Industrial Organisation Off and On the Internet

Industrial Organisation Off and On the InternetSome Lessons From the Past

Greg Taylor

Oxford Internet InstituteUniversity of Oxford

Economics

I The study of constrained choice.

I Build mathematical models of decision makers’ behaviours.I Typically gives us very sharp conclusions.I Suggests effects of policy changes—comparative statics.I But hard: the world is very complex, so we need assumptions.I Thus another advantage of the mathematical approach:

encourages transparency of assumptions.

I Let’s take a look at a textbook example of how some simpleassumptions can be turned into a model.

Economics

I The study of constrained choice.I Build mathematical models of decision makers’ behaviours.

I Typically gives us very sharp conclusions.I Suggests effects of policy changes—comparative statics.I But hard: the world is very complex, so we need assumptions.I Thus another advantage of the mathematical approach:



Economics


I Typically gives us very sharp conclusions.

I Suggests effects of policy changes—comparative statics.I But hard: the world is very complex, so we need assumptions.I Thus another advantage of the mathematical approach:



Economics


I Typically gives us very sharp conclusions.I Suggests effects of policy changes—comparative statics.

I But hard: the world is very complex, so we need assumptions.I Thus another advantage of the mathematical approach:



Economics


I Typically gives us very sharp conclusions.I Suggests effects of policy changes—comparative statics.I But hard: the world is very complex, so we need assumptions.

I Thus another advantage of the mathematical approach:encourages transparency of assumptions.


Economics





Economics





Outline

Price discrimination: from assumptions to policy statements

Assumptions and applicability

Price discrimination

I Price discrimination is the practice of pricing such thatdifferent groups of consumers yield different price-costmargins for the firm.

A price discrimination example

I Imagine a monopolist firm that sells some products of varyingquality.

I Assume that quality can be indexed by a number, q.I Let q be continuous.I Suppose that it costs C(q) to provide a product with quality q.

Let C ′(q) > 0 (increasing costs), C ′′(q) > 0 (convex costs),and C(0) = 0.

I There are two types of customer: low (L), and high (H).

I A type i ∈ {L,H} consumer enjoys surplus

Ui = θiq − p.

where p is the price to be paid to the firm, and θi is theconsumer’s willingness to pay for a one unit increase in quality.

I Let θL < θH .







Ui = θiq − p.


I Let θL < θH .







Ui = θiq − p.


I Let θL < θH .







Ui = θiq − p.


I Let θL < θH .







Ui = θiq − p.


I Let θL < θH .

First order discrimination

I In a perfect world, the firm would know the type of consumerit is facing.

I It could then design a product/price combination for eachtype.

I i.e. Sell a ‘budget’ product with q = qL at price pL to L-typeconsumers, and a ‘luxury’ product with q = qH at price pH .

I The firm’s objective would then be to

maxqi,pi

pi − C(qi)

subject to the constraint

θiqi − pi ≥ 0.

I This kind of behaviour is called first degree pricediscrimination.






maxqi,pi

pi − C(qi)


θiqi − pi ≥ 0.







maxqi,pi

pi − C(qi)


θiqi − pi ≥ 0.







maxqi,pi

pi − C(qi)


θiqi − pi ≥ 0.







maxqi,pi

pi − C(qi)


θiqi − pi ≥ 0.



maxqi,pi

pi − C(qi) s.t. θiqi − pi ≥ 0.

I In fact, since the firm knows θi, it can just set pi = θiqi.

I Substituting this into the maximisation problem gives

maxqi

θiqi − C(qi).

I Increasing qi by one unit increases revenue by θi, and cost byC ′(qi).

I It is therefore profitable to increase quality if and only ifθi > C ′(qi).

I So quality q∗i is produced where θi = C ′(qi), i.e. wheremarginal cost of qi is equal to marginal willingness to pay forit.


maxqi,pi




maxqi

θiqi − C(qi).





maxqi,pi




maxqi

θiqi − C(qi).





maxqi,pi




maxqi

θiqi − C(qi).





maxqi,pi




maxqi

θiqi − C(qi).





maxqi,pi




maxqi

θiqi − C(qi).




What can we say about these qs?

I Firstly, by giving firms so much information about consumers,we have left the latter with no surplus.

I However, that θi = C ′(qi) implies the chosen qualities areefficient!

I Social welfare given by consumer + firm welfare:

(θiqi − p) + (p− C(qi)) = θiqi − C(qi).

I This is exactly what the firm is maximising!

I That θi = C ′(qi) also implies that qL < qH , and hencepL < pH .












(θiqi − p) + (p− C(qi))

= θiqi − C(qi).
























Segmentation breakdown

I Now, firms typically cannot observe θi and so must depend onthe consumer to buy the product designed for them.

I Therein lies a problem: if high consumers buy the high qualityproduct, they get

θHqH − pH = θHqH − θHqH = 0,

whereas if they buy the low quality product, they get

θHqL − pL > θLqL − pL = 0.

I Thus, all consumers will buy the budget product—this iscalled adverse selection.













θHqL − pL

> θLqL − pL = 0.







θHqL − pL > θLqL − pL

= 0.
















Solution: mechanism designI Question: What can the firm do about this?

I Answer: Change it’s maximisation problem.I Suppose a consumer is of type L with probability α and of

type H with probability (1− α). The new problem is then:

maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))


θHqH − pH ≥ θHqL − pL (ICH)

θLqL − pL ≥ θHqH − pH (ICL)

θHqH − pH ≥ 0 (IRH)

θLqL − pL ≥ 0 (IRL)

I Solving such a problem is known as second degree pricediscrimination.

Solution: mechanism designI Question: What can the firm do about this?I Answer: Change it’s maximisation problem.

I Suppose a consumer is of type L with probability α and oftype H with probability (1− α). The new problem is then:

maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))







Solution: mechanism designI Question: What can the firm do about this?I Answer: Change it’s maximisation problem.I Suppose a consumer is of type L with probability α and of

type H with probability (1− α).

The new problem is then:

maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))









maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))









maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))









maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH))







IRL is ‘binding’

I Let’s begin by establishing that IRL holds with equality i.e.that θLqL − pL = 0.

I This means that home users are left with no surplus.

I ICH says

θHqH − pH ≥ θHqL − pL ≥ θLqL − pL

I Thus, if θLqL − pL > 0, then it must also be true thatθHqH − pH > 0 so that neither IRL nor IRH bind.

I But then the firm could increase both pL and pH withoutviolating any condition.

I This implies that IRL must bind at the optimum.




I ICH says

θHqH − pH ≥ θHqL − pL

≥ θLqL − pL







I ICH says








I ICH says








I ICH says








I ICH says





ICH is ‘binding’

I We next show that ICH holds with equality i.e. thatθHqH − pH = θHqL − pL.

I This means if the deal for the luxury product got any worsethen H type consumers would switch to buying the budgetproduct.

I Suppose that this weren’t true:

θHqH − pH > θHqL − pL ≥ θLqL − pL = 0

I Thus, if ICH does not bind then neither does IRH.

I But then the firm could increase pH without violating anycondition.

I This implies that ICH must bind at the optimum.





θHqH − pH > θHqL − pL

≥ θLqL − pL = 0








θHqH − pH > θHqL − pL ≥ θLqL − pL

= 0




































Can neglect IRH and ICL

I That ICH binds implies θHqH − pH = θHqL − pL.

I IRL implies θLqL − pL = 0.

I Thus we have

θHqH − pH = θHqL − pH > θLqL − pL = 0.

I So IRH can be neglected.

I This means that business customers get strictly positive utility.




I Thus we have







I Thus we have







I Thus we have







I Thus we have




Can neglect ICL

I It can also be shown that ICL does not bind.

I Briefly: since ICH binds θH(qH − qL) = pH − pL.

I But ICL says (after rearranging) θL(qH − qL) ≤ pH − pL.

I The inequality must be strict since θH > θL.

I This means that the home bundle is strictly more attractive tohome users than is the business edition.

Can neglect ICL


I Briefly: since ICH binds θH(qH − qL) = pH − pL.I But ICL says (after rearranging) θL(qH − qL) ≤ pH − pL.



Can neglect ICL





Can neglect ICL





qH is the set at the efficient level

I Now we will show that the chosen qH is q∗H—i.e. whereC ′(qH) = θH just like in the first order discrimination case.

I This implies that the quality offered to B-types is sociallyoptimal.

I Suppose that the optimal qH has C ′(qH) < θH .I The firm could change qH to qH + ∆, and increase pH topH + ∆θH without violating ICH, IRH, or ICL.

I When ∆ is small, the change in the firm’s profits isapproximately (1− α)∆(θH − C ′(qH)) > 0.

I Thus, original qH was not optimal.

I Similarly, if C ′(qH) > θH : The firm can reduce qH to qH −∆,provided it cuts its price for H by at least ∆θH .

I When ∆ is small, the change in the firm’s profits isapproximately ∆(C ′(qH)− θH) > 0




I Suppose that the optimal qH has C ′(qH) < θH .

I The firm could change qH to qH + ∆, and increase pH topH + ∆θH without violating ICH, IRH, or ICL.













































Optimal prices

I Now we can set about characterising the optimal prices.

I Since IRL binds, we know that pL = θLqL.

I Since ICH binds, we know that θHqH − pH = θHqL − pL, orequivalently, that pH = pL + θH(q∗H − qL).

I Combining these two statements: pH = θLqL + θH(q∗H − qL).

Optimal prices





Optimal prices





Optimal prices





Firm’s objective

I The firm’s objective is

maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH)).

I Substituting in the material we just derived (Note: sinceqH = q∗H , we only need to worry about the choice of qL.):

maxqL

α(θLqL−C(qL))+(1−α) [θLqL + θH(q∗H − qL)− C(q∗H)] .

I We can easily calculate the qL that maximises this bydifferentiating:

α[θL − C ′(qL)

]+ (1− α) [θL − θH ] = 0

I Rearranging: C ′(qL) = θL − 1−αα [θH − θL] < θL

Firm’s objective


maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH)).


maxqL




]+ (1− α) [θL − θH ] = 0


Firm’s objective


maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH)).


maxqL




]+ (1− α) [θL − θH ] = 0


Firm’s objective


maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH)).


maxqL




]+ (1− α) [θL − θH ] = 0

I Rearranging: C ′(qL) = θL − 1−αα [θH − θL]

< θL

Firm’s objective


maxqL,pL,qH ,pH

α(pL − C(qL)) + (1− α)(pH − C(qH)).


maxqL




]+ (1− α) [θL − θH ] = 0


Discussion of the model

I The name of the game is to separate clients into groups andmilk each group for as much as possible.

I The monopolist can squeeze more profit from high valuecustomers, who will pay more for a given increase in quality.

I But they can’t squeeze too hard—otherwise high valueconsumers will just buy the cheap product.

I Solution: deliberately degrade the usefulness of the budgetproduct to ensure that high-value customers refuse to buy it.

I Then the firm can charge a high price for the premiumproduct, without worrying about customers switching tocheaper versions.































Examples

£2/kg£2/kg £10/kg £18/kg

Examples

It is not because of the few thousand francs which would have tobe spent to put a roof over the third-class carriage or to upholsterthe third-class seats that some company or other has opencarriages with wooden benches. . . What the company is trying todo is prevent the passengers who can pay the second-class farefrom travelling third class; it hits the poor, not because it wants tohurt them, but to frighten the rich. . . (Ekelund [1970])

I Note that the distortion of qL away from its optimal level is amarket failure.

I However, it does not follow that the optimal policy is toprevent firms from second degree discrimination. . .

I Note that the distortion of qL away from its optimal level is amarket failure.

I However, it does not follow that the optimal policy is toprevent firms from second degree discrimination. . .

Second-degree discrimination & social welfareI What will the firm do if it cannot price discriminate?

I Will provide either q∗H at price θHq∗H , or q∗L at price θLq

∗L.

I In the efficient allocation, social welfare is

α [θLq∗L − C(q∗L)] + (1− α) [θHq∗H − C(q∗H)] .

(we can ignore the ps which simply move surplus around).I In the second order price discrimination case, social welfare is

α [θLqL − C(qL)] + (1− α) [θHq∗H − C(q∗H)] .

I If the firm offers only q∗H , social welfare is

(1− α) [θHq∗H − C(q∗H)] .

Thus social welfare falls.I If the firm offers only q∗L, social welfare is

α [θLq∗L − C(q∗L)] + (1− α) [θHq∗L − C(q∗L)] ,

so that welfare may fall or increase relative to second-orderPD.

Second-degree discrimination & social welfareI What will the firm do if it cannot price discriminate?I Will provide either q∗H at price θHq

∗H , or q∗L at price θLq

∗L.






(1− α) [θHq∗H − C(q∗H)] .






∗L.



(we can ignore the ps which simply move surplus around).

I In the second order price discrimination case, social welfare is



(1− α) [θHq∗H − C(q∗H)] .






∗L.






(1− α) [θHq∗H − C(q∗H)] .






∗L.






(1− α) [θHq∗H − C(q∗H)] .

Thus social welfare falls.

I If the firm offers only q∗L, social welfare is





∗L.






(1− α) [θHq∗H − C(q∗H)] .




More current examples

I In fact, when one thinks about it, there are similar-lookingcases in many information markets:






Outline

Price discrimination: from assumptions to policy statements

Assumptions and applicability

Assumptions, assumptions. . .

I But these examples are a little different to the ones consideredbefore:

I Cost to MS of “surprising” a customer by giving them theprofessional, rather than home edition of Windows is basicallyzero.

I Corresponds to C ′(q) = 0, C ′′(q) = 0—which is contrary toour assumptions.

I When we try to put this into the model things break down.Let’s see why. . .











Graphical treatment (assuming α = 1/2)

Price

QuantityQuality


Price

QuantityQuality

θH


Price

Willingness to pay

QuantityQuality

θH

qH


Price

QuantityQuality

C’(q)


Price

QuantityQuality

C’(q)Cost of production

qH


Price

QuantityQuality

θH

θL

C’(q)

First degree discrimination

Price

QuantityQuality

θH

qHqL

θL

C’(q)

* *

Graphical treatment

Price

QuantityQuality

θH

qHqL

C’(q)CS of high types from buyinglow quality good

qLθL=

pL

Graphical treatment

Price

QuantityQuality

θH

qHqL

C’(q)CS of high types from buyinglow quality good

qLθL=

pL

Graphical treatment

Price

QuantityQuality

θH

qHqL

C’(q)

qLθL=

pL

pHqH

Graphical treatment

Price

QuantityQuality

θH

qHqL

C’(q)CS of high types from buyinghigh quality good

qLθL=

pL

pHqH

Graphical treatment

Price

QuantityQuality

θH

qHqL qL+Δ

C’(q)

qLθL=

pL

Graphical treatment

Price

QuantityQuality

θH

qHqL qL+Δ

C’(q)Loss (must reduce pH to maintain ICH)

qLθL=

pL

Graphical treatment

Price

QuantityQuality

θH

qHqL qL+Δ

C’(q)Loss (must reduce pH to maintain ICH)

Loss (higher q is moreexpensive to produce)

Gain (can charge moreto low type consumers)

qLθL=

pL

Graphical treatment

Price

QuantityQuality

θH

qH

C’(q)

qL qL* *

qLθL=

pL

Constant marginal cost

Price

QuantityQuality

θH

C’(q)

qLθL=

pL

What goes wrong?

Price

QuantityQuality

θH

C’(q)

qL qL+Δ

qLθL=

pL

What goes wrong? (i)

Price

QuantityQuality

θH

C’(q)

qL qL+ΔqL qL+Δ

qLθL=

pL

What goes wrong? (ii)

Price

QuantityQuality

θH

C’(q)

qL qL+ΔqL qL+Δ

qLθL=

pL

Declining marginal willingness to pay.

Price

QuantityQuality

θH

θL

C’(q)

Declining marginal willingness to pay.

Price

QuantityQuality

θH

Δq Δq

Declining ΔWTP

First degree descrimination.

Price

QuantityQuality

θH

qHqL

θL

C’(q)

Profit effect of a quality increase.

θH

qH

θL

C’(q)

qL qL* *

Price Loss (Need to lower pH to maintain ICH)

Gain (Can charge more to low value consumers)

QuantityQuality

Other assumptions

In a similar manner, one can relax other assumptions e.g.:

I Oligopoly suppliers.

I Many consumer types.

I Non-continuous q.

Summary

I Social science is about understanding society.

I That, at least in part, means trying to understand thefundamental forces that drive social phenomena.

I Often, behaviour is fundamentally unchanged by newtechnology. Looking into the past can offer hints on how tounderstand and interpret the present.

I Moreover, the result of linking related phenomena is often aninsight that exceeds the sum of its parts.

I Sometimes the process works backwards: new contexts cangenerate insights into old puzzles—e.g. two-sided markets.

I A key ingredient in making these links is an understanding ofthe assumptions upon which alternative conceptualisations arepredicated.

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Education

Industrial Organisation Off and On the Internet