econ3200 class6 monopolistic competition

Industrial Organization AS/ECON 3200Class 6: Monopolistic competition

Andrey Stoyanov

[email protected]

Andrey Stoyanov ([email protected]) Industrial Organization AS/ECON 3200 1 / 27

Readings

Chapter 7 Monopolistic competition

Introduction (pp.200-202)

Di¤erentiated products and the e¤ect on a �rm�s demand curve(pp.202-205)

The representative consumer model (pp.206-214)

A representative consumer model with di¤erentiated products(pp.214-215)

Welfare with di¤erentiated products and �xed costs e¤ect(pp.215-218)

Suggested textbook problems: #1, #2, #5, #6.


Introduction

Monopolistically competitive markets combine elements of themonopoly and of the perfect competition.

As in the case of a monopoly, �rms in monopolistically competitivemarkets have market power. They face a downward sloping (residual)demand function for their product and can charge prices abovemarginal costs

As in perfect competition, there are no entry barriers so that �rmsmake zero economic pro�ts in the long run.


Introduction

How a �rm can face a downward sloping demand function for itsproduct with free entry? Why it will not be �at, as in perfectlycompetitive (PC) markets?

One reason is the assumption of homogeneous products we imposedfor PC. When consumers value di¤erent brands di¤erently, �rms mayincrease their price without losing all of their customers.

Another reason for downward sloping demand function is the presenceof �xed costs and lack of price-taking behavior. In this class wediscuss two models of monopolistic competition. First, we will keepthe assumption of homogeneous products. Then, we�ll look atmonopolistically competitive markets where �rms producedi¤erentiated products.


De�nition and assumptions

Assumptions of a monopolistically competitive market withhomogeneous products:

1 Free market entry - new �rms enter whenever they can make positiveeconomic pro�t

2 Firms produce homogeneous products3 Firms have market power - they can set prices above their marginalcosts

4 Firms compete in quantities

5 Increasing return to scale�falling average costs: ∂AC (q)

∂q < 0�

Assumptions 2 and 4 were used in all previous market structure models(Monopoly (M), perfect competition (PC), Cournot Oligopoly (CO)).Assumption 1 is speci�c to PC, and Assumption 3 is speci�c to M and CO.


Firms�output strategies

To make our analysis compatible with previous models, let�s also keepthe same assumption about industry cost and demand structure:

Market demand function DM : Qd = 1000� 1000pTotal costs of one �rm: TC (q) = 0.28q + 6.4

Note that total costs here has a constant component that re�ectspresence of �xed costs: FC = 6.4. From TC function we can �ndMC = 0.28 and ATC (q) = 0.28+ 6.4

q . Average costs are falling withoutput, so we have increasing return to scale production technology.

What will be an equilibrium output strategy of, for example, Firm 1 ifits cost structure is as above and if it believes that the rest of theindustry produce Q I units of output?


Firm 1 output strategies

See Figure 1 on the next slide

If Firm 1 believes that all other �rms in the industry together produceQ I , then its residual demand function becomes RD1(q1) = Qd �Q I

Knowing the residual demand function, the �rm acts as a monopoliston this function. As a monopolist, it picks the combination of priceand output from RD1 that maximizes Firm 1 pro�ts. This is why thecompetition in this market called �monopolistic�.

The pro�t-maximizing output level q�1 of Firm 1 is where MR = MC ,and the equilibrium price is determined from the residual demandfunction p� = RD1(q�1 )

Therefore, given the residual demand function, the pro�t-maximizingoutput strategy of monopolistically competitive �rm is exactly thesame as that of Cournot oligopolists.


Firm 1 output strategies graphically


Market equilibrium

In Figure 1, p� > MC and as a result Firm 1 is making positiveeconomic pro�t of $π1Positive economic pro�t means that other opportunities for Firm 1 areless pro�table, i.e. its accounting pro�t will be lower in other markets.The same is true for �rms operating in other markets: they could gethigher pro�ts in this market, as long as entry barriers are zero.Therefore, in the long run new �rms will enter until π1 = 0Entry of new �rms means that the total output by the rest of theindustry (from Firm 1 perspective) will increase from Q I to�Q I + qnew

�, where qnew is the output by new �rms.

Therefore, the residual demand functionRD1(q1) = Qd �

�Q I + qnew

�will shift further to the left.

New entry (and the leftward shift of the residual demand function)will continue until π1 = 0.The equilibrium strategy of Firm 1 and market equilibrium are shownon Figure 2.


Market equilibrium


Market equilibrium

The only strategy that maximizes Firm 1 pro�ts is point A. Thisstrategy gives zero pro�t but any other strategy will lead to losses.

Given the shape of ATC and RD1, producing more/less than q�1 willlead to losses since for q > q�1 or for q < q

�1 we have ATC > p

� andnegative pro�ts, as opposed to zero pro�ts at q�1

Therefore, only at point A where RD1 is tangent to ATC we can have2 conditions satis�ed together: Firm 1 has zero pro�t; Firm 1 acts asa pro�t maximizer.

Since q�1 is the pro�t-maximizing output level, it must be the casethat MR crosses MC at q�1 , as shown on the diagram.


Numerical solution to the model with homogeneousproducts

The monopolistically competitive equilibrium must satisfy twoequilibrium conditionsFirst, each �rm has to choose the output level that maximizes itspro�t. For Firm 1 this implies:

π1 =

�1� q1 + q2 + ...+ qN

1000

�| {z }

p

� q1 � 0.28 � q1 � 6.4

FOC :∂π1∂q1

= p � 11000

q1 � 0.28 = 0 (1)

Second, in the presence of free entry, each �rm has to make zeropro�t:

p � q1 � 0.28 � q1 � 6.4| {z }π1

= 0 (2)


Numerical solution to the model with homogeneousproducts

The system of equations (1) and (2) has two equations with twounknowns (p and q1). Solving this system, we obtain the market priceand �rm-level output that maximize �rm-level pro�t and ensure zeroeconomic pro�t:

p� = 0.36q�1 = 80

Again, since all �rms are symmetric in terms of costs, they have thesame output strategy: q�1 = q

�2 = ... = 80

Finally, we can �nd the equilibrium number of �rms N from themarket demand, substituting the equilibrium price p� and the totalindustry output N � q�1 into it:

Qd = 1000� 1000p ) N � 80 = 1000� 1000 � 0.36 ) N� = 8


Change in �xed costs

If �xed costs get lower for whatever reason, the ATC curve will fall.

With the old residual demand function, each �rm will start makingpositive pro�t, which will attract new �rms into this market.

When new �rms start to enter, the total industry output will increase,shifting the residual demand function of each �rm leftward, until ittouch a new ATC curve at a single point.

At this new equilibrium, the equilibrium output and price of each �rmwill decreasee. Since with lower price consumers will demand more,the number of �rms must increase in order to satisfy the growingdemand.


Welfare analysis

There are two reasons why monopolistically competitive markets areine¢ cient

First, each �rm produces less than the welfare-maximizing level ofoutput (which is at the level where p = MC ). Since p > MC , extraunit of output has greater value for consumers than its marginal costof production, and the welfare from producing an additional unit ofoutput will increase

Second, the number of �rms is too big. Each �rm has to pay �xedcosts of 6.4. With 8 �rms the total burden of �xed costs for thesociety is 8 � 6.4 = 51.2. One �rm can produce the same output levelas 8 �rms but with �xed costs of only 6.4.

Therefore, the welfare-maximizing equilibrium will be a single �rmpricing at the level of p = MC .


Welfare analysis and governmental policy

If the government wants to achieve the welfare-maximizing marketoutcome, it has to restrict the entry of new �rms and allow only one�rm to serve the whole market at the price equal to marginal costs.Essentially, the market will become a monopoly with regulated price.

However, achieving a welfare-maximizing outcome is practicallyimpossible for the government for two reasons. First, at p = MC the�rm su¤ers losses and has to be subsidized. Second, it will be verydi¢ cult/impossible to force a single �rm (monopolist) to price at thelevel of MC because we know that the monopolist tends to chargeprices well above MC .


Introduction

In monopolistically competitive markets �rms face downward-slopingresidual demand function and earn zero economic pro�t as a result offree entry.

One reason why the residual demand function is downward-slopinginstead of being �at, as in the case of perfectly competitive markets,is the presence of �xed costs of production together with price-settingbehavior of �rms in the market (as opposed to price-taking behaviorby perfectly competitive �rms). This case was covered in previousclass.

Another reason why the residual demand curve may be downwardsloping in the presence of free market entry is product di¤erentiation.If �rms produce di¤erent varieties of the same product, they maycharge di¤erent prices and stay in the market.


Product di¤erentiation

How substitutability of di¤erent varieties may a¤ect �rm�s residualdemand function?

With higher degree of product di¤erentiation, the residual demandfunction faced by each �rm in the market gets steeper. Consider twoextreme cases. On one side, when products are perfect substitutes toeach other, the market becomes perfectly competitive and theresidual demand function for each �rm is �at. On the other side,when products are completely di¤erentiated, each �rm becomes amonopolist since consumers cannot switch from one supplier of agood to another.

In general, when we move away from perfect homogeneity towardscomplete di¤erentiation, residual demand functions of �rms in thatindustry become more insulated and their market power becomesgreater (gets closer to monopoly�s market power).


Demand function for di¤erentiated products

Two �rms produce di¤erent varieties of the same product if consumersbelieve these products are di¤erent. Without product di¤erentiation itwill not matter for consumers which brand of the product to buy.

In all industries �rms produce di¤erent varieties of the product. Whatmatter is the degree of di¤erentiation between these varieties.

Usually, we measure the degree of di¤erentiation with the concept of�substitutability�. Highly di¤erentiated products that have manydi¤erent characteristics are bad substitutes to each other. Morehomogeneous products are good substitutes (consumers can moreeasily switch brands and get the similar product/service).



Product di¤erentiation is important for the analysis of marketequilibrium because its a¤ects the shape of the �rms�residual demandfunction.

Usually, how much �rm i can sell at any given price depends on howmuch other �rms sell in the market: pi = D (q1, q2, ..., qN ), where Dis the inverse residual demand function.

When products are homogeneous, then what matters for �rm�s iresidual demand function is how much of the product is produced bythe whole industry (Q): pi = D (Q) = D (qi +Q�i ), where Q�i isthe total output produced by all �rms in the industry other than �rmi , so that (qi +Q�i ) = Q.

For linear demand function and homogeneous products, we can writethe residual demand function for �rm i as:pi = a� bQ = a� b (qi +Q�i )



What will be the residual demand function if �rm i produce a good that isslightly di¤erent from (imperfect substitute for) what other �rms produce inthat industry?

If �rms produce di¤erent varieties of the same product, consumers viewthese products as imperfect substitutes to each other. As a result, theresponsiveness of price with respect to �rm�s own output will be di¤erentfrom the responsiveness of price with respect to the output of all other �rms.

With linear demand function, this is equivalent to having di¤erent slopes forqi and for Q�i : pi = a� b1qi � b2Q�i , where b1 > b2.The degree of di¤erentiation can be captures by the following measure:

DD = (b1�b2)b1

2 [0; 1]. If b1 = b2 (DD = 0), products are perfectlyhomogeneous and �rms cannot charge di¤erent prices (perfect competition).If b2 = 0 (DD = 1) markets are perfectly di¤erentiated (that is, �rmsproduce completely di¤erent products), and each faces no competition fromother �rms and becomes a monopolist.


Cournot oligopoly with di¤erentiated products

How does the Cournot oligopoly market equilibrium and strategieswould change if we allow for product di¤erentiation?

Lets take the same numerical example as we used for Cournotoligopoly. There are N �rms with TC = 0.28q + 6.4.

To allow for product di¤erentiation, suppose that the residual demandfunction of each �rm i is pi = 1� qi

1000 �Q�i2000 so that the price is

twice less sensitive to changes in Q�i than to changes in �rm�s ownoutput qi



Lets look at the output strategy that maximizes pro�t function of Firm 1:

π1 =

�1� q1

1000� q2 + ..+ qN

2000

�| {z }

p1

� q1 � 0.28 � q1 � 6.4

FOC: � 11000

q1 +�1� q1

1000� q2 + ..+ qN

2000

�� 0.28 = 0

Isolate for q1 to obtain the best response function of Firm 1 to the outputby the rest of the industry:

q1 = 360�q2 + ...+ qN

4

Comparing it to the case when products are homogeneous(q1 = 360� q2+...+qN

2 ), the best response function becomes lessresponsive to strategies by other �rms



Under the symmetry assumption, q1 = q2 = ... = qN , and theoptimum strategy becomes

q1 = ... = qN =1440N + 3

If N = 2, each �rm produce q1 = q2 = 288 and sets the pricep1 = p2 = 0.568. Both price and output are higher than in the caseof homogeneous products (0.52 and 240, respectively) so both �rmswill make higher pro�t if they di¤erentiate their product fromproducts of other �rms.Note that with di¤erentiated products assymetric �rms can chargedi¤erent prices and it is possible that p1 6= p2 in case of di¤erent coststructure of two �rms. With homogeneous products prices must beequal, otherwise the �rm with higher price lose all of its customers.Since we move further away from perfectly competitive equilibrium,product di¤erentiation with oligopolistic �rms reduces nationalwelfare.


Monopolistic competition with di¤erentiated products

Monopolistic competition analysis with di¤erentiated products willgive the same equilibrium as with homogeneous products.

Pro�t-maximization condition: ∂π1∂q1

= p � 11000q1 � 0.28 = 0

Zero-pro�t condition: p � q1 � 0.28 � q1 � 6.4| {z }π1

= 0

Both conditions are the same as with homogeneous product model,therefore, the equilibrium price and output will be the same.

The reason for such a surprising result is the way we capture productdi¤erentiation in the residual demand function. The demand functionpi = 1� qi

1000 �Q�i1000 (homogeneity) and pi = 1�

qi1000 �

Q�i2000

(di¤erentiation) have the same elasticity with respect to qi . Thismaterial is beyond the level of this course and will not be tested.


Monopolistic competition with di¤erentiated products

However, monopolistically competitive markets with homogeneousand di¤erentiated products have two important di¤erences.

Firstly, when �rms produce di¤erentiated products they may chargedi¤erent prices for the same reason as oligopolistic �rms withdi¤erentiated products.

Secondly, we cannot �nd the total number of �rms in monopolisticallycompetitive market if they produce di¤erentiated products. Thereason is that with di¤erentiated products we only observe �rms�residual demand functions, while the market demand function simplydoes not exist (see the notes on monopolistic competition withhomogeneous products on how to �nd the number of �rms in theequilibrium).


Welfare analysis of monopolistic competition withdi¤erentiated products

As in the case with homogeneous products, there are two factors thatlead to welfare ine¢ ciency of monopolistically competitive markets.

First, as with homogeneous products, each �rm sets the price abovemarginal costs and produces less than the welfare-maximizing level ofoutput (which is at the level where p = MC ).

Second, the number of �rms may be either too big or too small. Onone hand, each additional �rm has to pay additional �xed costs ofproduction. On the other hand, each additional �rm produces newvariety of the good and consumers are better-o¤ when they havemore varieties to choose from.


econ3200 class6 monopolistic competition

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