Slide 1

A Duopoly is market situation with two producers (sellers)

And an Oligopoly is a market consisting of a number of sellers

The number of sellers is sufficiently small such that changes in actions of any single Seller have a significant impact upon the decision of the other Sellers

Interdependence of actions of the sellers is the essential feature of both the market structures

Duopoly and Oligopoly Market StructureNote that distinguishing Oligopoly from Perfect Competition on the basis of the number of sellers or product differentiation is not sufficient

If the effect of output variations of one Seller on the profits of other sellers is insignificant that is

Then it satisfies the basic requirement of Perfect Competition or many seller case of monopolistic competitionHowever,

Then the industry is Duopolistic or Oligopolistic, Here the (p,q) combination and the profit of a seller depends on the actions of all the sellers in the market Duopoly and Oligopoly Market StructureDuopoly and Oligopoly Market StructureControl

A Seller in Duopoly or Oligopoly can control his own Output level (or price if product is differentiated)

But he has no control over the output levels of others

Profit of any Seller depends on the output level of all other Seller

Hence, profit of each seller is result of interactions of the decisions of all the market members

Duopoly and Oligopoly Market StructureSolution-Behavioral Assumptions

The solution to duopolistic/oligopolistic market depends on the various behavior assumptions

There are no generally accepted behavioral assumptions about duopolistic/oligopolistic markets

Hence a particular solution to such market is based on a given set of assumptions

Duopoly and Oligopoly Market StructureConsider a market with two firms producing a homogeneous product qThe inverse demand function states price as a function of the aggregate quantity sold

Quasi-Competitative Solution

Where q1 and q2 are the Duopolists output levels The Revenue function of each duopolist is given by

Hence Revenue of each seller depends on his own output level and the output level of othersThe profit of each seller is given by

A solution based on the assumption that each firm follows P=MC ruleUsing the Condition P=MC, we get the Quasi-Competitative Solution

Quasi-Competitative Solution

Solving the above for p, q1 and q2 will give us a Quasi-Competitative Solution

This may or may not be achieved depending on if the behavioral assumption is satisfiedLet the Demand and Cost functions be

Applying the above rule, gives

The Curnot solution to Duopoly/Oligopoly market structure is associated with French Economist Augustin Curnot

Here also firms (1 and 2) are assumed to produce a homogeneous product

Assumption:

Each firm assumes that the quantity supplied by his rival is invariant w.r.t his own quantity variations

Or Each firm treats the output of other firm as given/fixed (independent of his own quantity decisions) and decides his own output level so as to max profits

The Firm 1 maximizes his profits w.r.t. q1, while treating q2 as fixed

And the Firm 2 maximizes his profits w.r.t. q2, while treating q1 as fixed

Curnot SolutionAssume two firms (1 & 2) each owning a mineral well and operating with zero costEach firm treats the output of the competitor as givenSuppose, Firm 1 starts first producing mineral waterThe market demand for their output is

Curnot SolutionIt will produce the mineral water up to a level where MR=MC; That is OA, and sell it at price PNow suppose that Firm 2 joins production

Firm 2 assumes that Firm 1 will keep its output fixed at OA

Then the relevant demand curve for Firm 2 is given CD

Firm 2 will equate MR=MC and produce half of AD = AB

As a result price will fall to P1PADMR1oCBP1MR2PriceQuantityCurnot SolutionThus Firm 1s Initial output level is

Now, Firm 1 will assume that Firm 2 will retain his output at same levelThen, Firm 1 will produce output Now Firm 2, will react to the output decision of Firm 1 and produce

As firms behave Naively, without learning from past experience, this action reaction continuesIn Process, the output of firm 1 falls and Firm 2 risesPADMR1oCBP1MR2PriceQuantityFirm 2 will assume that Firm 1 will retain his output at same level, and produceCurnot SolutionEventually equilibrium occurs at point when each firm produces 1/3 of Total market demandOutput of 1 declines gradually and at equilibrium q1 is The expression in parenthesis is declining GPThe output of Firm 1 in successive periods is

Thus

Curnot SolutionSimilarly the output of Firm 2 in successive periods is given byThis is an expression for declining GS

Output of 2 increases at decreasing rate and at equilibrium q2 is

Thus if there are n firms, the equilibrium will occur when each firm will produce

Curnot SolutionConsider a market with two firms (1 & 2) which produce a homogeneous product QThe inverse demand function they face is given as

The Revenue function of each duopolist is given by

Hence Revenue of each depends on his own output level and the output level of othersThe profit of each is given by

Curnot SolutionAs each firm assumes others output fixed, we max. each profit function w.r.t to their respective output levels

And Second order condition requires that

Note that this profit Max. differs from monopolist with two plants, where single producer controls the output levels at both plantsHere each Duopolist Max. his profit w.r.t. single variable under his control i.e., his output level The Equilibrium occurs when the values of q1 and q2 are such that each duopolist max. his profit for given output levels of othersAt equilibrium neither firm desires to alter his outputThese reaction functions express the output level of each firm as a function of rivals outputThe whole process towards equilibrium can be described by Reaction functionsThe Reaction functions can be obtained by solving the respective optimality condition for q1 and q2

Curnot SolutionFor any specified value of q2, Firm 1s reaction function gives the output level q1 which is profit max. for 1Similarly, 2s reaction function gives the output level q2 which is profit max. for 2The Equilibrium solution is given by the output levels q1 and q2 which satisfy these functionsSuppose Demand and Cost functions are given asThe profit functions of the Duopolists are Setting partial derivatives w.r.t. respective output levels =0Curnot SolutionThe corresponding Reaction Function are

Curnot SolutionAs B, b1 and b2 are all positive, a rise of either duopolists output will cause a reduction of the others optimum output

The Equilibrium is given by solving the above equations for q1 and q2, that is

The Second order condition are satisfied

Curnot SolutionThe Respective reaction functions for this duopolistic market areComparison with Quasi-Competitative Solution the Curnot Duopolist produces a smaller total output, at higher prices, and also for larger profitsNow, the earlier Demand and Cost functions give the solution

And the Curnot Equilibrium Solution is

Curnot SolutionGraphically the reactions functions are given as q21q111s Reactions q12q20 q22q112s Reactions

q21q12q2*q1*1s Reactions2s Reactionse

Q2Q1Q1Q2Collusion SolutionIf we assume that Duopolists recognize their interdependence and agree to act in unisonto maximize the total profitsThen both the variables are under a single control and the industry in effect is monopoly with two plants

The equilibrium condition is given by

Under such solution total price will be higher and total output smaller than in Curnot Solution

The collusion solution is advantageous as it results in increase in total profits

Here the firm with lesser costs will produce more and will enjoy higher profits

Stackelberg SolutionHere, we assume that one firm will act as Leader and other will act as Follower

The Leader is able to determine reaction function of his Rival and takes it into consideration while max. his profits

Then the Leader maximizes his profits like a Monopolist

While assuming rivals output will vary in response, the Leader Max profits as

And the Rivals response is given by

Generally, Leaders profits function is given as,The output of the Rival is assumed to Vary in response

Stackleberg SolutionThen Firm 1 assumes 2s reaction function is valid

here, Firm 1s (Leader) profit is function of q1 alone

And Firm 1s maximizes profit w.r.t. single variable q1

Suppose, Firm 1 plays as Leader and Firm 2 as FollowerSolving it for q1 will give 1s profit max. output when he plays Leader (q1L)

Substituting this q1L into 2s reaction function, that isThus, Firm 1s Profit function is given byThis will give profit maximizing q2 when 2 plays as Follower (q1F)Stackleberg Solution

Similarly, the leadership output of Firm 2 (q2L) and Followership output of firm 1 (q1F) can be determined

Thus, there are Four possibilities and the corresponding Four OutcomesThe firms will choose the role which gives them maximum profitStackleberg SolutionGraphically Illustration;

q2Lq1F1s Reaction

E1s q2s q2s ReactionE1q1L1s Reaction

q2F2s ReactionFirm 1 Follower, Firm 2 Leader (E)Firm 1 Leader, Firm 2 Follower (E1)2s q1s qProduct Differentiation

This first condition implies that an increase in price of ith seller will result in reduction in the ith firms output demand

And the second condition implies that with the rise in price of ith seller, the output demand for all other sellers increases Suppose producers in oligopolistic market produce differentiated products

Then each producer faces distinct demand curve

Thus the demand function of each producer is given by Alternatively,

Solution

The solution in case of two Firms is given by maximizing the respective profit functionsThat isSimilarly for Firm Second firm,

Hence profits of each Duopolist is a function of both the pricesAnd each profit function is max. w.r.t. prices of both the commodities

Advertising Expenditure

Under Differentiated Duopolistic market structure advertising Outlay plays a crucial role

Effective advertising helps the firms to sell larger quantities at given prices or sell a given quantity at higher prices Then the demand curves are given as Each Duopolist then Max. his profit w.r.t. his advertising expenditure and output level And the profit function are as

Market Share Solution

Assume that Firm 2 desires to maintain a Fixed share of Total Sales of a differentiated product regardless of effect of his actions on his short-run profit

His major concern is long-run advantages that are derived from maintaining a given market shareThis implies that a quantity change by Firm 1 will be immediately followed by a proportionate change in quantity of Firm 2 Alternatively, it can be written as

Here, Firm 1 will always be a market Leader as his actions are always followed by Firm 2 in predetermined mannerSuppose, k is the share that Firm 2 wants to maintainMarket Share SolutionAssume that Firm 1s (Leader) demand function is given asHis profit function is Profits can be maximized w.r.t. single variable q1

That is setting and solving for q1 will give us value of the q1Substitute the Substituting this value of q1 into , will give the quantity q2 which Firm 2 wants to sell

Market Share SolutionAssume that Firm 1s demand function is given asLet Firm 2 want to maintain ; Substitute in the profit function Using this value of q1=10 in , we get

Thus Firm 1 max. his profit at q1=10 and Firm 2 reacts by producing q2=5As , then