticipated changes such as famine, floods,
earth quakes and or labor unrest (strike) are termed as random variations or
catastrophic movements. Most of the time, it is secular variations which are
considered in most statistical methods. The data below shows this. The analysis of
time series consists in separating these constituent parts.
THE USES OF TIME SERIES ANALYSIS
It enables forecasts to be made. If the trend line is continued into the future, a possible
figure for some future date is obtained. The future figure is predicted on the assumption
that the trend will continue. Any unforeseen circumstances may invalidate the forecast.
Time series forecast are useful in planning the various budges and in budgetary control.
57
Trends in Time series
Basic trends are of three types.
(a) the logistic trend.
(b) the arithmetic trend
(c) the compound interest trend.
(a) THE LOGISTIC TREND
This has been found appropriate to cases of natural growth, growth of production or
certain activity or even in sales. The trend is composed of an increasing rate of growth,
followed by a decreasing rate of growth and finally reaching a constant figure. This is
shown as follows:-
Sales
K60,0000 -
Total sales
K40,000 Saturatum
Increasing rate
K20,000 -
1970
Decreasing
rate
1975
Year
1980
1990
58
(b) The Arithmetic Trend
This means that a variable increases or decreases by constant amount each year
Sales
300
200
100
1950
1960
1970
1980
1990
(c) COMPOUND INTEREST TREND
This is similar to the arithmetic trend but in this case the variable increases or decreases
by the same proportion each year. (Note that the amount will be getting larger since this
is compound).
400
300
200
100
1970
1980
1990
2000
2001
Thus trends can be obtained by:-
59
(a) Curve inspection – plotting data on a graph.
(b) Moving averages.
(c) The method of least squares – done through regressions.
Time Series as Basic Data
Time series data may consider the demand pattern of a product over a period of
time. Consider the sales of a firm selling sugar.
Table 1
Year
1989
1990
1991
1992
1993
Sales in Tons
60
67
62
73
80
These can be plotted in a graph.
Sales
(‘000)
90
80
x
x
70
60
x
x
x
50
40
30
20
10
89
90
91
92
93
Years
60
The graph shows that sales have been fluctuating but the trend is increasing. Infact the
trend line show this. This trend line can also be found by developing an equation to find
the nature and magnitude of the trend.
The most common method to construct the line of best fit is by the Method of Least
Squares. The trend is assumed to be 1 metre. A simple linear trend is the relationship
between the dependent and the independent variable. The dependent variable is
represented on the Y axis while the independent variable is on the X-axis.
The equation for the line is
Y = a + bX
where a = intercept
b = shows the impact of the independent variable (rate
of change)
We can find the trend equation using either the method of Least Squares or using
simultaneous equations. The method we first apply is by using simultaneous equations.
b) Using Simultaneous Equations.
(1)
 Y = na + b  X
2
(2)
 XY = a  X + b  X
Using a the values in Table 1 above we obtain the values of X and Y as in Table 2 below.
Table 2.
Year
1989
1990
1991
1992
1993
N=5
Sales Y
60
67
62
73
80
 Y = 342
X(Years)
1
2
3
4
5
 X = 15
X2
1
4
9
16
25
 X2 = 55
XY
60
134
186
292
400
 XY = 1072
Substituting these values in the equations we obtain
342 = 5a + 15b
(3)
1072 = 15a + 55b (4)
Since the equations have values of a and b, we express equation 3v in terms of b so that it
is easily substitutable in equation 4. We obtain equation 5.
342 – 5a = 15b
61
342 – 5a = b
15
(5)
Substituting equation 5 in equation 4, we obtain
1072 = 15a + 55 (342 – 5a
15
Multiply all sides by 15
16080 = 225a + 55 (342 – 5a)
16080 = 225a + 18810 – 275a
16080 – 18810 = 225a – 275a
2730 = 50a
2730 = a
50
a = 54.6
Substitute a into equation 1
342 = 5a + 15b
342 = 5(546) + 15b
342=273 + 15b
342 – 273 = 15b
69 = 15b
69= b
15
b = 4.6
The Trend line equation then is
Y = 54.6 + 4.6x
To forecast for 1994
Y = 54.6 + 4.6 (6)
Y = 54.6 + 27.6
Y = 82.2
LINEAR REGRESSION USING THE LEAST SQUARES METHOD
The least squares method of linear regression analysis provides a technique for estimating
the Equation of a line it best fit.
62
The equation of straight line has the form y  a  bx where
x and y are related variables
x is the independent variable
y is the dependent variable
a is the intercept of the line on the vertical axis
b is the gradient 9slope) of the line.
The least square method provides estimates for the values of a and b using the following
formula.
b
n xy   x  y
a
 y  b x
n x 2   x 
2
n
n
where n is the number of pairs of data.
It is important to note that the line of best fit that is derived represents the regression of y
upon x .
Example
You are given the following data for output at a factory and costs of production over the
past five months.
Month
1
2
3
4
5
Output
X
‘000 units
20
16
24
22
18
Costs
Y
£’000
82
70
90
85
73
63
Calculate the regression equation and the correlation coefficient.
Workings
Y
82
70
90
85
73
Y  400
X
20
16
24
22
18
 X  100
b
XY
1640
1120
2169
1670
1314
 XY  8104
X2
400
256
576
484
324
2
 X  2,040
Y2
6724
4900
8100
7225
5329
2
Y  32278
n xy   x  y
n x 2   x 
2

5(8104)  100(400)
5(2040)  (100) 2

40520  40,000 520

10200  10,000 200
 2.6
a
 y  b x
n
n
400 2.6(100)5


 80  52  28
5
a  28
y  a  bx
y  28  2.6 x
It is important to note that the value of b is called the estimated regression coefficient
(rate of charge or the slope of the regression line).
64
MULTIPLE REGRESSION ANALYSIS
- A simple regression has only one independent variable.
- A multiple regression includes more than one independent variable.
A multiple regression is preferred because one can predict the dependent variable more
accurately than when one independent variable is used. The first step in multiple
regression is to identify the independent variables and them to specify the mathematical
form of the equation relating to the mean value of the dependent variable to the
independent variables.
For example if Y is the dependent variable and X and Z are the independent variables,
then one might specify that:Yi = A + B1Xi + B2Zi + e i
Where e i = the difference between Yi and the mean value of Y (given the values of Xi
and Zi
B1 and B2 = true regression coefficients of X and Z.
A = the intercept of the regression equation.
Please also note that if e i = 0 then the regression equation becomes:Y1  A  B1 X i  B2 Z i
In multiple regression we may even have more than two independent variables. At that
stage recourse to computing is the best.
CORRELATION.
If two quantities vary in much a way that movements in one are accompanied by
movements in the other. These quantities are correlated. For example an increase in the
amount and frequency of rains may be accompanied by an increase in the sales of
umbrellas.
These movements may be in the same direction i.e. an increase in the amount of rain
may lead to an increase in the sales of umbrellas. The movements may also be in
different directions i.e. an increase in the purchase of television sets may lead to a decline
in the sale of Cinema tickets. Thus here the correlation is negative.
It is important to know that even though movements in one variable may affect
movements in another there may knot be causation. Thus correlation is not causation.
65
Correlation can be determined by how incidents occur on a scatter diagram.
Age
of
wife
Tread








1970
1980
1990
2000

210
THE COEFFICIENT OF CORRELATION
This is the measurement of the degree of correlation between variables. It will vary
between +1 and –1. If there is perfect correlation the coefficient will be +1 in the case of
positive correlation (movement in the same direction) and –1 if there is negative or
inverse correlation.
If the coefficient of correlation is known, and the value of one variable is also known, it
is possible to find the probable value of the other variable.
The coefficient of correlation is computed using the following formular.
r
 xy
x  y
2
2
Note that small x and y mean the deviation from the one variable either X or Y.
For example
X
Product weeks
Y
output
1
2
3
4
10
5
20
25
60
2
3
5
6
16
x
y
-2
-1
+1
+2
-5
-10
+5
+10
x2
4
1
1
4
x
2
 10
y2
25
100
25
100
 y 2  250
xy
10
10
5
20
 xy  45
66
Thus for mean of x 
For mean of y =
16
4
4
60
 15
4
x = 2 – 4 = -2
Thus r 
 xy
x  y
2
2

45
10.250

45
2500
45
 0.9
50
In the example we have given, the means were whole numbers. In practice they would
probably not be so. To avoid tedious calculations deviations are taken form assumed
means and a more complicated formula used. The assumed means are usually taken as
zero, so that the deviations from the assumed means are the original data. The formula
then used is
 XY    X   Y 
r
 n  n 



2
2

X 2   X     Y 2   Y  








 
 
 n
 n    n
 n  
n
67
Using the data from the previous example we can then recomputed the coefficient of
correlation.
Example
Plant
X
Y
X2
Y2
XY
1
2
10
4
100
20
2
3
5
9
25
15
3
5
20
25
400
100
4
6
25
36
625
150
Y 60
X
TOTAL  X 16
r
2
74
Y 1150
2
 XY 285
283  16   60 
   
4  4  4 
 74  16  2  1150  60  2 
  
    
 4  4    4
 4  
71.25  (4)(15)
r
18.5  4 287.5  15 
2
2
r
71.25  60
(18.5  16)(287.5  225)
r
11.25
(2.5)(62.5)
r
11.25
156.25
11.25
 0 .9
12.5
68
r  0.9
The same answer as before.
If two quantities vary in such a way that the movements in one are accompanied by
movements in the other, these quantities are correlated.
69
MOVING AVERAGES
This method is utilized on the assumption that the future is the average of past events.
Hence on the basis of historical data the future can be predicted. When demand for a
particular good is stable, this method can provide good forecasts. The main issue in
moving averages is determining or choosing the ideal number of periods to include in the
average.
The method is appropriate when:(a) the historical data is representative.
(b) when we are considering short-term forecasts.
(c) when data or the economic environment is relatively stable. When there are business
cycle fluctuations, this may not be the best method. Business cycles are as
represented in the graph below. The cycles represent the booms and slumps over
time.
Boom
Slump
Years
The formula for moving averages is expressed as:-
S t 1 
xt  xt 1  xt  N 1
N
70
Where St = the forecast for time t.
x t = the actual value at time t.
N = the number of values included in the average.
For Example
We have data for sales for 13 months from January 2003 to January 2004. How do we
calculate the three months moving average? The formula above has been used to
calculate the moving averages in the table below. In this case the three months forecast
for January, February and March is 450 units. This is placed along side the February
sales, the middle item.
MONTHS
Jan 2003
Feb
March
April
May
June
July
August
September
October
November
December
January 2004
SALES
450
440
460
410
380
400
370
360
410
450
470
490
460
MOVING AVERAGE
450
436.6
416.66
396.66
383.3
376.6
380
406.67
443.34
470
473.3
This information can also be plotted in a graph in order to show the trend. The
information we have will certainly show an increasing trend especially after July 2003.
When using moving averages it is also important to note the following:(a) Different periods chosen will yield different moving averages.
(b) The greater the number of moving averages the greater the smoothing effect.
(c) Great care must be taken when data is too random.
71
The limitations to this method lie in:(a) equal weight is given to all the values used in the calculation of moving averages.
(b) the moving average calculation does not take into account data outside the period of
the average.
(c) the use of unadjusted moving average as a basis for the forecast can cause
misleading results especially when there is an underlying seasonal effect.
EXPONENTIAL SMOOTHING
This is another method of short-term forecasting. The only information required is:
a)
b)
the forecast for the current period.
the value for the current period (the observation)
It is then possible to make a forecast for the next period (the new forecast). The new
forecast is calculated as follows:
New forecast = old forecast +  (Observation – Old forecast)
Where  is the smoothing factor or smoothing constant
If  = 1, then the new forecast = to the latest observation. There is complete sensitivity.
In most instances, a smoothing factor between 0.1 and 0.2 will be found suitable. The
smaller the value of the smoothing factor, the smoother the forecast series, that is the
smaller the deviations.
The constant is also assumed but it is important to be within the range suggested above.
In mathematical terms then:
St+1 = St +  (Xt – St)
Where
St+1 = the new forecast
St = Old forecast
Xt = the observation
Consider the following data. The monthly production of a firm (New observation) is as
follows.
January
February
March
38,000
34,000
40,000
72
April
May
June
36,000
32,000
38,000
The old forecast was as follows:
January
February
March
April
May
June
32,000
33,200
33,400
34,700
35,000
34,400
It is important to arrange this data in table form.
Jan
Feb
March
April
May
June
Old
Forecast(a)
Observation
(b)
32,000
33,200
33,400
34,700
35,000
34,400
38,000
34,000
40,000
36,000
32,000
38,000
Error
Observation-Old
forecast)
(c)
6000
800
6600
1300
-3000
3600
 (error)
error = 0.2
New
forecast (d +
a)
1200
160
1320
260
-600
720
33200
33360
34720
34960
34400
35120
You can then plot information of the observations and the new forecast in the same
graph. You can see the smoothening effect of the technique.
Time series data also requires adjustment especially where we know that the currency is
unstable. So we may be required to adjust our figures using suitable price index to
deflate the data.
We may also adjust the data because of the varying number of days in a month. For
example February is 28 or 29 days while other months have 31 days. The formula for
adjusting this is
a)
Average number of days per month
Actual number of days in that month.
It is also possible to adjust the data using the number of working days in a month.
The formula then will be:
b)
Average number of working days per month
actual number of working days per month
73
BAROMETRIC METHODS
Under barometric methods, indices are discussed. Indices are good business barometers
in the sense that they indicate the likelihood of certain occurrences in the environment.
Index numbers provide a standardized way of comparing the values overtime of prices,
wages volume of output and so on. They are used extensively in business, government
and commerce. The most common indices are the consumer price and producer price
indices. Some indices are considered leading indicators while others lag behind. In the
leading indicator category, we can include the FTSI (500).
What is an Index?
An Index is a measure, over time of the average changes in the values (prices or
quantities) of groups of items. An Index consists of a series of Index numbers: Price
Indices and Quantity Indices:
(a)
A Price Index measures the change in the money value of a group of items over
time. The most common Index in many countries is the Consumer Price Index
(CPI) or the Retail Price Index (RPI).
This measures the costs of items of expenditure of the average household.
(b)
A Quantity Index (volume index) measures the change in the non-monetary
values of a group of items over time. (An example of this is the productivity
Index, which measures the productivity of the various department or groups of
workers).
Index Points
The term points refer to the difference between the index values between two years. For
example suppose the following data:
2000
180
2001
200
2002
220
2003
240
74
2004
280
The index has risen 100 points from the year 2000 to the year 2004. This increase however is:
100
 100  55.55%
180
So the index rose 55.55%.
Similarly between 2003 and 2004, the index rose 40 points which is:
40
 100  16.66%
240
The index rose 16.66%
The Base Period or Base Year
Index numbers take the value for a base date. The Base date is the chosen or starting
point for calculating the index base period. In the example, we have just given the base
year. If it is the year 2000 will yield the index 100.
Thus
180
 100  100
180
And so the index number for the rest of the years will be:
2000
=
100.00
2001
=
111.1
2002
=
122.2
2003
=
133.3
2004
=
155.5
Therefore, the index number for the base year is 100.
75
Simple Indices
(a)
The Price Index
=
Pn
 100
Po
Pn is the price of the current year
Po is the price of the base period.
(b)
The Quantity Index
=
Qn
 100
Qo
Qn is the quantity of the current year.
Qo is the quantity of the base year.
Fixed Base and Chain Base Indices
Given the time series data for values of some commodity, there are two ways in which
index relatives can be calculated. The fixed base method or the chain base method can be
utilized.
The fixed base method – involves selecting a fixed base year (index 100) and all
subsequent changes are measured against this base. Such an approach should only be
used if the data is very stable for a long period of time.
The chain base method involves calculating changes with respect to the values of the
period immediately before. This is used for data that is very volatile. In Europe, most
inflation are calculated this way. In fact this is the method used for monthly inflation
calculations.
76
For Example:
The price of a good was K270 in 2000, K311 in 2001, K342 in 2002 and K383 in 2003.
How do we construct both the chain base index and the fixed base index for the years
2000 and 2003 using 2000 as the base year?
To construct the chain base index, we proceed as follows:
2000
270
 100  100
270
2001
311
 100  115
270
2002
342
 100  110
311
2003
383
 100  112
342
For the fixed base index:
2000
270
 100  100
270
2001
311
 100  115
270
2002
342
 100  127
270
77
2003
383
 100  142
270
You notice that the difference arises from the fact that the chain base is measuring the
changes from year to year while the fixed base relatives show changes relative to prices
of the base year.
Changing the Fixed Base Relative
The base year can be changed or shifted especially when it falls to distant in the past and
when the price changes become too frequent. There can also be a change from the fixed
base relative to a chain base relative.
For example:
Consider the index numbers (1970 = 100)
1990
1991
1992
1993
1994
1995
251
91
94
100
103
105
If your are given to compare Index number with different bases, it is important to re-base
one of the indices so that all index numbers have the same base year. This is called rebasing.
Index Numbers as Deflators
Index relatives can be used as deflators in order to obtain the real values of a series of
transactions. For example, you may be paid a salary of say K12, 000 per year. This
salary may be increased annually by K500. If we consider a five year period, the income
of this person will form the following series. You may still be unhappy because you are
failing to maintain the standard:
78
Year
Salary
RPI
Real Wage
Real wage Index
1
12 000
250
12 000
100
2
12 500
260
12 019
100.2
3
13 000
275
11 818
98.5
4
13500
295
11 440
95.3
5
14 000
315
11 111
92.6
The real wage index is calculated as follows:
Real wage index =
Current Re al Wage
 100
Base Wage
Price Indices
Price indices are calculated as follows:
Price Index =
Q P
Q P
 100
o n
o o
Quantity Index =
PQ
PQ
o
n
o
o
Example:
Quantity Qo
Price 2000
PoQo
Price 2001 Pn
PnQ o
Bread
6
20
120
40
240
Tea
2
25
50
30
60
0.067
450
30
405
27
Sugar
200
327
79
Index number in 2001 =
327
 100  163.5
200
The Laspeyre, Paache and Fisher Indices
Laspeyre Price Index =
Quantity Index
Paache Price Index
Quantity Index =
=
PQ
PQ
 100
PQ
PQ
 100
n
o
o
o
o
n
o
o
PQ
PQ
=
PQ
PQ
n
n
n
o
n
n
o
o
 100
 100
The Fisher Index
This is found by taking the geometric mean of the Laspeyre Index and the Paache Index.
Fisher Ideal Index
=
Laspeyres Paache
2
e.g. Laspeyre Index
Problems

Basket may be too selective

Data may be incomplete

A national index may be irrelevant to a region.
80
COPPERBELT UNIVERSITY
SCHOOL OF BUSINESS
POSTGRADUATE STUDIES DEPARTMENT
MANGERIAL ECONOMICS UNITS 5, 6 AND 7
UNIT 5
PRODUCTION, COSTS AND THE REVENUE SIDE OF THE FIRM
In the previous lectures we did demand analysis and introduced supply analysis. We now
go into the factors that determine the quantities of goods firms will produce and offer for
sale.
We start this analysis by assuming that firms aim at Maximizing Profits.
If a firm aims at maximizing profits it needs to do two things:
a) Total costs must be minimized
b) The firm must select a price and corresponding output level that maximizes profits.
In this lecture we start with cost minimization. We analyze the firm’s technology and the
input prices.
To arrive at the rule for cost minimization, we must identify the technological
relationship between inputs employed and outputs produced.
Relating Outputs to Inputs
Inputs – Sometimes called factors of Production are the ingredients mixed together by a
firm through its technology to produce outputs.
Inputs may be defined broadly or narrowly. A broad definition might categorize all
inputs such as labour, land, raw materials or capital.
We can however specify these terms:
Labour inputs might mean Engineers
Accountants
Programmers
Secretaries
Managers
-
-
Raw materials might mean-Electricity
Fuel
Water
Capital inputs may include-Building
Trucks
Robots
81
Automated assembly
For any good, the existing state of technology determines the maximum amount of output
a firm can produce with specified quantities of inputs.
-
By state of Technology is meant the Technical or Organization recipes regarding
the various ways a product can be produced.
The Production function summarizes the characteristics of existing technology.
The production function is a relationship between inputs and outputs. It identifies the
maximum output that can be produced per time period by each specific combination of
inputs.
E.g. consider a firm that employs two inputs Labour (L) and Capital (K) to produce
output (Q)
Mathematically this may be expressed as
Q = f (L, K)
If there are many inputs this may also be expressed as
Q = f (X1 X2 ……..Xn, T)
Where Q = output
X1X2….Xn = inputs
T = state of the technology
(Give an Example of a bakery Manual Mixing machine)
One question we can ask ourselves at this stage is
“What happens to output when a firm can vary the use of one of its inputs over a given
period of time?”
Fixed input
Resources or inputs which a firm cannot feasibly vary over time are referred to as Fixed
Inputs.
These are normally inputs that are costly to alter in the short term
In the short run we can hold capital as the fixed Input and Labour (workers) as the
variable input
What happens to the Total Product of the firm in the short run as we vary labour?
82
Production with one variable Input
Amount
capital
3
3
3
3
3
3
3
3
3
3
of
Amount
Labour
of
0
1
2
3
4
5
6
7
8
9
Total Product
0
5
18
30
40
45
48
49
49
45
Average
Product
Labour
5
9
10
10
9
8
7
6.1
5
of
Marginal Product
of Labour
5
13
12
10
5
3
1
0
-4
The first column is included to simply show that capital is held constant.
-
The second and third column contains data that is necessary to analyze this
behavior.
To examine the relationship in the Table we introduce two concepts
a)
Average Product = the total output (total product) divided by the amount of the
input used to produce the output
b)
Marginal product = the change in total output that results from a one unit change
in the amount of an input holding the quantities of other inputs constant.
83
Graph Showing Total Output, Average Output and Marginal Output
Units
Of
Output
TP
APl
MPl
O
Units of Labor
84
Total output increases as more labour is added until it reaches a peak at 49 units MP L
reaches its maximum at 2 workers
APL reaches its maximum at four workers – declines
Note that:
1.
As long as marginal Product is positive Total Produce rises. It only declines
when Negative
2.
When Marginal Product is Zero (0) total product is at its maximum (8 units of
labour).
3.
Any rational producer will never operate were the Marginal product is negative
(beyond 8 workers).
This is so because employing a variable input at a level where the Marginal product is
negative is technologically inefficient.
What do these curves demonstrate? They demonstrate the fact that in production there is
a certain level at which diminishing Returns is set in.
What are diminishing returns
The Law of diminishing returns is a relationship between inputs and outputs that holds
the amount of some input is increased in equal increments, while technology and other
inputs are held constant; the resulting increments in output will decrease in magnitude.
In short, the Law holds that beyond some point the Marginal Product of the Variable
input will decline.
NB. In our graph diminishing returns set in when the amount of labour increased beyond
two workers.
Each Additional worker beyond the second adds less to the total product than the
previous one
The Marginal Product curve also drops downwards at that point.
It is important to state that this law holds when we assume that all workers are alike – that
their output (labour) is homogeneous.
Also for this Law to hold
a)
Some input (or inputs) must stay fixed
b)
Technology must remain unchanged. For a change in technology can cause the
entire Total product curve to shift.
85
PRODUCTION WHEN ALL INPUTS ARE VARIABLES
By investigating a case where one input is variable, we were in fact investigating the
short-run output response by a firm.
The Short- run is a period of time in which changing the employment levels of some
inputs is impracticable.
The Long-run is a period of time in which the firm can vary all its inputs. There are no
fixed inputs in the Long-run. All inputs are Variable inputs.
NB.
It is also important to note that there is no precise time period for the short-run
and the long-run. It depends on the nature of the Industry.
e.g. for a baker using Manual methods of producing bread, it would take him only
to purchase electric machines and installing them to change the level of
technology.
However, for other industries such changes may take over six months or a year.
Therefore, the short-run and the long-run are variable depending on the type of industry.
Production Isoquants
When we consider a product produced by using two inputs, the production options when
both inputs can be varied may be show with Isoquants.
Isoquants or An Isoquant is a curve that shows all the combinations of Inputs that, when
used in a technologically efficient way, will produce a certain level of output.
Isoquants may be drawn as follows:
Units of 5
capital
3
B
D
IQ50
2
C
IQ 30
1
A
IQ 18
0
1
2
3
4
Units of Labour
On IQ18 are units of capital when combined with
1. One unit of labour will produce 18 units of the product
86
-
equally 3 units of capital when combined with 2 units of labour will produce 18
units of the product
2 units of capital when combined with 3 units of labour will produce 18 units of the
product
What this means is that a firm can produce a specified level of output in a variety of
ways
That is using different combinations of inputs as indicated by points A B C and D.
Note that
a)
All combinations on the Isoquant are technologically efficient
b)
All Isoquants at the right are superior to those on the left
Characteristics of Isoquants
Isoquants have similar characteristics as indifference curves
a) The order the level of a Producers output. (Isoquants to the right are superior)
b) The Isoquants slope downwards as long as both inputs are productive.
c)
Two Isoquants can never intersect
d) Isoquants will be convex to the origin.
The Marginal Rate of Technical Substitution
The slope of the Isoquants measures the Marginal Rate of Technical substitution
(MRTS).
The Marginal rate of Technical substitution of labour for capital (MRTS LK) is defined as
the Amount by which capital can be reduced without changing output when there is a
small (unit) increase in the amount of Labour.
87
For Example
Units of
Capital 6
5
B
4
-2
D
E
F
G
3
IQ40
2
IQ48
C
1
A
IQ30
1
0
1
2
3
4
5
IQ18
6 Units of Labour
Between Points B and D, the MRTSLK is 2 calculated as
  2 unitsof captial 
 = 2
- 
 1unit of labour 
Please note also that as we move from points C to A the MRTSLK = 1
-
  2 unitsof captial 

 = 1
 1unit of labour 
This Demonstrates the convexity of Isoquants. The Marginal rate of Technical
substitution diminishes as we move down the Isoquant.
Underlying reasoning
It is important at this stage to recall the concept of scarcity.
For example:
From points B to D
Capital is abundant
Labour is scarce
So 1 unit of labour can replace 2 units of capital
From Points C to A
Capital is relatively scarce
Labour is abundant
Therefore, it is only logical that Labor cannot replace capital in the same Quantities.
88
Demonstration of Diminishing Returns
We can also demonstrate diminishing returns using this same graph.
Let us assume that we hold capital constant (fixed) at three units and start varying labour
(the variable input). What happens.
Units of
capital
5
4
D
K
E
F
G
3
S
2
IQ40
IQ30
1
IQ18
1
2
3
4
5
6 Units of Labour
We hold capital constant at Kf S (at 3 units)
Each unit of labour we add beyond 2 units adds less and less to output
Increasing labour from 2 to three results in increasing output from 18 to 30 units
(from point D on IQ18 to point E on IQ30) along the KfS line.
The additional output is 12 units.
-
-
-
If we increase labour from 3 to 4 units we increase output from 30 to 40 units.
(Movement from point E on the IQ30 Isoquant to IQ40). The increase in output is
only 10 units
If we increase labour from 4 units to 6 units we move on to the IQ48 Isoquant. The
increase in output is only 8 units
Increase in labour is 2 units
8
= 4 units
2
So as we increase labour while Capital remains fixed we can observe that the
additional increment to total output will increase at a Diminishing rate. Thus we
observe the Law of Diminishing returns.
89
MRTS and the Marginal Products of Inputs
Today we move slightly further to try and relate the Marginal Rate of Technical
substitution (MRTS) and the Marginal Products of Inputs.
Let us go back to our earlier example
Units of capital
5
B
3
D
2
C
A
0
-
1
2
3
IQ18
4 units of Labour
Consider again the MRTS, or slope, between points B and D
Between these points One (1) unit of Labour can replace two (2) units of capital
Therefore Labours Marginal product must be two times as large as capitals Marginal
product when the slope of the Isoquant (MRTS) is two units of capital to one unit of
labour.
Take the next two points C and A. Here the slope of the Isoquant is unity.
That is, One unit of labour can only replace one unit of capital
This means that the Marginal Products of Labour and Capital is Equal
Consequently,
Marginal Rate of substitution which is equal to (-) the slope of the Isoquant is also equal
to the relative Marginal Productivities of the Inputs.
Thus
MRTSLK = (-)
MPKL
K
=
MPLK
L
Note that we are not being told about the absolute size of the Marginal Products but only
the ratios.
We can also derive this relationship more formerly. Let us go back to our diagram
90
units of capital
5
D
E
F
3k8
S
2
0
1
2
3
units of labour
Consider the slope of the Isoquant IQ30 between points E and H, K / L
With a move from Point e to point C the reduction in capital, K by itself
reduces output from 30 to 18 units
The reduction in output must equal K times the Marginal Product of Capital.
E.g.
K = -1 unit
The Marginal Product is of the incremental unit of capital is 12 units of output.
Therefore the amount of capital by 1 unit reduces output by 12 units.
Expressing the change in output as Q
Q  K x MPK
Similarly
Q  L x MPL
Rearranging terms yield
K MPKL

L MPLK
RETURNS TO SCALE
We ask ourselves a question what is the relationship of outputs and inputs in the Long
run.
What will happen if both inputs labour and Capital doubled?
There are three possibilities
91
1)
A proportionate increase in all inputs may increase output in the same proportions
– if this happens Production is said to be subject to constant returns to scale.
2)
If all inputs are increased proportionately, there is also the likelihood that “Output
may increase in greater proportion than input use – output more than doubles”
When inputs double, Production is then subject to Increasing returns to scale.
3)
Finally, if all inputs are increased proportionately, there is also the likelihood that
“Output may increase less than the proportion to output use. This is referred to as
decreasing returns to scale.
NB: Note that these are only possibilities
The actual relationship may be difficult to pin down.
What factors give rise to increasing returns
a)
Workers can specialize
b)
Division of labour (people doing specific tasks)
(*Those two factors were first discussed by Adam Smith in the Wealth of the Nations).
Factors responsible for decreasing returns to scale
a)
Inefficiency in managing large operations
(loss of control of operations becomes difficulty)
- Loss of communication channels
The variation of constant, increasing and decreasing Returns to scale are dependent on
whether we are discussing a small, medium or large scale industry.
This is also exemplified the following example:
92
Costs in the short-run
In the previous lecture we dealt with the concept of supply and the determinants of
supply. The first two factors involved the Price of a good and the prices of other goods.
These constituted determination of revenue for the supplier. The other two factors:
a)
prices of factors of production
b)
state of technology
Constitute the suppliers costs. We now look at this concept of cost.
Meaning of cost
In economics cost refers to the concept of opportunity cost – which is the cost measured
in terms of the next best alternative foregone or the sacrifice made in doing it. The
opportunities forgone
To measure the opportunities foregone in a firm, we need to know the factors of
production it has used. These factors of production can be put into two categories
a) factors not owned by the firm (explicit costs)
b) factors already owned by the firm (implicit costs)
Factors not owned by the firm (explicit costs)
The opportunity cost of the factors that already owned by the firm is simply the price the
firm has to pay for them.
E.g. If a firm uses K10,000 worth of electricity, the opportunity cost is K10,000. These
costs on factors that are not owned by the firm are called explicit costs.
Factors already owned by the firm (implicit costs)
-
-
When the firm already has its own factors, it does not as rule have to pay out
money to use them
Their opportunity costs are thus implicit costs
e.g. If a firm owns buildings, the opportunity cost is the rent it could have
received by letting them out to another firm
If a firm draws out K100,000 from its bank account, the opportunity cost is not
just what it has drawn out but the interest foregone
If the owner of the firm could have earned K200,000 by working elsewhere, his
opportunity cost to the firm is this amount.
NB: If there is no alternative use, the opportunity cost is zero.
93
Costs and inputs
A firms cost of production will depend on the factors of production it uses. The more the
factor of production it uses, the greater the costs be. This relationship however depends
on two elements.
a)
The productivity of factors – the greater their physical productivity, the smaller
will be the quantity of them that is needed to produce a given level of output and
hence the lower will be the cost of that output. In other words there is a direct
link between Total physical product, Average Physical Product (APP) and
Marginal Physical Product (MPP) and the cost of Production.
b)
The price of the factors – The higher their price, the higher will be the costs of
production.
Distribution between Fixed and Variable cost (Short-run)
In the short-run however, some factors are fixed in supply, their total costs, therefore, are
fixed costs in the sense that they do not vary with output. (e.g. Rent is a fixed cost).
-The cost of variable factors however varies with output – the cost of a raw material is a
variable cost.
Total cost = Fixed cost + Variable costs
Total cost (TC) = Total Fixed cost + Total variable costs
TC = TFC + TVC
Consider the Table below
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(K)
12
12
12
12
12
12
12
12
TVC
(K)
0
10
16
21
28
40
60
91
TC
12
22
28
33
40
52
72
103
94
If we plot these we have graphs of the following nature
TC
TVC
Costs (K)
100
80
60
40
20
TFC
12
0
1
2
3
4
5
6
7
This graph also follows the principle of diminishing returns. The TVC starts from the
origin and rises slowly. When diminishing returns have set in …………….
From these graphs you can also calculate the Average and Marginal cost.
TC
Q
TC
Marginal cost (M  ) =
Q
Average cost (AC) =
OUTPUT
TFC (K)
TVC
TC
0
1
2
3
4
5
6
7
12
12
12
12
12
12
12
12
0
10
16
21
28
40
60
91
12
22
28
33
40
52
72
103
ATC
22
14
11
10
10.4
12
14.9
TC
Q
MC
10
6
5
7
12
20
31
95
The graphs for the average and marginal cost can be drawn as follows:
Costs
?
MC
20
AC
15
10
5
1
2
3
4
5
6
Output (Q)
7
8
The Average cost curve and the Marginal cost curve also follow the principles of
diminishing returns. They first follow the principle fall until at some point when
diminishing returns have set in.
Cost in the Long-run
-
When it comes to making long-run production decisions the firm has much more
flexibility
It does not have to operate with plant and equipment of a fixed size
It can expand the whole scale of its operations
Therefore, all inputs are variable in the long-run
*The firm may experience constant returns to scale Economies of scale or diseconomies
of scale.
-
-
Since there are no fixed factors in the long-run there are no Long-run fixed costs
e.g. The firm can rent more land, more managers, can expand production so no
fixed electricity costs etc.
The three positions of economies of scale, constant cost and diseconomies of
scale are exemplified below by the average cost curve.
96
Constant costs
Costs
Diseconomies
of scale
Economies of
Scale
0
Q1 output (Q)
Long-run
costs
(LRAC)
Q2
There are three assumptions made when constructing the long-run average cost curves.
a)
Factor prices are given – If the factor prices change both the short and long-run
cost curves will shift – Thus an increase in Wages and shift the curves upwards
b)
The state of technology and factor quality are given – these can only change in the
very long-run – if a firm gains economies of scale, it is because it is utilizing
existing technology well
c)
Firms choose the least-cost combination of factors.
THE REVENUE SIDE OF THE FIRM
If you may recall, we have already dealt with the cost side. There we dealt with the
concepts of
a)
total cost
b)
total variable cost
c)
total fixed cost
d)
marginal cost.
Firms obtain their Revenue from sales. On the revenue side we deal with the concepts of
a)
Price (= Average revenue)
b)
Total revenue
c)
Marginal revenue
97
Definitions
a)
Price – the value at which a unit of a good is bought or obtained
b)
Total revenue – this is the total quantity of goods multiplied by the Unit price of a
good. It is the total amount of money a firm makes by selling its goods over a
period of time
c)
The Marginal revenue – This is the revenue obtained by selling one more unit of
a good.
a)
Price
Price will normally vary with output. If the Production is low, the price is bound to be
high. As the production increases, (as economies of scale set in) the Price is likely to go
down. However there are exceptions to this rule.
In a perfectly competitive market, where the firm takes the price from the industry
(market), Price does not vary with output.
Let us provide ourselves with an example to show the relationships between the concepts
above.
Quantity
Price (AR)
Total Revenue
Marginal Revenue
0
1
2
3
4
5
6
7
8
9
200
180
160
140
120
100
80
60
40
20
0
180
320
420
480
500
480
420
320
180
0
180
140
100
60
20
-20
-60
-100
-140
NOTE:
The relationship between quantity and Price results into the Demand curve
98
e.g.
The Marginal Revenue lies below the demand curve. (Remember that the Price is
also the average revenue).
Average revenue is the Total revenue divided by the quantities.
Total Re venue 180
=
= 180
Quantity
1
=
Price
180
=
320
= 160 = 160
2
=
420
= 140 = 140
3
Therefore Price = Average Revenue.
We can plot the figures in the Table and we will get the following graphs.
d
Marginal
Revenue
Price
d = Price = AR
Positive
Negative
MR
Note also that in this example
P = AR > Marginal Revenue
99
UNIT 6: Pricing Techniques
Early in the semester, we did consider the four different market structures.
We
considered the four different Perfect competition, Monopoly, Oligopoly and
Monopolistic competition. We also to some extent did consider their pricing strategies
and output determination. To recap we present the market structures again:
1. PERFECT COMPETITION
We now start looking at Market structures. There are four principle market structures,
these are:
a)
Perfect competition
b)
Monopoly
c)
Oligopoly, and
d)
Monopolistic competition
We start with Perfect competition.
In everyday understanding, competition to the intense rivalry among businesses. For
example the competition between Microsoft and sun Microsystems, Nike and Reebok etc.
The economic market structure of Perfect competition bears little semblance to this
picture.
Perfect competition is distinguished largely by its impersonal nature. It is an economic
model characterized by:
1)
2)
3)
4)
A large number of buyers and setters,
Free entry and exit
Product homogeneity and
Perfect information
Assumptions
1.
Large numbers of buyers and sellers
There are many buyers and sellers and none of them is large enough in relation to
Industry sales and purchases and so cannot affect the price. The activities of the
firm can also not affect the Industry output.
2.
Free Entry and Exist
In this model, resources such as labor and capital can enter the market as long as
the Industry is expanding and equally resources can leave a contracting industry.
100
There are no barriers to entry – There are NO PATENTS or operating licenses,
which inhibit others from producing the same product (consider maize
production)
3.
Product Homogeneity – The industry as a whole produces standardized products
that in the eyes of the consumer’s are perfect substitutes for one another. This
assumption allows us to talk about a Total industry output as well as a uniform
price for the product. If the price of one producer is higher than the price of
another, then consumers will prefer the products of the later.
4. Perfect information – Firms, consumers and resource owners must have all the
information necessary to make the correct economic decisions. For firms the
following knowledge is important:
i)
ii)
iii)
Knowledge of the production technology
Input prices
Price of outputs
For consumers the following information will be necessary
a)
b)
c)
Knowledge about their own preferences
The prices of the various goods
The remuneration they can receive for supplying labor.
There are other important assumptions to make. These will include:
a)
All goods are purely private and they are economic goods
b)
That all producers aim at maximizing profits while consumers aim at
maximizing satisfaction. (They will prefer low prices).
What are the implications of these Assumptions?
a)
b)
c)
There is equal distribution of Market power
There are no collusive agreements
All firms then will be price takers as opposed to being price makers.
Firms are price takers because the market dictates this and their outputs are very
insignificant to affect market price.
2.
THE FIRMS SHORT-RUN DECISION
In the short-run:
a)
A perfectly competitive firm is referred to as a price taker/quantity adjuster
b)
The firm’s course of action is dictated by forces outside its control
c)
It is demand matched against price, which determines the price at which the
individual firm can sell its output
101
d)
The market is the price market.
FIRM
Price
Market
price cost
d
s
P
d
d
s
d
Q quantity
Quantity
We stated that the demand curve is perfectly elastic and that the demand curve (D) is the
Marginal Revenue (MR) curve and it’s the Average Revenue curve (AR) is equal to price
(P).
Summary
1)
2)
Demand curve is perfectly elastic
d = MR = AR = P
Units
output
1
2
3
4
5
6
Therefore:
of Price (K)
TR (K)
2
2
2
2
2
2
d= P =
2
AR(K)
2
4
6
8
10
12
AR
2
=
2
2
2
2
2
2
MR
2
2
2
2
2
MR
2
102
Let us now superimpose the firms cost curves on to the demand curve.
d
S
MC
MR=MC
P
p
AC
d
d=MR=AR
S
d
O
Q quantity
O
Q
Quantity
Note that:
a)
b)
c)
d)
The price P is determined by the Market forces of supply and demand
The Price P, is what the firm will take and that becomes the firms demand curve
which is perfectly elastic
This happens because in perfect competition
P= d = MR = AR
The actual profit generated is shown by the shaded area. PABC. This is because
Total profit
Total revenue
Total cost
Total profit
3.
=
=
=
=
PABC =
Total Revenue – Total cost
OPAQ
OCBQ
Total revenue – Total cost
OPAQ – OCBQ
What we have demonstrated is a situation where the Firm makes a profit. The
firm can also be in a situation where it makes neither Loss or Profit.
103
Price/
cost
Price
d
MC
S
AC
P
P
d= AR=MR
S
a
O
4.
Quantity
O
Quantity
The firm can also make a loss
d
b
B
C
L o
s s
MR=AR-P
P
a
S
O
Quantity
O
d
Q
Quantity
The area of loss is Pabc
The Long-run Equilibrium of the firm and the Industry
Consider the three positions discussed.
The Long-run equilibrium means a state of balance where no firms will enter or leave the
industry.
In the case of the diagram 1, firms will be attracted into the industry because of
profits. In the case of diagram 3, firms will be leaving the Industry because of
losses and no firms will be attracted to the industry.
-
Therefore the long-run equilibrium will be reached only when no firm in the
industry is making profit or losses. When this is attained no firm will leave or
104
will be attracted in the industry. This is what is referred to as the long-term
equilibrium of the firm.
Supply curves under Perfect competition
Let us now discuss the nature of the supply curve in the Short-run and the Long-run in
Perfect competition. Recall that the firm is a Price taker and a Quantity adjuster.
The Short-run supply curve
What does this demonstrate
a)
b)
c)
It shows how much a firm is willing to supply at different market prices
The supply curve is ex-ante because it relates to output plans
We can also predict the output of a firm since we can know that such a firm will
always aim at equating Price with Marginal Cost.
P = MR = AR = MC
The firms Supply Curve
The firms supply curve is that section of the Marginal cost curve which lies above the
average variable cost curve (AVC). Since no firm will produce if the variable costs are
not covered.
MC
S
P4
AVC
P2
P1
P1
105
The Industry Supply Curve
The Industry supply curve is derived by summing the Marginal cost curves for all the
firms. Remember that the supply curve of a firm is that part of the Marginal cost curve
which lies above the average cost curve.
MC A
MC
B
P2
P1
S
O
a1
a2
Output
O
b1
b2
Q1
output
Q2
output
Q1 = a1 +b1
Q2 = a2 + b2
At
P1 Oa1 + Ob1 = OQ1
P2 Oa2 + Ob2 = OQ2
The resulting supply curve is ex-ante because it refers to output plans.
Benefits Of Perfect Competition
In perfect competition
a)
All firms enjoy equal power
b)
All firms produce at full capacity in the long-run
c)
Consumers face a price per unit for a commodity which is just equal to cost
d)
Society receives maximum gains from the use of its resources and these gains are
maintained by the checks of the Market system which enforces firms to operate
with maximum competence at all times in order to survive.
106
Problems of Perfect Competition
a)
The model does not entertain government intervention, but then there are goods
which cannot be provided by individuals or individual firms. These goods are
normally referred to as public goods. For example, education, health and police
service or protection.
b)
It affects the distribution of income negatively especially when the long-run
equilibrium has been achieved. Only those who are in the Industry will continue
operating.
2. Monopoly
What is Monopoly?
We have just done perfect competition and we learnt that in this market structure, the
firm is a price taker and quantity adjuster and that there are many firms to ensure that no
single Producer/Seller affects the market price.
Monopoly is the polar opposite of perfect competition. It is a market structure with one
single Producer/Seller.
 It can choose any Price/quantity combinations on the Market demand curve.
 Even though pure monopoly is rare, firms may however have monopoly power
 This is the ability to set price above marginal cost.
Monopoly as a Price-Maker
A monopoly faces a market demand curve which is downward sloping. The monopoly is
a price maker because it supplies the total market and it can choose any price along the
market demand curve as it wants.
$1000
$ 800
$ 700
d = AR
0
1
3
4
107
Consider the demand curve above. It is downward sloping and demonstrates that a
monopolist can choose any point on it. Supply less and increase the price or supply more
and reduce the price.
In the diagram, it is clear that when the monopolist chooses to produce 1 unit of the good
the price will be $1000 and the total revenue (TR) = $1000.
-
If he increases output to 3 units, the price will fall to $800, his total revenue will
be $2400
If he further chooses to increase output to 4 units, the price will fall to $700 and
the total revenue (TR) = $2800
If he further chooses to increase output to 5 units at the price of $600, total
revenue (TR) = $3000
If he further increases output to 6 units at price of $500 the TR = $3000
At 7 units with a price of $400, TR = $2800.
Thus initially, the Increase in output, will bring in increasing amounts of revenue per unit
of output sold. Thus the Marginal revenue will be increasing until the monopolist
reaches seven (7) units of output. That is when the Marginal revenue decreases.
Thus there is a very close relationship between the demand curve, price average revenue
and the marginal revenue.
In monopoly, marginal revenue is always less than the price.
Let us present the information in the graph in table form.
Quantity
Price
1
2
3
4
5
6
7
$1000
900
800
700
600
500
400
Total
revenue
$1000
1800
2400
2800
3000
3000
2800
Average
revenue
$1000
900
800
700
600
500
400
Marginal
revenue
$800
600
400
200
0
200
108
Thus, in Monopoly
P = d = Average revenue (AR) ≠ MR
That is why the MR curve lies below the Demand curve
Price
d
d
0
output
It is only under Perfect competition that
P = d = AR = MR
Determination of profits in Monopoly
In order for use to determine the profits of a monopoly, we must bring the demand and
supply decisions together.
In monopoly as in perfect competition the profit maximization point is a point where:
MC = MR
109
Thus,
d
MC
p
AC
Profit
MR
Profit
maximization
point
d
output
Powers of a Monopoly
-
It can decide on price
Can decide on how much to supply
It has no rivals as the firm is the industry and normally, the firms demand curve is
the industry demand curve.
Causes of Monopoly
a)
Natural causes
This can happen by location – possession of Land with minerals which may not
be found elsewhere.
b)
Licensing
The state can permit monopolies through licensing laws
e.g. you cannot form an Auditing and Accountancy firm unless you are
registered as an Accountant.
c)
Indivisibilities
It is difficult to divide up certain goods
Railways
Electricity
Water supply
Although now it is known that you can run your railways as:
a)
rail track
110
b)
trains and wagons
or electricity as
i)
generation
ii)
transmission
iii)
supply
Advantages of Monopoly
It can bring about new developments through Research and development – in
perfect competition no one has time and R + D may just become cost centers
R + D are encouraged because of patents which project discoveries.
-
Control of Monopoly
Monopoly can be controlled or constrained by anyone of the following methods
a)
Consumer tastes and income
b)
Countervailing power
INPUTS
FIRM
Raw material suppliers
can squeeze the monopoly
through pricing
c)
OUTPUTS
Buyers and consumer
cooperatives can use
Trade unions can demand higher wages by bargaining using the purchasing
power principle or on profit
c)
Taxation
A tax can be imposed on a monopolist
d)
Price controls
Government can impose a price ceiling on a monopolist
Government can force a monopolist to equate Marginal cost to average
revenue (AR).
111
MC
P1
Profit
AC
P2
Profit
AR=d
MR
Q1
e)
Q2
Public control of monopoly
Government can decide to place the monopoly into public hands through
Nationalization.
3. Oligopoly
Definition
Oligopoly occurs when just a few firms between them share a large proportion of the
industry.
There are however, significant differences in the structure of industries under
oligopoly and similar significant differences in the behavior of firms.
The firms may produce a virtually identical product (metals, chemicals, sugar, and
petrol).
Most oligopolies, however, produce differentiated products e.g. (cars, soap
powder, cigarettes, and electrical appliances)
Much of the competition between oligopolies is in terms of marketing of their
brand.
Marketing practices may differ considerably from one industry to another.
The two key features of oligopoly
Despite the differences, there are two crucial features that distinguish oligopoly from
other market structures.
112
a)
Barriers to entry
Unlike firms under monopolistic competition and perfect competition, there are
various barriers to the entry of new firms
These barriers are similar to those under monopoly.
These relate to:
i)
Economies of sale – that a new entrant must be able to start
producing at a very large scale to reduce their average costs
ii)
Product differentiation and brand loyalty – A firm must be able to
produce a clearly differentiated product, where the consumer
associates the product with the brand
This barrier can occur, even where the market is large enough
iii)
Lower costs for an established firm: An established firm is likely
to have developed specialized production and marketing skills.
This may be difficult for new entrants.
b)
Interdependence of firms
Because there are only a few firms under oligopoly, each firm will have to take account
of the others
Each firm is affected by the rival’s actions – so they are interdependent
This interdependent will affect their decisions and at times force them to
collude.
-
Competition and collusion
Oligopolies are pulled into two different directions.
a)
The interdependence of firms may make them wish to collude with each other – if
they come together and act like a monopoly, they can jointly maximize industry
profits
b)
On the other hand, they will be tempted to compete with their rivals to gain a
bigger share of industry profits for themselves.
These two policies are incompatible. The fierce the competition the lesser the profits –
(through price competition) while competition in advertising raises industry costs).
We now examine collusive and non-collusive oligopoly.
Equilibrium of the industry under collusive oligopoly
When firms collude, they do the following
a)
agree on prices
b)
market share
c)
advertising expenditure
This reduces uncertainty faced by each firm.
113
A formal collusive agreement is called a cartel. A cartel therefore will maximize profits
if it acts like a monopoly.
The profit maximization of a cartel will be where MC = MR (like in monopoly). The
MC curve will be the sum total of MC’s of the members.
Price
MC
P1
AC
Industry D = AR
0
Q1
Industry
MR
Price = P1
Quantity
Quantities = Q1
The cartel can also divide the market between them. Each member is given a quota. The
sum of quotas must add up to Q1. The market may be divided by following the cost
structures of the firm
- The other method is to divide the market according to the current market shares of
each firm.
How can we express the activities of a price leader in the market.
Division of the market between Leader and followers
d
S
P=Equilibrium price
A=market D = market S
P(a)
P1
D Leader
S
(b)
The supply of the leader is zero
b = price=P1
market supply = zero
Supply for Leader
d market
(b)faces the full market demand
114
d
S
P1
a
bd
P2
S
D leader
But the Leaders profit will be maximized where it’s MC = MR
P1
I
f
t
PL
D market
P
D Leader
0
Q
QF
Qr
MR
- Price market P1
- Price for leader will be PL
- Quantities for Leader QL
- Supply all other firms QF
Total supply of other firms
QT = OQL + OQF + Leader = QT
Or alternatively, the Leader will only maximize its profit for a given market share.
115
d
MC
I
PL
t
d market
D Leader
0
QL
Qt
MR Leader
Where PL is the price of a leader
OQL = is the supply
Other firms take PL (the price of a leader)
Extended to the market demand the total supply is Oqt.
Factors favoring collusion
It is easier for firms to collude if the following conditions apply:
-
There are very few firms and hence they are well known to each other
They are not secretive with each other about costs and production methods
They have similar production methods and average costs and will thus be likely to
change prices at the same time and by the same percentage
They produce similar products and can thus more easily reach agreements on
price
There are significant barriers to entry and thus there is little fear of disruption by
new firms
The market is stable – there are no wild fluctuations in demand and production
costs
There are no government measures to curb collusion.
The Kinked Demand curve
In non-collusive oligopoly, the firm under oligopoly is likely to be faced with a kinked
demand curve.
116
Price
P1
Q1
Quantity
Assumptions
a)
b)
If an oligopoly cuts its price, its rivals will feel forced to follow suit and cut their
price to prevent losing customers to the first firm.
If oligopoly raises its price, however, its rivals will not follow suit since, by
keeping their prices the same they will thereby gain customers from the first firm.
On these assumptions, each oligopoly face a demand curve that is kinked at the current
price and out put.
-
A rise in price will lead to a large fall in sales as customers switch to the now
lower priced rivals
P1
P
0
Q1
Q
117
A fall in price on the other hand will lead only to a modest increase in sales
P
0
Q
q1
The firm will therefore be reluctant to lower its price.
What are the advantages and disadvantages of oligopoly
a)
b)
advantages
-
Oligopolies like monopolists can use some of their super profits for
research
E.g. Product design
Technological improvements (to cut costs due to competition)
-
Non-price competition through product differentiation may result in
greater choice for the consumer.
Disadvantages
-
If oligopolies collude then they act as a monopoly and so
They can charge higher prices and lower their output
This can result into an unequal distribution of income in society
Oligopolies are much more likely to engage in excessive advertising than
monopolists because of the element of competition.
Collusion in practice
Although collusion is illegal in some countries e.g. Britain (under the 1956 Restrictive
Trade Practices Act),
- It is practiced in many instances; especially where firms can demonstrate that
coming together is in the interest of the public
- Construction firms collude from time to time when tendering for local authorities
contracts.
118
Tacit collusion
-
-
There is also collusion where oligopolies take care not to engage in price-cutting,
excessive advertising or other forms of competition.
The firms in the industry may follow the dominant firm price leader. This may be
the oldest firm or one firm, who has emerged to be reliable to follow – The firm
becomes the barometer of market conditions
This is known as barometric firm price Leadership.
Price discrimination
-
Price discrimination involves the firm selling the same product at different prices.
There are three major varieties of price discrimination:
a)
First-degree price discrimination – where a firm charges each consumer
for each unit the maximum price which that consumer is willing to pay for
that unit (e.g. through bartering)
b)
Second-degree price discrimination – where a firm charges a consumer so
much for the first so many units purchased, a different price for the next so
many units purchased and so on.
c)
Third degree price discrimination – where a firm divides consumers into
different groups and charges a different price to consumers in different
groups, but the same price to all consumers within a group e.g. football
tickets – adults 5000
Children 500
d)
A regional differentiation in price – rural and urban (as long as people
cannot shift goods between regions) Price market.
4. MONOPOLISTIC COMPETITION
Monopolistic competition resembles both perfect competition and monopoly.
It is a market characterized by:
a)
Unrestricted entry and exit
b)
A large number of sellers producing differentiated products
In contrast to perfect competition, the firms do not produce a homogenous product. Their
products are heterogeneous or differentiated.
A differentiated product is a product which consumers view as different from other
similar products.
119
NB:
Note that it consumers who are perceiving products to be different.
These
products may be chemically the same.
Products may be differentiated by:
a)
Function
b)
Design
c)
Quality
d)
By advertising brand names
- Acer, Mercer, IMB, Compaq
Products may also be differentiated by the conditions related to sale
a)
Credit terms
b)
Availability
c)
Congeniality of sales helps (after sales service)
d)
Location or convenience (supply to shops)
Determination of market Equilibrium
-
When a firm sells a differentiated product with close substitutes, it has some
degree of monopoly power – hence, the “monopolistic” in monopolistic
competition
-
Thus the demand curve facing the monopolistic firm is downward sloping
-
However the degree of monopoly power will be slight because of the availability
of close substitutes
-
As a consequence of this the demand curve will be fairly elastic. That it will
tend to be flatter.
120
D
MC
P1
AC
C
D
MR
O
Q
Differences to note with monopoly
a)
The demand curve facing a monopolistic firm is for the firm alone and not a
demand curve for the market.
Why?
Because the firm is just one of the
producers of this differentiated product.
b)
Secondly, entry into the market is unrestricted as opposed to pure monopoly.
Therefore when existing firms make profit other firms are attracted to produce a
similar product, thus wiping out profits in the market.
Thus, the Long-run Equilibrium is attained when profits have been wiped out. So, under
monopolistic competition, Long-run equilibrium is attained as a result of firms entering
(or leaving) the industry in response to price incentives.
The activities of the other firms will lower the demand for the products of the competitor
firms. Until the economic profits are zero. Only then will there be no further incentive
for other firms to enter the market.
What do firms in Monopolistic competition compete about?
They compete about:
a)
Price
b)
Variations in their products intended to attract customers
121
Do Monopolistic competition firms produce efficiently?
No – because they do not produce at a point where the AC curve is the lowest (see
diagram)
Advantages
a)
The market structure is able to offer alternatives to consumers
b)
The market structure can give different prices to the consumers and so increase
their choice.
COMPARISON OF MARKET STRUCTURES
Actors
Profit
maximization
point
Demand curve
elasticity
Product
differentiation
Market entry
Demand curve
characteristics
Perfect
competition
Many
producers/sellers
MC = MR
Monopoly
Oligopoly
One dominant
producer/seller
MC = MR
A few dominant
producers/sellers
MC = MR
Perfectly elastic
Not very elastic
downward slope
Single product
Not very elastic
downward sloping
Differentiated
Restricted entry
Leader for demand
curve + market
demand curve
Partial
NIL
Market players
Market
Homogenous
products
Unrestricted entry
Market demand
Curve = firms
Demand curve
Market pone of
NIL
Restricted entry
Market demand
Curve is
………demand
curve
Total
Firm
Market
Outside
Monopolistic
comparison
Many producers or
sellers
MC = MR
Elastic downward
sloping
Differentiated –
design quality
Unrestricted entry
Market demand curve
faces all firms
Control of finance
122
In tradition economics prices are determined through Marginal Pricing. However, there
are some pricing techniques which depart from this rule. Pricing however is at the very
center of a marketing strategy. Clever manipulation of the price can win a firm a large
market. Wrong pricing has proved disastrous in many instances. Despite this importance
of pricing, firms may not be setting their prices in a logical faction. It is important to
consider both cost and demand factors in arriving at a price for a good.
Dimensions of pricing
There are factors which are important to consider before setting prices.
Pricing
Pricing has both applied and theoretical issues to consider. Traditional theory analyses
the relationship between Marginal cost (MC) and Marginal Revenue (MR) in all types of
market structures. However in practice firms may price without regard to the relationship
between marginal cost and marginal revenue. Pricing however is an important element of
a market strategy. Clever manipulation of prices can help win entire the market for a
product. Wrong pricing can also have disastrous effects. Despite this many firms may
not set prices in a logical way. Firms may consider costs only other than the demand
situation. Sometimes prices do not reflect the market situation. There are however
techniques of pricing which are practiced. Price setting or fixing is influenced by
a)
competition
b)
Time
c)
Geography
d)
The business environment
e)
The market mix
f)
The product life cycle
a)
Competition
Pricing is largely defined by the likely reactions of competitors. Thus the market
structure plays an important role here. In Perfect competition, firms will be price
123
takers while in Monopoly and collusive Oligopoly firms will be price makers. In
competitive oligopoly, firms will take the price of the leader firm.
b)
Time
Time plays a critical role in pricing because a price can have a lagged or
cumulative effect. The sales of a product in this period may be affected by the
prices of the same good in the preceding period or the current prices may affect
sales in future.
c)
Pricing may also be affected by location. Poor remote regions may enjoy lower
prices while urban areas may suffer from high prices. This common in the
electricity market. Where even in the same city people may pay different rates.
Here in Kitwe the rates in some areas are fixed while in some areas meters have to
be read.
d)
Business Environment
The Macro-business environment in which the firm operates is also important.
Technological advances, government regulations and taxes shape the environment
and thus both supply and demand which have an impact on prices.
There are other environment factors which affect pricing. This may include the
size and composition of the population and other social characteristics. The
distribution of income is also another factor.
e)
Market mix
This refers to the set of controllable variables that the firm uses to influence the
target market. These include the product, the place, promotion and price.
These
four ‘P’s are important. A product may not sell merely by changing price but also
by the advertising campaign which accompanies such change.
124
f)
Product life Cycle
The Sales and profitability of a product have a life cycle shown below.
Sales
Maturity
Decline
Growth
Introduction
Profits
Depending on the product life cycle, a firm may depend on different pricing strategies.
Objectives of Pricing
The most important objective of pricing is maximization of profits. Thus the price need
not be too low to fail to maximize profits. Equally, it need not be too high, because it can
result into the same effect. Other objectives involve:
a)
Price stabilization – keep prices stable
b)
Maintenance of market share – this requires a firm to keep in line with the
activities of competitor firms
c)
Maintain Liquidity – this might entail a firm keeping its prices low in order to
obtain money and remain liquid.
Pricing Techniques
There are four basic Pricing Techniques
a)
Profit maximization rule
b)
Demand related pricing technique
c)
Cost related pricing technique
125
d)
Competitive oriented pricing
Each of these pricing strategies may involve two or more variations.
a)
The Profit Maximization Rule
We have done this. It depends on whether the firm is a price taker or price maker.
The general rule is to equate Marginal cost (MC) to Marginal Revenue (MR).
Example
d
Break-Even
MR
Point
Range of
P
AC
prices
C
Break-Even Point
d
O
Q
MR
In Perfect competition, the level of market activity will decide the price range for
the firms.
b)
Demand Oriented Pricing
This involves setting prices in accordance with consumer preferences and
perceptions. Two rules are identifiable in this category:
a)
Perceived value pricing
b)
Demand differential pricing
126
a)
Perceived value pricing
This considers the buyer’s perception of the value the buyer’s perception of the
value of the product. The procedure is as follows:
1.
Manager makes an initial estimate of price
2.
Estimates how many units can be sold at this price
(the volume of sales so estimated would be considered in terms of plan
capacity. Investment and costs)
3.
The estimates will help management compare estimated revenue to
estimated costs to determine whether the product will yield a satisfactory
profit at the price stated in the initial step.
Problems
b)
a)
It is difficult to get the consumers perception of the good
b)
There is subjectivity in the process
Demand differential pricing
This is equivalent to price discrimination. It involves selling a product at different
prices in different markets. The differences in price between regions or locations
are due to price elasticity differentials in the various market segments or
locations. One example given is that an Airline seat can be offered to a student at
less than the price of the same seat sold to a business executive.
Cost Oriented Pricing Techniques
Most pricing models have selling prices based upon costs. The many variants of costbased pricing are:
a)
retail pricing
b)
target pricing
c)
cost-plus or mark-up pricing
d)
incremental cost pricing
127
a)
Retail pricing
In here, the managers at the retail level follow the price suggested by the
Manufacturer or supplier of the product.
e.g.
Coca-Cola = suggested retail price K1,300
mosi
= K2,800
The manufacturer always has a sound basis for arriving at the retail price
especially where the manufacturer or supplier delivers the product. The retailer
simply takes that price without the bother of fixing prices. This method is simple
and costless.
The problems are that
a)
it limits the flexibility of the retailer
b)
the policy does not take into consideration different economic conditions
(especially where the supplier does not deliver).
b)
Target pricing
In target pricing, the firm determines the price that will give a specified rate of
return on its investment. What steps are involved in this?
1.
the firm estimates what its total costs will be at various levels of output
2.
it will estimate its capacity utilization
3.
when quantities are estimated, the firm will find the total cost producing at
that level
4.
It will then divide the total cost with the quantities at a particular level of
production
5.
It will be add a target rate of return on the cost of producing an item.
128
Example
Total units to be produced K50,000
Total cost = K500,000,000
Cost per unit =
500000000
= K10,000
50,000
K10,000 x 20% rate of return
10 000 x 1.20 = K12,000.00
Price per unit = K12,000
Target pricing will be successful under the following conditions
a)
the firm should be in a highly concentrated industry (monopoly)
b)
it should have substantial fixed costs
c)
it should have a large degree of market control over price
The major weakness of the approach is that it assumes that the demand will be set by a
firm.
c)
Cost-plus or Mark-up pricing
Cost plus pricing or full cost pricing is by far the most prevalent method adopted
by business firms (cost + a certain percentage of mark-up)
In this method
a)
the average variable costs are first estimated
b)
overhead charges are added
c)
a percentage mark-up is added
For example
A firm producing 10,000 units of a product has fixed costs of K40,000. the variable costs
amount to K60,000. If the firm wants a 20% profit margin – it will do the following
Average fixed cost per unit =
Total fixed cost
40 000
=
= K4
Total output
10 000
129
Average variable cost =
Total var iablecost
60 000
=
= K6
Total output
10 000
Average total cost = K4 + K6 = K10
Profit margin 20%
10 x 20
200
=
= K2
100
100
Price = K10 + K2 = K12
Alternatively you can add up the fixed and variable costs and divide with the total output
multiplied by the factor (1 + r).
Thus
TFC  TVC
X (1 + r)
Q
Where TFC
d)
=Total fixed costs
TVC
= Total variable costs
Q
= Quantities of output
r
= Expected Net Profit Margin.
Mark-up pricing
similarly a firm can mark-down its price. The procedure is the same. If the gross
profit margin is 20% (while the net profit margin is 15%), it is possible for a firm
to mark-down its price.
In the previous example
AVC =
60000
= K6
1000
AFC =
40000
= K4
10000
If Net profit margin is 15%
Then
K10 x15
= K1.50
100
130
A mark up will entail a price of K11.50n while a mark-down will yield the price
of K8.50n (recall that this price covers all costs).
The formula to calculate the mark-up on price is
Mark-up on price =
Mark-up on cost =
Mark  up on cost
1  mark  up on cost
Mark up on price
1  mark  up price
Incremental cost pricing
It is one of the most current pricing tools. It resembles the marginal list pricing approach
as it focuses on the impact of changes in output on revenue, cost and profit.
The approach has the following guidelines
a)
Any pricing decision that increases revenue more than cost is acceptable
b)
Any pricing decision that decreases cost more than revenue should be accepted.
Example: If it costs Zambia Airways K10m to operate a flight between Lusaka and
Ndola, Zambia Airways should than operate any flight which brings in revenue of K10m
or more even if the flight is not full.
It should also be considered that where a firm deals in complimentary goods, it may be
advisable to operate a loss on one good if the sale of another (complimentary) good will
bring in more revenue and wipe out the loss.
Advantages of incremental pricing policy
a)
It helps a firm follow a more aggressive price policy
b)
It helps firms selling complimentary goods.
Disadvantages
a)
it cannot be utilized over long periods of time
b)
it does not guarantee a firm operating at break-even point
131
e)
Competition Oriented Pricing Techniques
Where competitive conditions exist, the most suitable techniques are competitive
oriented pricing technique. This involves firms fixing different prices for similar
goods because of product differentiation. The most common techniques are:
a)
a)
the going rate pricing technique
b)
the sealed bid pricing technique
The going rate pricing
This requires a firm to fix its price along the lines of other competing goods in the
market. The firm has power to fix its own price because of product
differentiation, but it adjusts its price to the general pricing structure of the
industry.
Advantages
a)
b)
it represents the collective wisdom of the industry
it removes uncertainty associated with competitive reactions to price
changes by other firms
c)
firms adjust their costs to match the market prices
This strategy is however common in oligopolistic condition. (Price-leaders pricing
strategies).
b)
Sealed bid
This involved bidding for a contract. The firm has only got a single opportunity
to get a contract.
-
The price/contract manager has to estimate what the other competing firms
bids will look like.
-
The principle behind is that while the firm must meet all its costs, it must at the
same time come up with a price well below the competitors prices.
132
Problems
-
There is a lot of uncertainty
-
Because of uncertainty, there is a likelihood of collusion behind the scenes
with a possibility of some firms receiving sub contracts at a later stage.
133
Unit 7: Investment Analysis.
A firm is a sum total of investment decisions. Investment which is the act of postponing
current consumption (opportunity cost) for a future flow of income (future consumption)
is a risk process. It involves spending what you have in the hand for a flow of income
into the future which is very uncertain.
Investment can be in many forms. It can take the firm of:
a)
A savings account
b)
It can be in the form of real estate
c)
It can be in the form of stocks or shares
d)
It can be in the form of machinery.
If a company (firm) or an individual investor puts money into an investment or financial
return will be expected. If an investor saves he expects interest in return, if he invests in
real estate he expects rent and if shares (stocks), he expects dividends and if in machinery
or capital, Profit.
Therefore investors always wish to know the following:
a)
How much return will be obtained from investing money for a given period say
‘n’ years
b)
How much will be obtained in ‘n’ years time by investing some money every year
for ‘n’ years.
Thus from these questions, Time is a very important element of investment decisions.
The Longer the investment the greater will be the return required by an investor.
For example, if a firm invests in mining, it expects a huge return. On the contrary, if an
individual invests in selling beans or kapenta, he expects a modest return. Similarly if a
Bank lends K200m to a company, it expects a higher return in interest payments if the
loan lasted for many years than one.
134
This is the expectation of an investor, the longer the investment the higher the returns.
There are two major techniques used in investment analysis
a)
Compounding
b)
Discounting
a)
Compounding
Before compounding, it is important that simple interest is understood. Interest is the
amount of money which an investor earns over time. It is interest which is earned in
equal amounts every year (or month) and it is a given proportion of the original
investment (the principal).
If a given sum of money is invested for a period of time, then the amount of simple
interest which accrues is equal to the number of periods X interest X amount invested.
Thus
Pn = Po(1 + nr)
Where Pn = the sum expected sum
Po = the original sum invested
N = the number of periods (normally years)
r = rate of interest
Example
i)
How much does firm A obtain in five years for investing K1 million at 10%
interest per annum.
Pn = 1m (1 + 5 x 0.1)
Pn = 1m (1 + 0.5)
Pn = K1,500,000
135
Note that if the period is less than a year then
n=
X
365
If the periodic for a few months then it will be
X
12 months
ii)
Compounding
Interest is normally calculated by means of compounding
The normal formula for compounding is
Pn = Po (1 + r)n
Where Pn
= is the expected future sum
Po
= is the original investment
r
= interest rate
n
= period of investment in years
Example: if a sum of 1m is invested at 10% per annum for 2 years, the future
value will be
Pn = 1 (1 + 0.1)2
Pn = 1 (1.1)2
Pn = 1 (1.21)
Pn = 1,210,000
Interest = K210,000
136
Sinking funds
A sinking fund is an investment into which equal annual installments are paid in order to
earn interest so that by the end of a given period or number of years, the investment is
large enough to pay off a known commitment at that time.
Sinking funds are commonly used for the repayment of a debt. Sinking funds can also be
used to replace an asset at the end of its life. To ensure that the money is available to buy
a replacement, a company might decide to invest cash in a sinking fund during the course
of the life of the existing asset.
The formula for a sinking fund is
 1 r  n 
1

 r

Pn = Po
Where Po = is the annual investment
r = the rate of interest
Example: Suppose we require K1,2000 to replace an asset in for years and the rate of
interest is four years. How much shall we require investing every year to make the
K1,2000?
 1 0.12 4 
1,2000 = Po 
 1
 0.12

1,200 =
0.5735193Po
0.12
Po = 2510.81
Sinking funds can be set
a)
to pay a loan
137
b)
to pay mortgage
Discounting
Discounting is the reverse of compounding. The basic principle of discounting is that if
we invest KP now for n years at r% interest per annum, we should obtain KP o (1 + r) n
‘n’ years.
Thus
Present value (PV) = Pn x
Or
1
1  r n
Pn
1 r n
When P n is the expected sum
r = interest rate
n = number of years
Pv = P o = the current sum
This formula is commonly used to evaluate capital expenditure proposals. (investments).
There are two basic methods of using Discounted techniques (DCF)
a)
the Net Present Value (NPV)
b)
the Internal Rate of Return (IRR)
The NPV
The NPV is the present value of the future stream of benefits from investment. Thus
NPV =
Pa
1+r
+ Pb
+ ………. Pn
+ Pc
2
(1 + r)
3
(1 + r)
(1 + r)n
138
This formula can be applied to a stream of benefits which differ and to annuities. An
Annuity is a constant sum of money for each year for a given number of years.
Rule: If NPV > Zero then accept the project
For Example
Consider a project with the following cash flow of benefits
Pa = K110, Pb = K121, Pc = K133.1
What is the NPV if the interest rate is 10%
NPV = 110
+
121
(1.1)1
=
+
(1.1)2
133.1
(1.1)3
110 121
133.1
+
+
1 .1
1.331
1.21
= 100 + 100 + 100
NPV = 300
We can also utilize Tables especially for complicated cash flows.
For example:
Cash-flow
Discount factor
NPV
Pa =
110
x
0.9091
=
100.0010
Pb =
121
x
0.8264
=
100.9944
Pi =
133.1
x
0.7513
=
98.4954
Total
299.4954
K300
139
So K364.1 is equivalent to K300 today.
We can work out another example:
Year
Net Cash-flow
Discount factor
Present value
10%
(NCF X DF)
0
-15000
1.0
-15000
1
4000
0.9091
+3636
2
4000
0.8264
+3306
3
4000
0.7513
+3005
4
4000
0.6830
+2732
5
4000
0.6209
+2484
NPV
163
Since there are Constant flows (An Annuity we can refer to Table B).
Table B (Using Annuity Tables)
Net cash flow is K4,000 (constant)
The discount factor in year 5 at 10% is
= 3.791
Therefore 4000 x 3.791 = 15164
NPV - Co = 15164 – 1500 = 164
NPV = 164
The Internal Rate of Return
The internal rate of return is that rate (interest rate) which equates the stream of benefits
of any project to zero.
140
It is normally calculated by trial and error
NPV =  Sn – Co = 0
(1 + r)n
In IRR we are looking for (r) rate of interest
For example
Year
Cash flow
DF
Present value
0
-15000
1
-1500
1
-1400
0.9091
+3636
2
4000
0.8264
+3306
3
4000
0.7513
+3005
4
4000
0.6830
+2732
5
4000
0.6209
+2484
NPV
163
This is positive
TRY
11%
DF
NPV
0
-15000
1
-15000
1
4000
0.900901
36036
3
4000
0.73.1191
3246.5
4
4000
0.658731
2634.9
5
4000
0.593451
2373.8
NPV
-216.5
So the IRR lies between 10% and 11%. There is a formula you use to find the exact IRR.
141
Initial Positive NPV
Initial Positive NPV + Negative NPV
=
163
163
=
= 0.4329
163 216.5
376.5
So the IRR is 10.4329
It must be appreciated though that there are risks associated with investment
a)
b)
Economic risks
-
obsolescence (Products losing the attraction)
-
changes in economic patterns
Financial risks
-
c)
Prices may change with new competitors coming on the scene
Risks associated with the law. etc
All these cause uncertainties. However, whatever the case business must continue.
142
UNIT 8: RISK ANALYSIS
Nearly all decisions made by firms are made under conditions of uncertainty. Managers
select a course of action from the perceived alternatives with less than perfect knowledge.
There is also uncertainty about the effect of the outcome. At times there is also
uncertainty about the ultimate consequences of the outcome.
Because of uncertainty, Risk and Risk analysis need to be explored in managerial economics. In
fact, it will be recalled that in managerial economics we try as much as possible to omit the
assumptions that microeconomics makes in the operations of the firm.
If however risk is to be minimized, it has to defined and measured.
Definition of Risk
Risk is defined as a hazard or peril, exposure to harm, and in commerce a chance of loss. Thus
risk refers to the possibility that some unfavorable event will occur even with the best of plans or
will.
In economics there are some investments, which are made which can be termed as being risk free
for example an investment in government bonds or treasury bills. These involve buying a piece of
paper bearing a valve and an interest rate to be earned, i.e., £1m Treasury bill with interest of 10%.
This is almost risk free.
If however, you invest £1m in a firm that is prospecting for minerals, this can be very risky business
because the outcome is difficult to determine.
Some writers do distinguish between Risk and Uncertainty. However, in both situations the actual
outcome is not known.
Risk is defined as a situation where the probabilities can be estimated objectively on the
basis of actuarial calculations. Insurance companies do this. For example, the premiums
paid in life insurance become heavier as one grows old or if one smokes.
Uncertainty is a situation where not all of the possible outcomes might be perceived and those that
are can be given only subjective probability estimate.
This distinction however, is unnecessary for our purposes.
143
Probability Distributions
The probability of an event is defined as the chance or odds that that event will occur. For
example, we can say that there is a 90% chance that we will get a contract or alternatively that the
chances of loosing the contract are 10%
All probabilities then add up to 100% or 1, thus:
Event
Get a contract
Does not get a contract
Probability of Occurrence
90% = 0.9
10%
100% = 0.1
Risk then can be read from this simple probability distribution that there is a 10% chance that the
undesirable event will occur (the possibility of not getting a contract).
We can however consider a slightly complicated problem.
“Suppose a firm is considering two investments each requiring an initial investment outlay of £1000
and the levels of profit expected are related to the general economic situation or activity in the
following year as follows.
Profits
State of the Economy
Recession (slump)
Normal
Boom
Project A
400
500
600
Project B
0
500
1000
The expected probabilities of many of these economic conditions occurring is estimated to be as
follows:
Recession
Normal
Boom
0.2
0.6
0.2
144
How can we evaluate these alternative investments?
Projects
Project
A
Project B
State of the
Economy
(a)
Recession
Normal
Boom
Probability of the
State Occurring
(b)
0.2
0.6
0.2
Outcome if State
Occurs
(c)
400
500
600
(bxc)
(d)
80
300
120
Recession
Normal
Boom
1.0
0.2
0.6
0.2
1.0
Expected Profit A
0
500
1000
Expected Profit
500
0
300
200
500
From this analysis one can conclude as follows:
1. Project A is superior when the economy is in recession.
2. Project B is superior when the economy is in a boom.
3. In a normal economy, the project offers the same profit potential.
The expected profit (which is the weighted average of the profits is calculated as:
N
Expected Profit      i Pi
l 1
Where  i is the point level associated with the ith event
Pi is the probability of occurrence for outcome.
N is the number of possible outcomes.
Thus using Project A data we can calculate the expected outcome (profit) as follows:
 A  3  i  Pi
i 1
  1  P1   2  P2   3 P3
 4000.2   5000.6   6000.2 
 80  300  120
 500
We can also plot bar charts and graphs for the probability distribution of the returns of
Projects A and B. The rule is that:
145
a)
the tighter the probability distribution, the more likely that the actual outcome will be close
to the expected value or that the less likely it is that deviations fro the actual outcome will
be from the expected value.
That is the tighter the probability distribution the lower the risk.
Let us first look at the bar chart.
Probability of
Occurrence
Project A
0.6
0.4
0.2
0
200
400
600
800
1000
profit
(Expected Values)
Project B
0.6
0.4
0.2
0
200
400
600
800
1000
The spread in Project B is too wide
146
* From the rule, that the tighter the distribution the lesser the risk, then Project A is less risky.
However, we need a measure of tightness if the conclusion is to be more useful.
One such a measure is the standard deviation symbolized as  (sigma). The smaller the
standard distribution and so the lower the riskiness of the alternative.
To calculate the standard deviation we follow the following procedure.
1. Calculate the expected value or mean of the distribution.

n
Expected Value      i Pi 
i 1
Where
 is the profit or return associated with the I the outcome.
P is the probability of occurrence of that outcome.
 the expected value (weighted average of the various possible outcome).
2. Subtract the expected value from each possible outcome to obtain the deviations about the
expected value.

Deviation i   i  
3. Square each deviation and multiply the squared deviation by the probability of occurrence
(This then is the variance).
2



Variance       i    Pi

i 1 
n
2
4. Take the square root of the variance to find the standard deviation.
2



Standard Deviation       i    Pi

i 1 
n
147
Following the same example above:
State of the
economy
(a)
Recession
Normal
Boom
Project
A
Project B
Recession
Normal
Boom
Probability of the
state occurring
(b)
0.2
0.6
0.2
1.0
0.2
0.6
0.2
Outcome of state
occurs
(c)
400
500
600
Expected Profit
0
500
1000
Expected Profit
d (bxc)
80
300
120
500
0
300
200
500
Let us take Project A
1.
Calculation of the expected value (profit)

   1P1   2   3  P3
400 2  500 6  600 2  500

  500
2.
Calculation of Deviation

Deviation     Deviation2
Recession
Normal
Boom
3.
400 – 500 = 100
500 – 500 = 0
600 – 500 = 100
Deviation multiplied by the probability (variance)
Recession
Normal
Boom
10000 (.2) = 2000.00
0 (.6)
= 0
10000 (.2) = 2000.00
Variance
4.
(100)2 = 10,000
(0)2 = 0
(100)2 = 10,000
4000.00
Standard deviation
  var iance
 4000.00  63.25
148