Aggregation andDisaggregation of Indevelopment Goods: Implications for Bundling, Site Licensing and also MicropaymentSystems

Yannis Bakos*and Erik Brynjolfsson**

This Draft: June 1997

Presented at the Conference onWeb Publishing and Beyond: The Economics of DigitalInformation and also Intellectual Property.

You are watching: In general, for digital goods, the marginal cost of producing another unit is about zero.

Kennedy School of Government, Harvard University, Cambridge,Massachusetts


We analyze pricing techniques that are based upon aggregation ordisaggregation of digital indevelopment products. For circumstances,bundling, website licensing, and subscription pricing can beanalyzed as tactics that aggregate customer utility acrossvarious products, different consumers, or various time periods,respectively. On the various other hand also, unbundling magazine short articles forindividual sale, or utilizing micropayments for renting software"applets" correspond to a strategy of disaggregation.We present that reductions in marginal costs made feasible bylow-price digital processing and storage of information will certainly favoraggregation, while reductions in transaction and distributioncosts made feasible by common networking tend to makedisaggregation of information goods more profitable. Our analysisdemonstprices exactly how the raising availability of information goodsover the Internet will certainly result in enhanced use of bothdisaggregation-based pricing methods taking benefit ofmicropayment technologies, and also aggregation techniques whereindevelopment products will certainly be offered in bundles, website licenses, andsubscriptions.

1. Introduction

The emergence of the Web as a method to distribute digitalindevelopment such as software application, news stories, stock quotes, music,photographs, video clips, and research reports has created newmethods for the pricing of indevelopment products. Providers ofdigital indevelopment items are uncertain just how to price them and arestruggling through a range of revenue models. Because perfectduplicates of these goods deserve to be created and spread almostcostlessly, some of the old rules, such as "price shouldequal marginal price," are not wise (Varian, 1995).

It has actually been argued that bereason electronic sectors lowersearch and transactivity costs, the Internet will promote theproduction of new markets, leading to an boosted number ofsectors in individual goods and also services (Bakos, 1997; Malone,Yates and Benjamin, 1986). The result has also been likened to"friction-free capitalism" (Gates, 1995). Thesepredictions, but, focus on physical items and also solutions. Inthis paper, we discover that for indevelopment items, the decline inthe marginal price of reproduction linked through digitizationregularly provides a countervailing pressure to the reduction intransaction costs associated via ubiquitous netfunctioning.Consequently, some of the disaggregating impacts of the Internetare mitigated or even reversed.

As listed by Varian (1995), Bakos and Brynjolfskid (1996),Odlyzko (1996), Chuang and Sirbu (1997) and others, the Internethas likewise produced new methods for repackaging contentthrough bundling, site licensing, subscriptions, rentals,differential pricing, per-use fees, and various various other mechanisms;others might yet be created. All of these schemes have the right to be thoughtof as either aggregating or disaggregating information goodsalengthy some dimension. For instance, aggregation can take placethroughout commodities, as once software programs are bundled for salein a software program "suite" or when accessibility to the variouscontent of an on-line business is gave for a resolved fee.Aggregation can likewise take area across consumers, as through theprovision of a site license to multiple individuals for a addressed fee, orover time, as through subscriptions (Odlyzko, 1996; Varian, 1995,1996). Fishburn, Odlyzko and Siders (1997) analyze some relatedelements of bundling in a duopoly setting and argue that abundling strategy will frequently prevail when marginal productionand also distribution prices become negligible.

In this paper, we extend the analysis of bundling introducedin (Bakos & Brynjolfsboy, 1996) by modeling the distributionand also transaction costs linked through giving informationproducts. Considering the distribution and also transaction prices inaddition to the marginal expense of production, we compare pricingtechniques based upon aggregation and also disaggregation. We discover thatlower transactivity and also distribution expenses tfinish to make unbundling(disaggregation) more attractive for sellers, while lowermarginal prices of production tfinish to make bundling (aggregation)more attractive. We likewise show that some of our earlierresults on bundling can be generalized to other forms ofaggregation, such as website licensing and also subscriptions. We findthat, as through bundling, aggregating indevelopment goods acrossconsumers or time is frequently an reliable strategy that maximizessocietal welfare and the sellers’ profits; yet,aggregation is much less attrenergetic as soon as marginal costs are high oronce consumers are extremely heterogeneous.

In area 2, we present the fundamental dispute for the impact ofaggregation on earnings and also effectiveness and also administer a graphicalintuition. In area 3, we present a straightforward mathematical modeldemonstrating just how transforms in manufacturing and transaction costsinfluence the profitcapacity of bundling and also unbundling goods. Insection 4, we show how the formal outcomes can be applied toaggregation in various other dimensions, such as website licensing andsubscriptions. Section 5 discusses extensions of the model to"mixed" aggregation—the simultaneous sale of bothaggregates and also their sub-components—and addresses issuesrelated to micropayments. Section 6 discusses some implicationsfor practice and also says concerns for further study.

2. Aggregation Changes Demand

Many goods deserve to be assumed of as bundles of smaller sized goods(Lancaster, 1966). For circumstances, a spreadsheet routine includesnumerous components, such as the capability to calculate sums, tocreate charts and also to print in assorted fonts (Brynjolfskid andKemerer, 1996). Similarly, the purchase of a resilient goodsynchronizes to a series of rental contracts (Christensen andJorgenkid, 1966), and also sharing of books or videocassettes isidentical to multiple sepaprice transactions (Varian and also Roehl,1996).

Why Aggregate?

Tbelow are two primary factors that sellers might wish to aggregateinformation goods. First, aggregation have the right to directly increase thevalue accessible from a collection of products, because of technologicalcomplementarities in production, distribution, or consumption.For circumstances, it is even more cost-efficient to supply a few hundredpperiods of news posts in the create of a Sunday newspaper than toseparately deliver each of the individual components only to thecivilization that check out them, even if a lot of of the Sunday bundle ends upin the recycle bin without ever being check out. Likewise, purchasinga movie on videocassette might be cheaper than consistently rentingit or attempting to individually charge members of the householdfor viewing it. These price savings increase the excess availableto be divided in between the buyer and also seller, although they maylikewise affect exactly how the excess is split. Similarly, includingparticular kinds of functionality together in a software program applicationcan produce worth greater than the amount of its components.

2nd, aggregation have the right to make it simpler for the seller toextract worth from a offered collection of products by allowing a kind ofprice discrimination. This impact of aggregation is subtler and,in the case of bundling, has been studied in a number of articlesin the economics literary works (e.g., Adams and Yellen, 1976;McAfee, McMillan and Whinston, 1989; Schmalencheck out, 1984). Whilethe benefits of aggregation because of technologicalcomplementarities are reasonably simple to check out, the pricediscrimination effect does not seem to be as commonly recognizedoutside the economics literary works, although it deserve to dramaticallyinfluence both performance and also earnings (Bakos and Brynjolfsson,1996).

The Effects of the Internet and also Digitization

Ubiquitous low-expense networking and also low-price digital processingand also storage of indevelopment will profoundly affect the incentivesof sellers to aggregate items that have the right to be yielded in digitalcreate, enabling them to take advantage of cost savings and also toprice discriminate. For instance, the Net is making itfeasible to disaccumulation news stories that previously wereaggregated in a newspaper ssuggest to economize on transaction andcirculation expenses. The Internet has also made detailedsurveillance and micropayment devices feasible, making it moreattractive to offer tiny systems of indevelopment, perhaps for use ina minimal period of time, by a minimal variety of world, or in alimited set of situations. As an outcome, many type of observers havepredicted that software and other forms of content willsignificantly be disaggregated and also metered, as on-demand also software"applets" or as individual news stories and stockquotes. For circumstances, Bob Metcalfe writes: "When theWeb finally gets micromoney devices, we"ll rent tiny bits ofsoftware for seconds at a time. Imagine renting a French spellingchecker for one record once" (Metcalfe, 1997).

On the various other hand also, the near-zero marginal prices forredeveloping digital items make many types of aggregation moreattrenergetic. While it is uneconomical to carry out goods toconsumers that value them at much less than the marginal price ofproduction, when the marginal cost is zero and customers deserve to freelydispose of products they do not choose, then no consumers willvalue the items at less than their marginal expenses. Consequently,economic efficiency and often profitability are maximized byproviding the maximum number of such goods to the maximum numberof consumers for the maximum amount of time. In this paper, weshow that marketing items in large aggreentrances will frequently achievethis goal.

In the brand-new indevelopment economic climate goods that had previously beenaggregated to conserve on transaction or circulation prices might bedisaggregated, but new aggregations of products will emerge toexploit the potential for price discrimicountry, developing newefficiencies and also profit opportunities. We present that strategiesinvolving bundling, site licensing, and also subscriptions have the right to each beunderstood as responses to the radical declines in production,circulation and transactivity costs for digital information items,while micropayments have the right to be viewed as both a consequence and a causeof radically reduced transaction and also circulation prices.

Graphical Intuition: The Case of Bundling

The influence of aggregation on the profitability of sellingindevelopment goods have the right to be portrayed by graphically analyzing theeffect of bundling on the demand also for indevelopment products. Considera simple direct demand curve for all products, and assume that theinitial resolved expenses of creating an excellent are considerable, yet thatafter the first unit, marginal manufacturing expenses, deprovided by c,are close to zero. At price p, the variety of unitspurchased will certainly be q, resulting in earnings of pq.However, as lengthy as p > c, some consumers that valuethe great at even more than its manufacturing prices will not be willing topay as a lot as p. As an outcome, these consumers do not getaccess to the excellent, developing a deadweight loss, denoted by theshaded area in Figure 1. In addition, there are consumers whowould certainly have been willing to pay even more than p for access tothe good, however that just have to pay p to obtain it. Theseconsumers gain a consumers" excess as indicated in Figure 1.


Figure 1: Deadweight loss from sales of azero-marginal-cost indevelopment good

If the seller is able to price discriminate, chargingdifferent prices to eexceptionally consumer based upon their willingness topay, it will be able to increase its revenues. Perfect pricediscrimicountry will certainly maximize the sellers" revenues and willget rid of both the consumers" surplus and the deadweight loss(Varian 1995). If the seller cannot price discriminate, however,the only single price that would certainly eliminate the inperformance fromthe deadweight loss would be a price equal to the marginal cost,which is close to zero. Such a low price would certainly not generateadequate revenues to cover the fixed expense of manufacturing and isunlikely to be the profit-maximizing price. Yet, any kind of significantpositive price will inefficiently exclude some consumers.

Aggregation can sometimes get rid of this dilemma. Consider twoindevelopment goods, say a journal post and a music video, andmean that each is valued by consumers between zero and also onedollar, generating direct demand curves favor the one in Figure 1.Suppose even more that a consumer"s valuation of one good is notcorrelated through his or her valuation for the various other, and thataccess to one great does not make the other more or lessattrenergetic.

What happens if the seller aggregates the 2 goods and sellsthem as a bundle? Some consumers —those that valued bothitems at one dollar— will certainly be willing to pay 2 dollars forthe bundle, while others —those who valued both products atnearly zero— would certainly not be willing to pay also a penny. Thetotal area under the demand also curve for the bundle, and hence thetotal potential excess, is precisely equal to the amount of the areasunder the separate demand also curves. However, most interestingly,bundling alters the form of the demand also curve, making it flatter(more elastic) in the community of one dollar and steeper(much less elastic) near either too much, as presented in Figure 2A. As even more products are added, this impact becomesmore pronounced. For example, Figure 2B mirrors the demand for abundle of 20 items, each of which has an independent, lineardemand ranging from zero to one dollar.


Figure 2A: Demand curve for a bundle of two indevelopment goods via separately distributed unicreate valuations Figure 2B: Demand also curve for a bundle of 20 information goods with individually dispersed unidevelop valuations

A profit-maximizing firm marketing a bundle of 20 products will certainly setthe price slightly listed below the mean worth of the bundle of $10, andalmost all consumers will find it worthwhile to purchase thebundle. In contrast, just fifty percent the consumers would have actually purchasedthe products if they had been individually offered at the profitmaximizing price of 50 cents, so selling the products as a bundleleads to a smaller deadweight loss and greater economicperformance. Furthermore, the seller will certainly earn greater profits byselling a single bundle of 20 goods than by offering each of the20 products separately. Hence, the form of the bundle"s demand curveis far even more favorable both for the seller and for overallfinancial performance.

Why does the form of the demand also curve adjust as products areadded to a bundle?

The legislation of big numbers implies that the average valuationfor a bundle of items with valuations attracted from the samedistribution will certainly be increasingly concentrated close to the meanvaluation as more products are included to the bundle. For example,Figure 3 shows the uniformly dispersed probcapability of aconsumer’s valuation for a good through the direct demand also shownin Figure 1.


Figure 3: Unicreate probcapacity density attribute for agood"s valuation

If a second great is bundled with the first, the probabilitythickness attribute for the consumer’s valuation for the bundleof 2 products is the convolution of the 2 uniform distributions,which will be shaped like an inverted "V" (Figure 4).As more and also more products are included to the bundle, the amount ofvaluations becomes even more concentrated roughly the mean, reflectingthe law of huge numbers. That is, the high and low worths forindividual products tfinish to "average out" so thatconsumers’ valuations for the bundle encompass proportionatelyeven more moderate valuations. For instance, some civilization subscribe toAmerica Online for the news, some for stock quotes and also some forhoroscopes. It is unmost likely that a solitary perboy has actually a really highworth for eincredibly single excellent offered; rather most consumers willhave actually high values for some items and low worths for other items,leading to modeprice worths in its entirety.


Figure 4: Convolution of two unicreate probabilitythickness functions

Sellers can take benefit of the reality that demand for thebundle (adjusted for the number of goods) will certainly be morefocused approximately the suppose valuation than in the instance ofindividual products. Thus, bundling deserve to be believed of as a type ofprice discrimicountry, except that rather of raising the menuof prices to much better match the heterogeneous circulation ofconsumers, bundling reduces the effective heterogeneity of theconsumers’ willingness to pay, so that a solitary price caneffectively and also properly alfind goods to them. Like theProcrustean bed, bundling changes consumer’s demand so thata single price fits them all.

If consumers’ needs remajor heterogeneous also afterbundling, then a combined bundling strategy, which uses a menu ofvarious bundles at different prices, will conquer purebundling (which is ssuggest a special case of combined bundling).However before, once consumers’ valuations for the items in thebundle are not correlated, the profit benefit of blended bundlingover pure bundling diminishes as the number of goods in thebundle increases.

Comparable results cause various other types of aggregation, such asaggregation throughout consumers, as in the situation of selling a singlesite license for use by multiple consumers. This analogy isexplored more totally in section 4. The legislation of big numbers, whichunderlies these aggregation effects, is remarkably basic. Forcircumstances, it holds for virtually any initial distribution, not justthe straight one shown graphically above. Furthermore, the law doesnot need that the valuations be independent of each various other oralso that the valuations be attracted from the same distribution.

Bundling may not market a preferable tool for pricediscrimicountry when consumers’ valuations are correlatedthrough one or more prevalent variables, although price discriminatingfor various bundles might mitigate this trouble (Bakos andBrynjolfschild, 1996). Similarly, as shown in the following section,once marginal costs are high unbundling might be even more profitablethan bundling.

3. A model for aggregation and also disaggregation

The over insights have the right to be modeled more formally. Inspecific, the aggregation of information products right into bundlesentails several forms of costs:

Production cost: the expense of producing additional devices for inclusion in the bundle. For instance, storage, processing, or interactions costs incurred in the procedure. Distribution cost: the expense of distributing a bundle of information goods. Transaction cost: the expense of administering transactions, such as arranging for payment. Binding cost: the price of binding the component items together for distribution as a bundle. For example, formatting transforms essential to incorporate an excellent in the bundle. Menu cost: the cost of administering multiple prices for a bundle. If a blended bundling strategy for n products is sought, as many type of as 2n prices (one for each separate sub-bundle of one or more goods) may be compelled.

We currently focus on the impact of production expenses anddistribution/transaction prices, which seem to be most importantfor determining the desirability of aggregation; similarthinking have the right to be used to the binding and price administrationexpenses.

Consider a setup via a solitary seller giving ninformation goods. Let

, and
denote theprofit-maximizing price per good for a bundle of n items,the corresponding sales as a fraction of the populace, and theseller’s resulting earnings per great. Assume that:

A1: The marginal price of creating copies of all information items and the marginal circulation and also transactivity price for all indevelopment products are zero.

A2: Each buyer can consume either 0 or 1 units of each information good and resale is not allowed.

A3: For all n, buyer valuations are independent, identically spread (i.i.d.) via constant thickness attributes, non-negative support, finite expect

, and finite variance

By using the regulation of large numbers to the above setting, weacquired the complying with Proposition and matching Corollary in(Bakos and Brynjolfskid 1996):

Proplace 1 (Minimum profits from bundling zero marginalexpense i.i.d goods):

Given presumptions A1, A2, and also A3, bundling n goodsallows the seller to capture as revenues at a fraction

of the maximumpossible consumers’ excess (i.e., the location under the demandcurve).

Corollary 1 (Bundling via symmetric distribution ofvaluations):

Given assumptions A1, A2, and also A3, if the distribution ofvaluations is symmetric about the intend, then a portion of thearea under the demand curve of at

deserve to be recorded by bundling nitems.

We now extfinish the original version by substituting Assumption A4for Assumption A1:

A4: The marginal cost for developing each information excellent is c, and also the amount of circulation and also transactivity prices for any kind of individual great or bundle is d.

Assumption A4 suggests that the complete incremental expense ofgiving a bundle of n information goods is nc+d.

Corollary 2 (Bundling through production, distribution andtransaction costs):

Given presumptions A2, A3, and also A4, bundling n goodsresults in profits of

for the seller, where

Selling the goods individually, the seller deals with a downwardsloping demand also curve

for each individual excellent, and will select theoptimal price
andmatching amount
that will maximize profits
, causing revenues of

When the variety of products is large, bundling will be superiorto unbundled sales in the limit as lengthy as

. Additionally, if thereis no consumer through a valuation higher than
, then unbundled saleswill be profitable just as long as



Distribution Costs

Figure 5: Phase diagram for bundling and also unbundlingmethods as a duty of marginal price andtransaction/distribution cost.

Figure 5 depicts the impact of c and d on thedesircapacity of bundling big numbers of goods. In Area I,unbundled sales dominate bundling. In Area II, bundling is moreprofitable than unbundled sales. Finally, in Area III, themarginal manufacturing, circulation and also transaction expenses are highsufficient to make both bundled and unbundled sales unprofitable.

A reduction in distribution or transactivity costs have the right to makeunbundling even more attrenergetic than bundling (a relocate from A toA’). For instance, it is often argued that as micropaymentinnovations and also electronic distribution minimize d, therewill be a move toward "fine-grained" pricing, e.g.,price per use (Metcalfe, 1996, 1997). However before, as soon as themarginal expense drops below a particular threshold

, bundling becomes moreprofitable than unbundling, also if distribution and transactionexpenses are zero, as demonstrated by the relocate from A" to A".While bundling is optimal in the neighborhood of A greatly as away to economize of distribution and transactivity expenses, thebenefits of bundling in the community of A" derive fromits capability to allow the seller to extract even more earnings fromconsumers. Thus, the types of bundles observed in a world ofhigh production, circulation and transactivity costs (close to A) maydiffer substantially from the types of bundles observed in ahuman being via extremely low production, distribution and also transactionexpenses.

A reduction in c, d, or both have the right to relocate a goodfrom Area III (no trade) to either Area I (unbundled sales, ifthe primary reduction is in the distribution and transactioncosts), or Area II (bundled sales, if the primary reduction is inthe marginal cost of manufacturing.)

The threshost level

listed below which bundling becomes unambiguously moreprofitable than unbundling depends on the distribution of theunderlying valuations. For instance, consider consumer valuationsthat are uniformly distributed in
, which synchronizes to a linear demandattribute. Selling the items individually, the seller deals with adownward sloping demand also curve
for each individual great, leading to amonopolistic equilibrium price of
for each great, and also corresponding profitof
as lengthy as
. Selling theinformation items in bundles of n products results in profits
, wbelow

When the variety of items is huge, bundling will be superiorto unbundled sales in the limit as lengthy as

, and also
, then unbundledsales will be unprofitable, while bundled sales will certainly beunprofitable if
.In this case c0 is around 0.41
. Figure 6 shows a"phase diagram" of the corresponding profitabilityareas.


Figure 6: Phase diagram for bundling and unbundlingtechniques as a role of marginal production cost andcirculation or transaction expense once valuations are uniformlydistributed

It deserve to be suggested that direct demand also attributes and also thematching uniform distribution of valuations are notcorrect for indevelopment items. For instance, a lot of consumersmay have specifically zero valuation for 90% of the news storiesprovided by a news company, and a direct demand for the remaining10%. The resulting piecewise straight demand also curve would certainly be similarto the one provided by Chuang and Sirbu (1997) and to severalnumerical examples presented in Odlyzko (1996).

When many kind of consumers have zero valuations for any kind of provided good,the results of any kind of marginal costs will certainly be intensified and also theregion in which bundling is profitable will certainly be reduced. This isbecause any bundle will certainly likely encompass countless products via noworth to any given consumer; if these goods are costly tocarry out, they will certainly tfinish to alleviate the worth created by providingthe bundle to that consumer. For circumstances, once consumers havenon-zero valuations for just 10% of the items, the thresholdvalue, c0, at which bundling becomesunprofitable relative to bundled sales declines by a factor of 10to 0.041



Figure 7: Phase diagram for bundling and also unbundlingtactics as a role of marginal production expense anddistribution or transactivity price once valuations aretremendously distributed.

As an additional instance, as soon as valuations are distributedsignificantly —so that only a small variety of human being havehigh valuations and also a lengthy tail of civilization have low valuations butno one rather has actually a zero valuation— and also marginal costs areclose to zero, bundling can allow sellers to profitably provide theitems to the long tail of that have a reasonably low valuefor the great. Due to the fact that the number of such might be veryhuge, the efficiency and profit results can be comprehensive. Forexample, one can generate significant revenues by offering ajoke a day to numerous human being, even if the majority of just valuedthe joke at a penny or much less. In fact, organization models based onthis and also similar ideas were proposed in the earlier days of theinternet. However, as shortly as marginal expenses start to technique theaverage consumers’ valuation, bundling becomes unprofitable.In contrast, because the exponential distribution assumes thereis always a positive probcapacity that someone will have actually avaluation equal to or better than any kind of finite number, unbundledsales are never before entirely unprofitable; they simply need aprice greater than the sum of manufacturing, distribution andtransactivity costs. Figure 7 reflects the "phase diagram"through the corresponding 2 locations of profitcapacity.

4. Aggregation by Other Means: Site licensing andSubscriptions

The coming before area concentrated on the benefits of aggregationin the context of bundling. Parallel debates have the right to be made foraggregation in other dimensions, such as website licensing(aggregation across users) and also subscriptions (aggregation overtime). For circumstances, Odlyzko (1996) gives an instance in whichwebsite licensing works analogously to bundling and also enables a sellerto extract even more excess develop sales of a software application package. Ofcourse, site licensing deserve to be helpful also in the lack ofaggregation impacts. For circumstances, Varian (1997) creates a modelfor sharing indevelopment goods that highlights the tradeoffsin between production expenses and sharing costs; this version have the right to alsobe used to site licensing. In comparison to our assumption thatthe valuation of an agent representing a team of nconsumers is the sum of the n individual valuations, heassumes that the agent"s valuation is n times the minimumvaluation in the team (so that all last consumers areimplicitly charged the same price). Consequently he obtains noaggregation impacts, but still finds that site licensing deserve to beprofitable as soon as sharing expenses are fairly low.

Site licensing

Similar to bundling, there are many kind of reasons that a firm maypick to sell its products through a site license instead ofoffering them to individual individuals. For circumstances, website licensingcan alleviate bureaucratic prices and transactions costs; mitigate orremove the need to inspect for piracy at a offered customer"ssite; facilitate interoperability and also foster positive networkexternalities; and also minimize maintenance prices throughstandardization of software program configurations. Many of these costsdeserve to be modeled as creating a resolved transaction price per sale,analogous to the distribution and also transaction expense parameter, d,in area 3. When this expense is sufficiently high, aggregation(website licensing) will certainly be more profitable than disaggregation(individual sales).

Our evaluation reflects that website licensing deserve to additionally be seen as asystem for aggregation that boosts seller profits andreduces the inefficiency of withholding an excellent from consumersthat value it at more than its marginal expense. Where bundlingaggreentrances a single consumer"s valuations for many kind of commodities, sitelicensing aggregates many consumers" valuations for a singleproduct. Just like bundling, the legislation of huge numbers will certainly lead toa circulation of valuations for the website license that, afteradjusting for the variety of users, is less dispersed and morepredictable than the circulation of individuals" valuations forthe same excellent.

For circumstances, some researchers at a university may have actually highvaluations for Mathematica and also be willing to pay $500 for accessto it; other users can worth it only at $50; and still othersmight be willing to pay $5 to have straightforward access to the regime incase it is necessary later on. Wolfram Research, themanufacturer of Mathematica, might collection a high price and excludepotential customers with low valuations, or collection a low price thatfails to extract the majority of of the excess from the high value users.Additionally, Wolfram could sell a website license to theuniversity that provides all potential individuals accessibility to Mathematica.The value of such a website license to the university is equal tothe amount of all potential users" individual valuations. Thisamount is larger than the revenues that deserve to be obtained throughindividual sales. If the seller does not market the goods for saleto individual customers, then in principle it could sell the sitelicense for a price simply slightly less than the intended sum ofindividual valuations (i.e., at a price p = Svi,-e = mm- e wbelow ve are thevaluations of individuals at the site, m is the number, m is the averagevaluation in the populace, and eis a little number). Almany all sites would uncover this priceacceptable, and also thus virtually all customers would gain accessibility to thegood. Under similar presumptions to those applied in the analysisof bundling, aggregation deserve to considerably reduce inefficiencyand increase revenues, at the cost of consumers" surplus.

One important distinction between website licensing and bundlingis that the site-licensing strategy calls for an agent who hasauthority to purchase information goods on behalf of theirultimate consumers. An agent may not have perfect informationaround the choices of end users, and his or her incentives maynot be perfectly aligned through those of the end users; this maymitigate the benefits of a site licensing strategy. Furthermore,the implicit presumption that the institutions are price takersmay be less appropriate for big sites. In fact, therepresentative of a website might be in a place to baracquire for ashare of the full excess. (See Bakos and Brynjolfschild (1997a)for a further discussion of these concerns through respect to sitelicensing.)

Subscriptions across time and space

Our version of aggregation deserve to additionally be used to dimensionssuch as time and also area. For example, once the excellent have the right to becostlessly gave over multiple time durations, it may be moreprofitable to market it as a long-term subscription than to sellindividual uses in short durations of time. Due to the fact that a provided user maysometimes have actually high valuations for the good and also sometimes lowvaluations, per-use (or short-term) pricing could inefficientlyexclude usage during low-value periods, also as soon as the price ofprovision is zero. By charging a single subscription fee andoffering the user long-term accessibility to the excellent, higher efficiencyand earnings deserve to outcome by an discussion corresponding to those forbundling and website licensing.

Of course, a subscription may provide the user through different(yet perhaps related) goods over time, as with magazine orjournal subscriptions. In such situations, the logic of bundlingapplies directly. As stated in (Bakos and also Brynjolfschild,1996), if customer valuations are associated to an underlyingvariable, such as their interests, seller profits might bemaximized by supplying information bundles that induce consumersto self-choose according to their underlying kind. For instance, abetter price might be extracted from readers of a specialtymagazine because all posts are related to a topic of interestto them, while the aggregation benefits deserve to still be derived asvarious readers will area better worth on different short articles.

The aggregation results may still be important even when asubscription provides the exact same good in different timedurations. For instance, a 1-year subscription that providesboundless accessibility to the online version of Encyclopedia Britannicaaggregates valuations even more than hourly charges execute. As valuationsfor the same great by the exact same user are most likely to be seriallycorrelated over time, the benefits of aggregation over time perhaps reduced than they are for uncorrelated goods or individuals (Bakos andBrynjolfsboy, 1996).

Similarly, permitting the user to accessibility the good from multiplelocations may additionally administer some of the benefits of aggregation; anecessity that the excellent be supplied only on a details machine orin a specific area would certainly weaken these benefits. Withoutaggregation, some users can forgo accessibility to the great in placeswright here their valuations were low; once the expenses of providingadditional accessibility are even reduced (or zero), this would certainly develop aninperformance.

5. "Mixed Aggregation": Simultaneouslyaggregating and disaggregating goods

Aggregation or disaggregation can be exercised on multipledimensions all at once. For instance, bundles of products have the right to beavailable on a site license basis to multiple customers for an extendedperiod of time. Even as soon as the seller does not have actually great knowledgeof exactly how specific items are valued by specific customers atcertain times, this strategy may permit the seller to getclose to complete effectiveness and earn better revenues, sinceaggregation alengthy one measurement will generally not exhaust thebenefits of aggregation in various other dimensions. Undoubtedly, underproblems analogous to A1-A3 disputed above, the optimalstrategy will be to market the biggest feasible bundle of goodsvia the biggest feasible website license for the broadestpossible collection of conditions, and to charge a price low sufficient toobtain virtually all customers to get involved. Under these conditions, thisstrategy captures as profits virtually the entire possible surplusfrom the products.

In practice, finish aggregation of this develop is not likelyto be optimal. Usually, some develop of "mixedaggregation," which requires concurrently providing thecomplete aggregation together with subsets of the aggregate for saleat the same time, will certainly be even more profitable. This approach oftenprovides it possible to induce consumers through greater valuations topay even more for bigger aggregateways without pricing lower-valueconsumers out of the industry. In addition, it may make feeling toaggregate in some dimensions while disaggregating in otherdimensions. The seller can select to disaccumulation (or avoidaggregating) on those dimensions that are a lot of efficient ingetting users to reveal their valuations while aggregating onvarious other dimensions. For instance, if the seller knows that utilizing aproduct in the time of certain "prime hours" is highlyassociated via high user valuations, it could make sense todisaggregate alengthy that measurement to charge a premium for thosetime durations. Similarly, if user valuations for particular products areassociated (e.g., magazine short articles on a special-interestsubject), it might be useful for the seller to disaggregatearticle collections on various topics, practicingsecond-level price discrimination.

Sellers deserve to also sell a functional "menu of bundles"from which buyers design the actual bundle they purchase. Forcircumstances, the seller of a arsenal of N goods couldpermit buyers to pay a price

and pick any kind of n goods (
). This strategy maylead to higher revenues bereason, among other points, the numberof products schosen may be a good proxy for the buyers" willingnessto pay, for this reason allowing the sellers to price discriminate.

Disaggregation may additionally be correct if marginal prices arenot negligible. In this situation it might make feeling to sell onlysubsets of the items to subsets of users for subsets of timeperiods so that customers can choose the subsets they find mostpractical, and stop the manufacturing cost for the ones they do not.This logic additionally uses if consumers incur a non-negligiblemarginal expense for goods in the bundle they purchase, such as acognitive, storage or search cost.

Aggregation and also disaggregation on multiple dimensions

Tright here are many kind of various other methods to accumulation or disaggregate goods.Technologies choose micropayment systems, cryptolopes, autonomousagents, and also object technology are enabling sellers to chargedifferent prices when indevelopment goods are disaggregated inassorted ways. For instance, the seller of a software appletcould, in principle, charge customers a price each time a particularattribute of the product is invoked on a specific machine whilecertain other programs are also running and specific various other steustatiushistory.orgare logged into the network-related, and so on In principle, a good could havea price for eextremely potential state of the civilization that is observableand verifiable.

Such fine-grained "micro-pricing" is increasinglyfeasible and also it plainly opens the door to sophisticateddifferential pricing schemes that may permit a seller to extractgreater earnings from a given excellent. However before, our analysissuggests that micropricing will likewise reduce or remove thebenefits of aggregation. As such, it can alleviate efficiencyand earnings, specifically when the buyers" valuations for usage incertain situations are even more heterogeneous than their totalvaluations.

When to usage micropayments

Our analysis suggests that in three circumstances completedisaggregation or "mixed aggregation" can be moreprofitable than a strategy of aggregation.

First, if marginal expenses are non-trivial, then disaggregationdeserve to economize on these costs by allowing users to"opt-out" of components through a marginal expense greaterthan their marginal advantage. For instance, if the marginal expense ofproviding a secondary component or servicing an additional useris c, then a seller that charges a solved price p plusan additional price of c per component or user, will avoidthe ineffectiveness of including too many kind of components in the sale, orservicing also many type of customers. If c is very low, thanmicropayment modern technology might be required to permit the seller topursue such a strategy profitably. An implication of thisanalysis is that it may make sense to unbundle costly orcontestable solutions such as bandwidth usage, data storage orcomputationally intensive attributes from a package of digitalinformation goods and services. The benefits of aggregation perhaps outweighed by the expenses of providing these solutions easily, asindicated in location I of figure 5.

2nd, if some consumers are willing to pay more for allitems, then blended aggregation may be helpful if it deserve to helpsort consumers. For circumstances, if consumers via high valuationstend to favor to use even more goods or usage the goods more regularly, ablended aggregation strategy have the right to induce them to self-select and also paygreater prices for bigger aggregations. Furthermore, if consumersare heterogeneous in their all at once valuations and the seller hasan excellent concept of exactly how these valuations are correlated through use ofthe good in various situations, then disaggregation willfrequently be even more attrenergetic. For instance, it might make feeling tocharge additional for real-time stock quotes or accessibility to data duringcompany hours, even if these services are not even more costly tocarry out, bereason consumers of such goods are most likely to havesystematically higher valuations than various other consumers. Incontrast, if consumers have actually fairly homogeneous totalvaluations (yet are not necessarily homogeneous in theirvaluations for using the good in specific circumstances) thenaggregation is more most likely to be efficient.

Third, also as soon as marginal prices are negligible and also consumersare homogeneous, big aggregations of goods (or users) may beforced to fully extract profits and also to maximize efficiency.Because of this, if the seller can only accumulation over a small numberof goods, consumers, or time durations, then it may be optimal toalso market some goods exterior the bundle, site license, orsubscription.

6. Conclusion

The Internet is precipitating a dramatic reduction in themarginal prices of manufacturing and distribution for digitalindevelopment items, while micropayment modern technologies are reducingthe transactivity costs for their commercial exadjust. Theseadvancements are developing the potential to use pricing strategiesfor indevelopment items based upon aggregation and also disaggregation.Since of the capability to cost-properly accumulation very largenumbers of information items, or, at the various other finish of thespectrum, offer little components for individual sale, thesetactics have actually effects for indevelopment goods that are notwidespread in the human being of physical goods.

In certain, aggregation have the right to be a powerful strategy forservice providers of indevelopment items. It have the right to bring about better profitsfor sellers as well as a socially preferable bigger distribution ofthe items, but it is less effective as soon as the marginal productioncosts are high or once consumers are heterogeneous. Aggregationtechniques can take a variety of creates, including bundling(aggregation throughout different goods), site licensing (aggregationthroughout various users), and also subscriptions (aggregation overtime). These tactics can alleviate buyer heterogeneity byaggregating a big number of items, individuals, or time periods, anddeserve to additionally minimize circulation and transaction costs. Therefore, adecision to accumulation indevelopment products need to be based on thetrade-off between the benefits of aggregation and also the marginalcosts of manufacturing and the distribution. Low distribution costsmake aggregation less attractive, while low marginal productionprices make aggregation even more attractive.

On the various other hand, the low distribution and transaction costsreadily available by common networking and micropayment technologiesallow the usage of disaggregation strategies such as per-usage fees,rentals, and also sale of tiny components. Dissagregation strategiespermit sellers to maximize their earnings by price discriminatingonce consumers are heterogeneous. For example, the number ofproducts preferred by individual consumers may be associated withtheir valuation for these items, as when a skilled stocktrader needs even more financial news stories and has greater valuefor these stories than an individual investor. The seller cantake benefit of this correlation by incorporating the signalthat reveals the consumer’s valuation, i.e., the number ofnews stories purchased, in the pricing of the products, resulting insome form of pay-per-use pricing. In general, the pricing schemeused have to incorpoprice all signals that may expose aconsumer’s willingness to pay, and also micropayment technologiesdeserve to permit the implementation of such schemes.

The optimal pricing strategy will certainly frequently involve mixedaggregation, i.e., the simultaneous availcapacity of informationproducts in aggregateways of various sizes and also complace, as wellas individually. Mixed aggregation will be even more preferable inthree cases: First, when consumers are incredibly heterogeneous, as itoffers a maker for price discrimicountry. 2nd, as soon as themarginal manufacturing prices are considerable, as this increases thecost of offering goods to consumers that perform not value them.Finally, once the number of products for sale is reasonably little,as the aggregation benefits of the law of big numbers will notbe as powerful and also the food selection costs of administering the prices forall bundles offered will not be as high.

Our evaluation of aggregation gives a structure to understandthe pricing strategies of on-line content suppliers such asAmerica Online and also the Microsoft Network, the widespcheck out use ofsite licensing of software and information access by providers likeWolfram Research and also Reuters, and also subscription pricing in thesale of information products by service providers favor Netscape and also the WallStreet Journal. It can additionally define exactly how the dramatic reduction inmarginal manufacturing, circulation and also transactivity costsprecipitated by the Internet is causing pricing strategiesbased upon both aggregation and also disaggregation.

Due to the fact that the factors for aggregating information products whenproduction and also distribution expenses are very low differdramatically from the reasons for aggregating items once theseprices are high, the content and also nature of the aggregations (e.g.,bundles) might differ substantially in these 2 instances. Inparticular, the Web is most likely to result in the disaggregationof digital items that were previously aggregated for purelytechnical reasons, yet then to aggregations of these goodsbased on consumer demand also. In some instances, the complace of thelast aggreentrances will certainly be established by the consumers of thesedigital goods fairly than their producers.

Finally, aggregation also has actually substantial effects on socialwelfare. Specifically, aggregation techniques have the right to substantiallyreduce the deadweight loss from monopoly, yet they deserve to additionally lowerthe surplus left to consumers.


We thank John Chuang, Anattracted Odlyzko and Hal Varian for theirpractical comments and suggestions, as well as seminarparticipants at Harvard, Stanford, UCLA, and also the Workshop onEconomics, Video Game Theory and the Web at Rutgers University. Welikewise say thanks to Marciano Sinicalchi and Miriam Avins for providingresearch study assistance and comments.


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