Oligopoly

OLIGOPOLY
Oligopoly is an imperfect monopoly. Like the despotism of the Dual Monarchy, it is saved only by its
incompetence.
-John Kenneth Galbraith
Prasad S
Assistant Professor
Department of Economics
Sree Sankara College, Kalady, Ernakulam - Kerala

Oligopoly Defined
▪ Oligopoly is the market situation in which there are few sellers/producers of a
commodity, they control the entire market.
▪ The word oligopoly is derived from the Greek word "oligo" meaning few and "polo"
meaning to sell
▪ Thus the term ‘oligopoly’ means “few sellers” – 2 to 10 or 15 firms
▪ If there are only two producers/sellers, we have a duopoly
▪ The actions of each producer will affect the other producers
▪ When a market is shared between a few firms, it is said to be highly concentrated.
▪ To determine price and output, one has to make specific assumptions about the
reactions of other firms.
▪ Therefore, we don’t have any general theory of oligopoly
▪ Instead have different models

Oligopoly Defined
▪ Oligopoly is the most prevalent form of market organisation
in the manufacturing sector of modern economy
▪ It arises out of economies of scale, control over the source
of raw materials, patents, government franchises etc.
Pure Oligopoly and Differentiated Oligopoly
▪ Pure Oligopoly
▪ If the product is homogeneous – cement, steel etc.
▪ Differentiated Oligopoly
▪ If the product is differentiated – cars, cigarettes etc

Oligopoly – Characteristics
▪ Interdependence: The interdependence among the firms in the industry is
one among the most important characteristic feature of oligopoly. It is the
natural result of being few. In this circumstances the actions of one firm
affects the actions of other – Suppose one firm tries to enhance its sales by
lowering price, advertising, product differentiation etc., the demand curve of
other firms will shift down; the other firms react accordingly.
▪ Strategy: The firms under oligopoly cannot act independently. They operate
with the assumption that, the rival firm will respond according to their
actions. They make strategy to work out a range of possible options based
on how they think rivals might react
▪ Whether to compete with rivals, or collude with them.
▪ Whether to raise or lower price, or keep price constant.
▪ Whether to be the first firm to implement a new strategy, or whether to wait and see what
rivals do

▪ Barriers to Entry: This is one of the major characteristic features of
Oligopoly. Entry restricted due to natural reasons or artificial reasons
▪ Natural Barriers:
Economies of scale – economies of large scale production
Ownership or control of key scarce resources
High set up cost – high initial cost deters others to enter into the
market
▪ Artificial Barriers:
Predatory Pricing – the firms deliberately price push down
drastically to prevent others from entering into the market.

Limit pricing: involves reducing the price sufficiently to
deter entry – implementing such policy along with
heavy advertising or continuous product differentiation
make entry unattractive. As a result, the entrants
cannot make profit at that price
Superior knowledge: Superior level of knowledge of the
market, its customers, and its production costs – firms have
significant competitive advantage
Predatory acquisition: Acquiring significant volume of
shares of rival firms by way of take-overs, mergers etc.

Advertising: Heavy advertisement to prevent other firms to
enter
Strong brand: Strong brand creates loyalty
Other Loyalty schemes: Building up of loyalty using loyalty
cards, discount cards etc.
Exclusive contracts, patents and licences: Contracts with
suppliers, ownership of patents and licences etc.
Vertical Integration: Setting up of own retail chain, own
servicing centres and such strong linkages with other related
marketers

▪ Collusive oligopoly: Firms collude among themselves to set
up strategies instead of competing each other. The
collusion may be in the form of:
Overt: No hidden or no secrecy in agreements – trade
association etc.
Covert: The agreement is not open. Firms wont reveal the results
of collusion (to avoid interreference by regulators etc.)
Tacit: The firms act together – tactically; there will not be any
formal or informal agreement or so. Accordingly the firms arrive
at some sort of ‘agreement’ (a tacit agreement)

Non-collusive Oligopoly
The various models of oligopoly can be classified under two main
headings: non-collusive or competitive oligopoly and collusive
oligopoly.
▪ Non-collusive Oligopoly
▪ The strategy of firms is not to collude with its rivals though there exist
some level of interdependence
▪ Thus, there exist rivalry among the firms due to the interdependence.
▪ Each firm develops an expectation about what the other firms are is
likely to do.

▪ Price Stickiness: The property of price stickiness explains
that once a price has been determined, there is a tendency
to stick the price at the same level.
▪ Price stickiness (or sticky prices) is the resistance of market
price(s) to change quickly despite changes in the broad
economy that suggest a different price is optimal (as a
result of changes in input cost or demand patterns).
▪ It is the tendency of prices to remain constant or to adjust
slowly despite changes in the cost of producing and selling
the goods or services.

Non-collusive Oligopoly – three approaches
▪ Observe the behaviour of rival firms but make no attempt to predict
their possible strategies on the basis that they will not develop
counter strategies. each firm acts independently on the assumption
that its decision will not provoke any response from rivals – Cournot
Model named after French economist, Augustin Cournot
▪ Another approach is to make an assumption that a given strategy will
provoke a response from competitor firms, and assess the nature of
the response using past experience. This is the basis of the kinked
demand curve model, in which it is assumed that any price cut by one
oligopolist will induce all others to do likewise, whilst a similar price
increase would not be matched.
▪ Formulate a strategy and try to anticipate how rivals are most likely to
react, and be prepared with suitable counter measures.

Non-collusive Oligopoly – Game Theory
▪ This is the basis of game theory in which competition under oligopoly is seen as
being similar to a game of chess in which every potential move must be regarded as
a strategy, and possible reactive moves by opponents and subsequent counter-
moves must all be carefully considered.
▪ The application of the theory of games to economics was first introduced in 1944 by
J. von Neuman and O. Morgenstern.
▪ Game theory involves the study of optimal strategies to maximise payoffs, taking
into account the risks involved in estimating reactions of opponents, and also the
conditions under which there is a unique solution, such that an optimum strategy for
two opponents is feasible and not inconsistent
▪ A zero-sum game is one in which one player's gain is another's loss, and a non-
zero-sum game is one in which a decision adopted by one player may be to the
benefit of all.

Non-collusive Oligopoly – The Prisoner’s Dilemma
▪ The prisoner’s dilemma is a popular introductory example of a game analysed in
game theory that demonstrates why “rational” individuals are unlikely to cooperate,
even when it could be in both of their best interests to do so, a win-win scenario.
▪ The traditional prisoners dilemma works as follows, you and your accomplice get
caught committing a crime. The police interrogate you separately. Before you are
carted off, you promise not to snitch on each other.
Over the course of the “interrogations” by police the following things can happen:
▪ If you both remain silent then you each get 1 years in jail.
▪ If you confess you get 0 years in jail, but your friend gets 20, and vice versa for you.
▪ If you both confess you each get 5 years in jail

Each criminal knows that if no-
one confesses and informs on
his co-partners in crime, he will
get off scot-free or at least with
modest sentence.
If one partner confesses, and
the others do not, he will go free
while the others received severe
sentences
If all confess, then all will be
sentenced but less severely
than if only one confesses.

The incentive here, for the rational
actor, concerned only with his own
survival, is to confess and let the
others suffer the consequences
But, as all will be motivated to act in
this way, they end up with an outcome
that is worse for all than if they had
been able to make a binding
agreement among themselves than
on-one confesses.
The model shows how rational
behaviour at the micro-level leads to
an apparently irrational macro
outcome.

Game Theory
▪ A theory of individual rational decisions taken under conditions of less than full
information concerning the outcomes of those decision.
▪ Modern Game Theory begins with The Theory of Games and Economic Behaviour
(1944) by Von Neumann and Morgenstern
▪ The theory examines the interaction of individual decisions given certain
assumptions concerning decisions made under risk, the general environment, and
the co-operative or non co-operative behaviour of other individuals.
▪ Traditional microeconomic theory explains with a theory of decision making under
conditions of certainty.
▪ Here the rational individual has to take a decision under conditions of uncertainty
and interaction.
▪ The theory shows how rational behaviour at the micro-level leads to an apparently
irrational macro outcome.

Game Theory
▪ Game theory is the mathematical modelling of strategic interaction among rational
(and irrational) agents.
▪ It includes the modelling of conflict among nations, political campaigns, competition
among firms and trading behaviour in stock markets etc.
▪ Zero-sum game: one person’s gain is another’s loss
▪ Non-zero sum: where all players may gain from an individual decision
▪ Cooperative: where collusion is possible
▪ Non-cooperative: where non-collusion or antipathy is the rule - how intelligent
individuals interact with one another in an effort to achieve their own goals

Kinked Demand Curve Model – Sweezy Model
▪ The Sweezy Model (Named after Paul Marlor Sweezy - An American Marxian
economist (1910-2004)
▪ The model explains the price rigidity observed in oligopolistic markets
▪ Suppose that an oligopolistic firm increases its price, others in the industry will not
raise theirs and the firm would likely to lose most of its customers.
▪ On the other hand, if the firm decreases its price to capture market, other firms will
follow the price and the firm will not be able to increase its market share
▪ Therefore, under oligopoly, the firms have a tendency not to change the prevailing
price, but rather to compete for a greater share of the market on the basis of
quality, product design, advertisement, services etc.
▪ The kinked demand curve model assumes that a business might face a dual
demand curve for its product based on the likely reactions of other firms to a
change in its price or another variable

▪ The demand curve is 𝐶𝐸𝐽 and has a kink at
the prevailing quantity of 𝑄1 units of output
and 𝑃1 price.
▪ The demand curve above the kink is more
elastic – it is assumed that other firms will
not match price increases but will match
price cuts
▪ The 𝑀𝑅 curve is 𝐶𝐹𝐺𝑁; 𝐶𝐹 is the segment
corresponding to the 𝐶𝐸 portion of the
demand curve; 𝐺𝑁 corresponds to the
𝐸𝐽 portion of the demand curve.
▪ At point 𝐸, 𝑀𝑅 curve is discontinued (from
𝑆𝑀𝐶 to 𝑆𝑀𝐶’) – without inducing the
oligopolist to change sales level and the
prevailing price
P
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SMC
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P1

▪ Even when there is a large rise in marginal cost, price
tends to stick close to its original, given the high
price elasticity of demand for any price rise.
▪ At price 𝑃1, and output 𝑄1, revenue will be maximised.
▪ Profits will always be maximised when 𝑀𝐶 = 𝑀𝑅, and
so long as 𝑀𝐶 cuts 𝑀𝑅 in its vertical portion, then
profit maximisation is still at𝑃1.
▪ IF 𝑀𝐶 changes in the vertical portion of the 𝑀𝑅
curve, price still sticks at 𝑃1
▪ If 𝑀𝐶 moves out of the vertical portion, the effect on
price is minimal, and consumers will not gain the
benefit of any cost reduction.
▪ Equilibrium of the firm is defined by the point of the
kink because at any point to the left of the kink 𝑀𝐶
is below the 𝑀𝑅, while to the right of the kink 𝑀𝐶 is
larger than the 𝑀𝑅
P
C
SMC’
SMC
C
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F
G
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Q
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0
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P1

Collusive Oligopoly
▪ In the non-collusive oligopoly, firms determine price and quantity
under the condition of uncertainty
▪ One way of avoiding the uncertainty arising from oligopolistic
interdependence is to enter into collusive agreements
Two Types
▪ Cartels: A cartel is a formal agreement among firms regarding pricing
and/or market sharing.
▪ Price leadership: One frim (the dominant firm – the low cost firm) sets
the price and the others follow it in order to avoid uncertainty about
the their firms’ reactions.

Collusive Oligopoly - Cartels
▪ Cartels imply direct (secret/tacit) agreements among the competing
oligopolist with the aim of reducing the uncertainty arising from their
mutual interdependence.
▪ It is a formal organisation of producers within an industry that
determines policies for all the firms in the cartel with a view to
increasing total profits for the cartel
▪ We assume that the firms deal in homogenous product, that is pure
oligopoly
▪ The firms appoint a central agency, and the agency has the authority to
determine total quantity and price with a view to maximise profit
▪ This central agency is also responsible for allocation of production
among the members of the cartel, and the distribution of the maximum
joint profit.

Collusive Oligopoly - Cartels
MC1
AC1
P
C
P c
b
a
0
X1 X
e1
P
h
f
e2
X2
0 X
P
e
MR
D
MC = MC1 = MC2
0 X = X1 + X2
C C
PP
X

Market-sharing Cartels
▪ This form of collusion is more common in practice because
it is more popular.
▪ The firms agree to share the market, but keep a
considerable degree of freedom concerning the style of
their output, their selling activities and other decisions.
▪ There are two basic methods for sharing the market:
non-price competition and determination of quotas.

Market-sharing Cartels – Non-price competition agreements
▪ In this form of 'loose' cartel the member firms agree on a common
price, at which each of them can sell any quantity demanded.
▪ The price is set by bargaining, with the low-cost firms pressing for a
lower price and the high-cost firms for a high price.
▪ The agreed price must be such as to allow some profits to all
members.
▪ The firms agree not to sell at a price below the cartel price, but they
are free to vary the style of their product and/or their selling activities
▪ Thus the firms compete on a non-price basis.
▪ Each firm hopes that it can attain a higher share of the market.

▪ If all firms have the same costs, then the price will be agreed at the monopoly level.
▪ However, with cost differences the cartel will be inherently unstable, because the
low-cost firms will have a strong incentive to break away from the cartel openly and
charge a lower price, or to cheat the other members by secret price concessions to
the buyers.
▪ However, such cheating will soon be discovered by the other members of the cartel,
who will gradually lose their customers.
▪ Thus others may split away from the cartel, and a price war and instability may
develop until only the fittest low-cost firms survive.
▪ Another possibility is that the members of the cartel in conjunction may decide to
start a price war until the firm which split off or cheated is driven out of business.
▪ Thus this form of cartel is generally called as ‘loose’ cartel
▪ This policy will be successful depends on the cost differential (cost advantage)

The firm B has lower costs than A, and hence B will have the incentive to
cut the price below the monopoly level, thus driving the high-cost competitor A out
of business.

Market-sharing Cartels – Sharing of the market by agreement
on quotas
▪ Agreement on the quantity that each member may sell at the agreed price (or
prices).
▪ If all firms have identical costs, the monopoly solution will emerge, with the market
being shared equally among member firms.
▪ For example, if there are only two firms with identical costs, each firm will sell at the
monopoly price one-half of the total quantity demanded in the market at that price.

on quotas
▪ The monopoly price is 𝑃 𝑀 and the quotas which will be agreed are 𝑥1 = 𝑥2 =
1
2
𝑋 𝑀
▪ However, if costs are different, the quotas and shares of the market will differ.

on quotas
▪ Allocation of quota-shares on the basis of costs is again unstable.
▪ Shares in the case of cost differentials are decided by bargaining.
▪ The final quota of each firm depends on the level of its costs as well
as on its bargaining skill.
▪ During the bargaining process two main statistical criteria are most
often adopted: quotas are decided on the basis of past levels of
sales, and/or on the basis of 'productive capacity’.
▪ The 'past-period sales' and/or the definition of 'capacity' of the firm
depends largely on their bargaining power and skill.

on quotas
▪ Another popular method of sharing the market is the definition of the region in
which each firm is allowed to sell – Regional Market Sharing Cartels
▪ In this case of geographical sharing of the market the priceas well as the style of the
product may differ.
▪ There are many examples of regional market-sharing cartels, some operating at
international levels.
▪ However, even a regional split of the market is inherently unstable.
▪ The regional agreements are often violated in practice, either by mistake or
intentionally, by the low-cost firms who have always the incentive to expand their
output by selling at a lower price openly defined, or by secret price concessions, or
by reaching adjacent markets through advertising.

Cartel
▪ Cartel models of collusive oligopoly are 'closed' models.
▪ If entry is free, the inherent instability of cartels is intensified
▪ It is not certain that a new firm will join the cartel.
▪ If the profits of the cartel members are lucrative and attract new firms
in the industry, the newcomer has a strong incentive not to join the
cartel, because in this way his demand curve will be more elastic, and
by charging a slightly lower price than the cartel he can secure a
considerable share in the market, on the assumption that the cartel
members will stick to their agreement.
▪ Thus cartels, being aware of the dangers of entry, will either charge a
low price so as to make entry unattractive, or may threaten a price
war on the newcomer.

PRICE LEADERSHIP
▪ One firm sets the price and the others follow it because it is advantageous
to them – they prefer uncertainty due to competition
▪ This is one of the widespread form of oligopoly
▪ Price leadership – informal agreement or explicit agreement
▪ Most of the price leadership oligopolies are based on tacit agreement – as
open collusive agreements are illegal in most countries
▪ Price leadership is more widespread than cartels – it allows the members
more freedom regarding their product and selling activities
- Cartel requires surrendering of all such freedom
▪ If the product is homogeneous and firms are highly concentrated in a
location, the price will be identical.
▪ If the product is differentiated prices will differ.

PRICE LEADERSHIP - Types
▪ According to the traditional theory of price leadership, the leader sets
his price on marginalistic rules – the point where 𝑀𝐶 cuts 𝑀𝑅
▪ For the leader, the equilibrium level is defined by 𝑀𝑅 = 𝑀𝐶
▪ Various forms of price leadership are:
1. Price leadership by a low-cost firm
2. Price leadership by a large (dominant) firm
3. Barometric price leadership

PRICE LEADERSHIP – Low cost price leader
▪ Two firms produce homogeneous product at different costs, which
clearly must be sold at the same price
▪ The firms may have equal markets
- with an agreement to share the market equally
▪ or may have unequal markets
- With an agreement to share the market with unequal shares
▪ But the firms have unequal costs.

Firms with equal market shares Firms with unequal market shares

PRICE LEADERSHIP – Low cost price leader (Firms with equal market shares)
▪ The firm with the lowest cost will charge a lower price
(𝑃𝐴) and this price will be followed by the high-cost firm
▪ However at this price the high-cost firm does not
maximise its profits – the firm can maximise profit at
𝑋 𝐵 𝑒 (which is lower) level of output for a 𝑃𝐵 (a higher
price).
▪ The low-cost firm, thus sacrifices some of its profits in
order to avoid price war
▪ For the leading firm, maximises profits at 𝑃𝐴 at 𝑋1 level
of output.
▪ At price level 𝑃𝐴, the low-cost firm can also follow the
price, but without maximising profit.
▪ Out of the total market demand 𝑋, firms share market
equally, 𝑋1by frim B and 𝑋2 by frim A.
Firms with equal market shares

PRICE LEADERSHIP – Low cost price leader (Firms with unequal market shares)
Firms with unequal market shares
▪ The low-cost firm can set a price at 𝑃𝐴 by
producing 𝑋𝐴 level of output – profit
maximisation output where MC cuts MR from
below.
▪ For the high-cost firm though the profit
maximising output is 𝑋 𝐵 𝑒, they are forced to
follow the leader and can produce at 𝑋 𝐵 for 𝑃𝐴
price – by sacrificing some of its profits.
▪ Here the marginal revenue is different
▪ The production level is also different
▪ Obviously the leader firm produces large volume
of output.
▪ But the low-cost firm follows the price set by the
leader to avoid price var

▪ The leader sets the price; the follower agrees to it
▪ The firms must follow an agreement on market sharing, formally or informally
▪ The low-cost firm follow the price set by the leader by sacrificing some of its profits
to avoid price war
▪ However, the low cost form is not just passive.
▪ They will force the leader to have formal or informal agreement regarding a quota
sharing
▪ Otherwise the follower could produces lower quantity than the level required to
maintain the price set by the leader in the market by following the price set by the
leader.
▪ This may push the leader to a non-profit maximising position
▪ Therefore, usually there will be a formal or informal price agreement between the lo-
cost and leading firm regarding market share

PRICE LEADERSHIP – Dominant-firm Price Leader
▪ A situation where a large dominant firm has a considerable share of the total
market, and some smaller firms with small market share
▪ It is assumed that the dominant leader knows the 𝑀𝐶 curves of the smaller firms
▪ By horizontally adding these 𝑀𝐶 curves, the dominant firm can find the total supply
by the small firms at each price
▪ With this information the leader (dominant firm) can obtain his own demand curve
▪ At each price the larger firm will be able to supply the section of the total market not
supplied by the smaller firms
▪ That is, at each price the demand for the product of the leader will be the difference
between total demand at that price and the total supply

PRICE LEADERSHIP – Dominant-firm Price Leaders
▪ At 𝑃3 total demand is 𝐷3 and the total quantity is supplied by the leader since at that
price the small firms do not supply any quantity.
▪ Below 𝑃3 the market demand coincides with the leader’s demand curve
▪ At 𝑃1 price the demand for the
product of the leader will be zero.
▪ At this price the difference between
total demand, 𝐷 and the total
supply, 𝑆1 is zero
▪ As price falls below 𝑃1the demand
for the leader’s product increases.
▪ At 𝑃2, the total demand is 𝐷2; the
part 𝑃2 𝐴 is supplied by the small
firms and the remaining 𝐴𝐷2 is
supplied by the leader

▪ 𝐵𝐶 in Figure 1 is same as 0𝑥 in Figure 2
▪ The dominant firm maximises his profit by equating his 𝑀𝐶 to his 𝑀𝑅
▪ Small firms are price takers and may or may not maximise their profit, depending on
their cost structure.
▪ Let the derived demand curve of
the dominant firm as 𝑑 𝐿 (Figure 2)
▪ The dominant firm will set the price
𝑃 at which 𝑀𝑅 = 𝑀𝐶 and his
output is 0𝑥.
▪ At price 𝑃 the total market demand
is 𝑃𝐶 (Figure 1)
▪ Out of 𝑃𝐶, 𝑃𝐵 is supplied by the
small firms and 𝐵𝐶 by the
dominant firm. Figure 1 Figure 2

▪ Small firms cannot sell more (at each
price) than the quantity denoted by
𝑆1.
▪ For the leader to maximise profit, he
must make sure that the small firms
will not only follow his price, but that
they will also produce the right
quantity (𝑃𝐵, at price 𝑃).
▪ Without such tight sharing of the
market agreement, the small firms
may produce less output than 𝑃𝐵
and thus force the leader to a non-
maximising position

Barometric Price Leadership
▪ All firms will be agreed to follow (exactly or approximately) the changes of the price
of a firm which is considered to have a good knowledge of the prevailing conditions
in the market and can forecast better than the others the future developments in the
market.
▪ The firm chosen as the leader is considered as a barometer, reflecting the
conditions of the ongoing economic environment
▪ The barometric firm need not be a low-cost or large firm
▪ The barometric firm has the property of having the quality of a good forecaster of
the economic changes.
▪ A firm belonging to another industry may also be chosen as the barometric leader
▪ Eg., a firm in steel industry may be agreed as the (barometric) leader for price
changes in the motor-car industry.

Barometric Price Leadership – Reasons
▪ Rivalry between several large firms in an industry may make it impossible accept one
among them as the leader.
▪ Followers avoid the continuous recalculation of costs, as economic conditions
change
▪ The barometric firm usually has proved itself as a ‘reasonably’ good forecaster of
changes in cost and demand conditions in the particular industry and the economy
as a whole – so that the other firms can relay on their decisions on choosing the
correct price policy.

Pricing
▪ A price is a value in monetary terms that one party pays to another in a transaction in exchange for
some goods or services.
▪ Price is the amount of money the buyer will pay as consideration to the seller in exchange for goods
or services.
▪ Pricing isn’t always as easy as setting a price the seller hopes to obtain. It involves aspects such as
demand and supply, cost of the product, its perception and value for the customer and many such
factors.
▪ If the price is too high or even too low the product will fail in the market.
▪ A company changes the prices according to the market conditions and other circumstances.
The Determinants are:
▪ Cost of the product
▪ Demand for the product
▪ Price of competitors
▪ Government regulations

Cost Plus Pricing
▪ It is the simplest pricing method. The firm calculates the cost of producing the good and
adds on a percentage (profit) to that price to give the selling price.
▪ It is the most common way of establishing a profitable selling price for a product or service,
since it ensures that a company sells a product for more than it had cost the company to
make the product
▪ Thus it is a pricing method that attempts to ensure that costs are covered while providing a
minimum acceptable rate of profit for the entrepreneur.
▪ Cost-plus pricing is common in oligopolistic markets where a few firms dominate and share
similar production costs.

Limit pricing
▪ A policy followed by a firm in an oligopoly/monopoly market by reducing
the price sufficiently to deter entry – implementing such policy along with heavy
advertising or continuous product differentiation make entry unattractive. As a
result, the entrants cannot make profit at that price
For an effective limit pricing, the monopolist
needs to decrease the price to the point where
a new firm will not be able to make any profit
on entering the market. By reducing the price
to 𝑃0 , the new firm sacrifices supernormal
profit in the short-run. But, the price is low
enough to discourage a new firm entering. At
𝑃1, a new firm faces average costs higher than
the market price
LRACProfit Margin
New firm
Existing firm
P1
P0
Q1
Q0
P
Q0

Oligopoly

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