Network externalities, technological progress, and the competition of market contracts

International

Journal

Network progress, contracts

of Industrial

Organization

12 (1994) 269-289.

North-Holland

externalities, technological and the competition of market

Marcel Thum* Department Final version

of Economics,

Uniuersitiit Miinchen, Munich, Germuny

received June 1993

Network externalities are used to describe the fact that many modern products become more valuable the more users adopt products of the same technology. Where network externalities and technological progress exist, the various kinds of inefficiencies discussed in the recent literature can be explained by different types of contracts. The main categories analysed are simple market contracts, update contracts, and service contracts. It is shown that these types of contract emerge endogenously from the incentive structure of protit-maximizing Iirms. Competition between these contracts may substantially reduce inefficient allocations caused by network externalities. JEL

classification:

Lll;

D62

1. Introduction

During the past ten years, attention has increasingly become focused upon two particular features of technology. The first is the acceleration of technological change. Every year a new computer generation replaces the old one, software programs with improved capabilities compete for customers, and communication technology increasingly offers worldwide access to all pools of information. The second aspect is network effects. For many new technologies it is no longer plausible to view its users as being independent from one another. The benefits from buying one particular product depend largely on the number of people using the same technology. For example, more complementary products are available for a widespread computer standard, and compatibility in software increases the availability of external information (e.g. handbooks or specialist journals). Together with technical progress these network externalities are an important source of potential Correspondence to: Marcel Thum, Seminar fiir Versicherungswissenschaft, Miinchen, Schackstr.4/1, 80539 Miinchen, Germany. *I thank Ursula Arlt, Kai Konrad, Ronnie Schob, Hans-Werner Sinn, Christian two anonymous referees for helpful comments and suggestions. 0167-7187/94/$07.00 % 1994 Elsevier Science B.V. All rights reserved SSDI 0167-7187(93)00420-S

Universitat Thimann,

and

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progress

inefficiencies. This paper will argue that some of these inefflciencies can be eliminated by market forces through competition between various contracts. The seminal contributions, see, for example, Arthur (1985) and David that previous decisions may determine today’s adoption (198% argued process. If compatibility is important for users, the positive externality of networks may prevent the socially desirable switching to a superior technology. Farrell and Saloner (1985) have developed the precise conditions under which the users follow the previously described inferior adoption path. In a second article Farrell and Saloner (1986) have shown that not only too little, but also too much technical change may result from network externalities. Other economists concentrated on questions of standardization: Katz and Shapiro (1985, 1986a) have discussed the possibility of excessive or too little standardization in an unregulated oligopolistic market.’ However, contributions so far have mainly excluded the possibility of repeated purchases and consequently neglected the inventiveness of markets in creating multiple forms of contracts. Fast technological progress requires the consideration of repeat purchases, because adopters may want to participate in the advances of the products they purchased previously. Although every year a new generation of each product is put on the market, it is not always necessary to purchase a complete new package to take part in technological progress. (Think of standard software such as word processing or spreadsheets.) Producers can select various contracts in order to pass over the product improvement to consumers. Here three basic contracts will be distinguished. First, under simple market contracts price discrimination between old and new users is impossible, and new contracts have to be negotiated for each product generation. Secondly, firms could offer update contracts, which allow price discrimination between new and old users. Thirdly, under service contracts the price paid for the product in the first period of usage includes the delivery of all future versions. Profit-maximizing firms may use these different types of market contracts as strategic variables competing for larger market shares. In the following model we formalize a simple adoption process with network externalities and exogenous technological progress (section 2). In section 3 the welfare optimum is derived as the surplus-maximizing adoption structure. In section 4 the three different forms of contracting will be compared with the welfare optimum. The basic findings are that simple market contracts and update contracts may lead to an inferior amount of standardization; too much variety and, hence, too little compatibility will be obtained in oligopolistic settings. Service contract give an advantage to the tirm that produces the better product in the future; too much technological ‘A recent symposium on compatibility investigates more closely the performance of markets in the presence of network effects. See Gilbert (1992).

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change may happen (excess momentum).2 Next we allow competition between these contracts and describe the conditions under which each contract will be superior for the firms (section 5). A comparison with the welfare optimum shows that the competition of the contracts may reduce but not eliminate potential inefficiencies. 2. A simple model of network externalities

under technological

progress

To address the question of market performance we will set up a simple model. Basically, it is a two-period game reflecting the sequence of adoption and of technological progress. The participants are two firms as suppliers and two generations of consumers (which may be firms, too) on the demand side. The two firms sell inherently incompatible products and compete for potential adopters.3 As an example of such products, we can think of standard software like word processors. Incompatibility means that you cannot use the data/texts from one program for the other. Although switching between two technologies would therefore be extremely costly for the adopter, incompatibility will only become an allocation problem if there are network externalities. Ceteris paribus, every adopter prefers to have a product compatible with as many users as possible. This would make it easier for him to exchange data with others, to get complementary goods for support (handbooks, etc.), or to find a secretary already trained on this word processor. The larger the group using the same product the more preferred is this technology. This network effect involves an externality, because every adopter only considers his own benefits from compatibility and does not take into account that positive benefits also accrue to all other adopters of the same product. Another feature of our model is lechnological progress. The competing firms improve their product over time to make it more attractive for consumers. All versions allow upward and downward compatibility of data within one firm’s product to take full advantage of the network effect. In order to avoid difficulties of modelling the innovation process itself, we take the technological progress as given for every firm.4 Here a firm faces two types of costs. First, the effort of research and development (R&D) causes fixed costs. We will assume that these costs will always be lower than profits in the market equilibrium, and hence irrelevant for entrepreneurial decisions. Secondly, there are no capacity constraints and costs per unit of sales are ‘For a definition see Farrell and Saloner (1986). jThe paper could be generalized in several ways. For instance, there could be more than two suppliers, or firms could be allowed to communicate on the type of technology which would require an endogenous compatibility decision. This is beyond the focus of the paper. 40bviously, this is a critical assumption for the modelling of technology diffusion. With oligopolistic interaction of the producers, a firm with an initially small headstart could gain further advantage by strategically using R & D effort and learning effects.

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negligible, for instance the cost of duplicating a disc on which the software program is saved (i.e. marginal costs = 0). Thus the price paid for the product equals the marginal profit of the firm. The demand side is divided into two consumer generations of equal fixed size. Each consumer has only the choice of buying or not buying the good, but he cannot decide on the time of purchase. Whereas a member of the first generation who purchases the good in the first period may also demand a unit of the improved product in the second period, the demand of the second generation has only an impact on the second and last period. The early adopters forecast perfectly the future technological development.5 Furthermore, we will assume that each generation is homogeneous. Its members are able to agree on the adoption of the most preferred technology.6 This allows each generation to be treated as a single representative person. With these assumptions, we can set up a formal model of adoption in a market system. The two firms (A and B) produce the goods A and B respectively, at marginal costs of zero. In any period TV { 1; 2) they charge profit-maximizing prices P,, and PBt.7 Beside the prices, the adoption decisions of consumers depend on two kinds of benefits: first, on the technical capabilities of the product itself, given by a, and b,, respectively, and second, on the network effect n (that is, whether the other generation adopts the same technology). All benefits are measured in terms of the adopters’ willingness to pay. Technical progress of both products implies that a,-~,>0

and

b,-b,>O.

(1)

Consumers’ propensity to pay is higher for the improved product in the second period. One more definition has to be introduced for notational convenience: we define the relative lead of technology B over A in period t Finally, we assume that all with A,, i.e. A, =bl -a, and A,=b,-a,. participants have perfect information and act as Nash players taking the actions of others as given. To select unique equilibria we will use the concept of subgame perfectness.

3. Welfare optimum The welfare optimum is defined as the surplus-maximizing adoption structure of the two technologies A and B. Since marginal production costs are zero, a social planner should maximize the sum of gross value for the 5We abstract from uncertainty and the formation or expectations. The effects of different informational structures are discussed in, for example, Farrell and Saloner (1985). Cowan (1991) for instance, discusses the importance of small events in an uncertain environment. 6For a more detailed argument on that point, see Katz and Shapiro (1986b). ‘The precise conditions of price setting depend on the type of contract and are discussed in section 4.

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two consumer generations. He can choose between the four possible adoption structures (A,;AL), (A,; B2), (B,;A,), and (B,;B,).8 Since the cost for an extra unit of that good is zero and the consumers’ valuation is positive, the first generation should participate in the technological progress for efficiency reasons and receive the improved product in the second period. The social planner therefore selects the maximum value of social benefits from a, +2a,

+2n,

with (A,; A,),9

+a2

+b,,

with (A,; B2),

bl +b +a,,

with (B,; AZ),

b, + 2b, + 24

with (B,; B,).

a1

For a given network effect of n, the optimal adoption depends on the relative lead (A, and AZ) of technology B. Fig. 1 illustrates the adoption pattern that would be selected by a social planner, where n is used as unit of measurement. We draw the lead of technology B in period 1 on the horizontal axis (A,) and the lead in period 2 on the vertical axis (AZ). The north-eastern sector represents the cases in which technology B is superior in both periods. In the north-western sector technology B is inferior in the first period, but better in the following period. In order to use the same graphical presentation in the case of market solutions we have to reduce the degrees of freedom. For that reason we suppose the technological progress for good A to be a2 -a, = 4n. This - together with the assumption of positive technological progress (b2 -b, > 0) - limits the possible solutions to the area left of and above the line LL: AZ-A,

= -4n.

(2)

The points beneath the straight line would imply a negative progress for technology B. The social planner’s calculation leads to the adoption pattern as shown in fig. 1. It will be optimal to standardize on either (A,;AJ or (B,;B,), if the difference of technological capabilities (-A,, AZ) is close to the size of the network effect (n). Variety in technologies (A,;B,) will be desirable only if both of the following statements are true. First, comparing standardization on A with non-standardization, the benefit from the second-period lead of technology B (A,) must be higher than the loss of the network for both ‘The first letter determines the technology for generation 1 and the second letter generation 2. ‘The social benefit consists of a, + a2 + n for generation 1 and a, + n for generation 2.

for

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progress

Fig. 1. Optimal adoption.

consumers (2n). Secondly, comparing variety with the standardization on B, the temporary lead of technology A (-A 1) can overcompensate the loss of a network (2n) plus the lead of technology B in t =2 (A,). These two conditions, A, >2n and -A, >2n+ A,, describe the triangle of nonadoption structure standardization in fig. 1. lo The surplus-maximizing constitutes the benchmark for the outcome under market contracts.

4. Market contracts 4.1. Simple market contracts What lies behind the notion of ‘simple market contracts’? The purchase of the good only involves a product of current technological state. The availability of improved versions in the future is not part of such contracts. This is a very common contract in many real-world exchanges. In terms of our software example, consumers have to purchase every improved version at current market prices if they want to participate in the technological improvement of their word processing system. Producers do not deliver any loThe margins

A2 = 2n and

-A 1 = 2n + A, are represented

by lines MO and NO, respectively.

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215

update versions. From the viewpoint of the firms, such contracts imply that price discrimination between old and new users is not possible. Promises to charge lower prices in the future for all adopters are not credible. (Recall the concept of subgame perfectness.) To determine the adoption structure under these market contracts, we have to set up the consumers’ calculation. Because of the network effect, the decision of every generation depends on the other generation’s adoption. So the two consumer groups face the following decision problem: The player of the first generation prefers A 1 { ><}B,, if

n+a, +a2-PA,

-P,,{2j}b,+b,-P,1-P,,

supposingA,

(3)

supposing&.

(4)

or aI +a,-PP,,

-P,,{><}n+b,+b,-P,,-P,,

The equivalent decision, A, { ><}B,, for the player of generation 2 is n+a,-P,,{s)b,-P,,

supposingA,

(5)

a,-PP,,{><}n+b,-P,,

supposingB,.

(6)

or

Given the adoption of the other generation, any consumer chooses the technology with the highest net benefit (i.e. gross benefit minus payments).” To solve the game we have to find the equilibrium prices of the firms. Bertrand competition leads to an equilibrium in prices, where the successful entrepreneur still earns positive profits while the defeated one has zero profits. All profits are defined relative to the best alternative. For example, winning the next period for sure a firm has to compare the profits from winning both periods with the profit from second period alone. (Recall that the difference is higher than first-period profits because of the network effect.) Take first period consumer decision as given by A,. Then the secondperiod consumer has to consider the adoption calculus of (5). So he will also purchase the A technology (AZ), if the price P,,Sn-A,+P,,.

The producer

of technology

(7)

A has an incentive to fulfil that condition

if

“To be slightly more precise, we have to point out that the preceding formulation implies that the first generation purchases an improved version of the product in the second period. But second-period prices may be higher than the valuation of the technological progress the product contains. In those cases, consumers would not buy the new version and would remain with the old level of technology. In the formulation of the model, this is equivalent to replacing secondperiod prices for the older generation with the value of technological progress (PA2 =a2 -a, or P,, = b2 -b,). Recall that first-period consumers can never switch to the other technology in the second period.

M. Thum, Network

276

externalities.

technological

there are still positive profits to be earned generations, which is equivalent to

from

progress

selling

to both

consumer

If the price attainable is lower, the firm would be better off selling only improved versions to the old generation; it could then ask for P,, =a2 -aI. To avoid a reaction from the competitor, the producer of the B technology has to be on his zero profit level P& = 0. Combining

(9)

conditions

(7), (8), and (9), we obtain

Therefore, technology A will win the competition in the second period if there is a price P,, that fultils the inequalities. Such a price always exists for (az --al) 12(n - A,).” The profit-maximizing firm would set the price at the maximum level, which is marginal1 below n-d,. For simplicity we say P,, =n- A,. Turning the argument around, technology B would win the second-period competition for (a2 -a,) > 2(n - AJ with a price of PBz= -n+A,+37?.

Because of first-period adopters, technology A would still have positive sales in the second period. The first generation would buy an improved version for the maximum price of P,, =uz --a,, which reflects the value of technological progress. Undertaking the same calculations for the case where first-period condecision of (6) subject sumers bought B,, we have to consider the adoption to A’s profit constraint P,, 20 and B’s zero profit constraint P,, = (b2 -b,)/2. A is successful for all parameter constellations with

-

Osp

Using

-

AZ5-n-A

(~2 -a,)

“In our graphical AA in fig. 2).

=4n,

2

+h-hl

this yields

example,

2

(11)

’

an adoption

where (a 2-a,)=4n,

of A,,

the condition

if A, + A, 52n,

reduces

to A,5

and

an

-II (below line

M. Thum, Network externalities,

Fig. 2. Adoption

technological

with simple market

progress

217

contracts.

adoption of B, with price P,, =n+ A,, if A, + A, > 2n. If technology B is defeated in the second period, the firm will sell the updated version for P,, = b, -b, to the old adopters. The economic interpretation is straightforward. The new adopter is confronted with an installed base of the technology chosen by first-period consumers. If the technological lead of one technology is large enough, it is always superior to adopt that technology independent of other users. But if the technological lead changes over time or is small relative to the network effect, the adopter is better off choosing an incompatible technology. The reason is that producers make higher profits delivering the improved versions to the old users than selling to new adopters. The second-period decision is illustrated by lines AA: A 2 = - n and BB: A 1 + A, = 2n in fig. 2. Below the line AA consumers will adopt A, in the second period if first-period purchases are A,. The area above the BB line represents the parameters where B, is the best response to B,. In between these two lines adopting the nonstandardization technology is the best action for second-period consumers. Given the second-period prices, we can calculate the adoption decisions of the first generation. Given that technology A, will be successful in period 2

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M. Thum, Network externalities, technological progress

the adopter decides as described in condition (3). Substituting P,, = n - A, and P,, = b, -b, leads to the decision Ai(g1BioA2

-A,--PA,

Using the positive profit condition of Bi3 gives A, + A, <6n-(a2

the prices with

Wbr-a&‘,1.

constraint

for producer

A and

the

zero

profit

--al)

as the condition for the adoption of A in the starting period. This condition is always true under the assumptions made of successful technology A in period 2 [(IO) and (1 l)] and the conditions of technological progress C(l)]. An analogous reasoning confirms the result for technology B. If B is successful in the second period independent of first-period outcome, technology B will also be chosen in the first period. Therefore, we get standardization on (A, ; A,) or (B,; B2) in the dark shaded areas of fig. 2. To describe the full allocation, the triangle of non-standardization in fig. 2 has to be explained. Every adopter knows that he cannot reach standardization because of the price-setting behavior of firms. The calculation of lirstperiod adopters compares A, {P)Brea,+a,-P,,

-P,,

{PPr+b,-P,,-P,,.

Firms make higher profits selling only updates during period 2. Competing for the second generation would require prices to be lowered so much that total profits would fall. Hence, second-period prices will be equal to the value of technological progress. An analogous calculation to the one above gives A, gA2 as the condition for (A,;B,) and A, > A2 as the condition for (B,; Ax). The lirm that has a comparative technological advantage in the first period can attract adopters. First-period success allows higher profits due to the ‘update’ versions in the next period. The solutions of non-standardization contain a kind of implicit collusion. The impossibility of price discrimination and the relatively large technological progress eliminate competition during period 2. Each firm concentrates on one of the two consumer generations. One important point is still missing. So far we have assumed that the first consumer generation always purchases the improved product. But the second-period price may be higher than the value of technological progress. In a limited range the producer would decrease the price a little to the level of technological progress. However, the technological progress may be so low 13The profit constraint results from the comparison of profits in both periods with profits from winning only the second period. The zero profit condition says that the producer of technology B must be indifferent between winning first period (plus selling updates in the second period) and not selling at all. By assumption, he will never win the second period.

M. Thum, Network externalities, technological progress

1 2 3 4 5 6 7

219

AB instead of AA AB instead of BB BA instead of AA BA instead of BB AA instead of BB a, instead of a2 b, instead of b,

Fig. 3. Suboptimal allocation with simple market contracts.

that including the first generation lowers the firms’ profits. Under these circumstances, prices are set too high to let the old generation take part in the technological advances. That will happen whenever the technological lead in the second period (d2) is relatively large, but the technological progress from the first to the second period is relatively small. Then, earning twice the value of progress is less than the proceeds from selling to the second generation alone. Consumers of A will not buy the improved version of their product if n-d, > 2(a, -al). In fig. 2 this case is represented by the area below the line CC. The analogous condition for technology B (n+d, > 2(bz -b,)) is satisfied right of the line DD in fig. 2. The adoption structure is the same as in the rest of the shaded area. Adopters work with standardized products, but the technology used does not incorporate the state of the art. To apply welfare analysis we have to compare the market outcome with the optimal adoption derived in section 3. A comparison between fig. 1 (optimum) and fig. 2 (market) shows the following deviations from the welfare-maximizing adoption structure (fig. 3): too little standardization results in cases 1 to 4. Optimally requires homogeneous technologies, but the

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technical progress of the lirst-period winner is high. In a market environment profit-maximizing firms set prices too high for second-period adopters and sell only improved products to old users. Standardization on the wrong technology - as illustrated in area 5 - comes from an asymmetry between the two generations: the second generation does not care about first-period benefits and adopts technology A independent of the first generation’s action. Therefore, the old generation - anticipating that behavior - is better off choosing the compatible product to gain the network effect instead of adopting the technologically higher valued B product. The third form of misallocation relies on the incapacity of simple market contracts to discriminate between old and new users. Under the parameter values of cases 6 and 7, the older generation cannot get an improved version for a price reflecting the amount of technological progress. The delivery of an update version would improve total welfare, because marginal costs of production are zero and the value of progress is clearly positive. Summing up these results leads to the conclusion that simple market contracts generate an inferior allocation of adoption paths for a wide range of parameters. Overall there is too little standardization with the market solution.

4.2.

Update contracts

Update contracts, too, capture only the delivery of the current period. Although intertemporally effective contracts are still unavailable, firms can distinguish between old and new users. This allows the selling of so-called ‘updates’ exclusively to customers who purchased the product in earlier periods.i4 In other words, firms can engage in price discrimination between the consumer generations. However, there is a natural upper limit for update prices: a firm never will sell an update for a higher price than it charges for a new product. Hence, update contracts only exist where the value of technological progress is lower than the current market price. This kind of contract improves the appropriability of benefits for the suppliers only in a small range of parameters and, as we will see, leaves the competition between firms unchanged. Therefore, the transition from simple market contracts to update contracts only eliminates the case where old adopters could not get the improved product, but does not change the adoption structure. Although update contracts are a common feature in markets with high technological

14This definition of price-discriminating updates is restrictive. Another type of update contracts could also offer lower prices to the old users of the competitor’s product to facilitate switching and establish quickly an installed base. Some software producers use this strategy to overcome a potential lock-in on the rival’s technology. This possibility might be relevant for some products and it would be interesting to pursue the implications. Here it was assumed that switching costs are too high and preclude this type of contract.

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change such as standard software, the allocative advantage of these contracts is low. This result will be shown formally in the slightly modified model of the previous sector. First-period consumers’ adoption decision gives the relation A, { p} B, for - Py, { ><>b, + b, - P,, - Pj,

supposing

A,

(12)

- P& ( 2 } n + b, + b, - P,, - Pi,

supposing

B,,

(13)

n+a, +az-PA, or al +a,

-PA,

where P:, and Pj, denote the update prices for technology A and technology B, respectively. The calculation of second-period adoption obviously is the same as for the simple market contracts [I(S) and (6)]. To calculate first-period adoption we have to determine the second-period price the producer will charge his old customers. To show that the adoption structure will be the same under both update contracts and simple market contracts, a simple consideration saves a lot of calculations. Using update contracts, the profit-maximizing supplier tries to appropriate the full benefit of technological progress. Therefore, the update price will be equal to the value of the product improvement (P”,, =a2-a, and Pi,= b, -b,). Under simple market contracts also, these prices were set in the second period whenever a firm could only win first-period competition. Therefore, no difference between update and simple market contracts can occur for the allocations A, B, and B,A,. What will happen if a producer succeeds in both periods? An update contract will only be accepted by customers if the technological progress is below the market price for new users. Otherwise the users would buy a fully new product instead of the update version. For the cases P,, =n-Ad, a2 -a, given A, (below EE) and n + A, > b, -b, given B, (right of FF). Looking at the welfare effects of update contracts, we can refer to the corresponding analysis for simple market contracts in fig. 3. As shown above, the allocation of non-standardized technologies is the same for both contracts. Therefore, update contracts cannot reduce the problem of too little standardization that we recognized in our analysis of simple market contracts (sectors 1 to 4 in fig. 3). However, update contract offer an efficiency gain for the provision of improved products (sectors 6 and 7 in fig. 3). The price discrimination between old and new users allows firms to sell their new

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products to both old users (as updates) and new users. The first generation should take part in technological progress because marginal cost is zero and will do so because the firms have the possibility of discriminating between update prices and new product prices.

4.3. Service contracts As a last stylized contract we discuss agreements with intertemporal commitment. Under a service contract, the consumer simultaneously buys all improved future versions with the initial purchase of the good. The contract binds the producer to a free delivery of technological advance. Therefore, the price will also cover the benefits of all future periods. Obviously we cannot observe many contracts of this type in the real world. The main reason for the lack of such contracts may be the moral hazard problem. Service contracts could create a principal-agent relation between user and producer, because this long-term contract may lead to a hidden decrease in the innovation effort. The problem of moral hazard could keep customers from accepting contracts of the service type. Therefore, service contracts can only be seen in those lields where technological progress is exogenously given and objectively observable. In practice, service contracts are made, for example, for anti-virus programs, where the necessary technological progress is given by the emergence of a new computer virus, or for accounting software, where the necessary improvements are defined by changes in laws or modified requirements of trading partners.r5 Again, a slight modification of the simple market approach allows us to implement the adoption decision under service contracts in our model. The older generation pays only in the first period, and the payment is denoted by The decision problem for the second generation P;, and Pf,,, respectively. remains unchanged C(5) and (6)]. The first generation’s adoption decision A1 (2 ) B1 can then be written as n+a,+a,-PS,,{~)b,+b,-Pi,

supposingA,

(14)

a,+a,-PslI{p},+bl+b,-P~,

supposing&.

(15)

or

As in the preceding sections, the adoption problem has to be solved backwards. Starting with the second period, we solve the purchasing problem for the new consumer group. Assume that technology Ai was successful in the preceding competition. Then second-period consumers will also buy

l5To turn the argument examples), the market cannot

around, whenever service contracts are observed exhibit hidden action on the producers’ side.

(as

in these

283

m

[I] AB instead of AA

a

[2]

BB instead of AB

131BB instead of AA 141

AA instead of BB

Fig. 4. Adoption and suboptimal allocation with service contracts.

technology A, if A2 5 11.l6 For a first-period purchase of technology B the new generation will buy technology B, if A2 > --n. Fig. 4 makes these conditions intuitively more appealing. The conditions just tell us that, if the second-period technological lead of one technology is larger than the network effect, this technology will be adopted independent of first-period consumers’ choice. Above the line GG, the B technology is better for the consumer (even if the older generation uses the A technoiogy) and below the line NH the A technology is always superior. In between these two lines the decision of a second-period adopter depends on the first-period choice. The new generation follows the old one in its decision because the network effect is large relative to the technological lead of one product. For the older generation’s technology choice we have to differentiate between the three possible second-period outcomes: A, will be chosen in any case, B, will be chosen in any case, and A, or B, will be chosen dependent on the first-period choice. In the first case A will also be successful in the first period (below HN). Given B, we know from (15) and from the profit lbThe only diKerence to the preceding section concerns the modification to the positive profit condition for A (PAI 20).

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progress

conditions that firm B can always set a price to win the first period as well if d 1 + A, > -3n. In the graph (fig. 4) this condition is represented by the line JJ. Below JJ (but above GG) the first generation is better off adopting the A technology alone than joining the next generation that will choose the B technology in any case. Let us turn now to the most interesting case where the second generation’s decision depends on the choice of the previous consumers (-ns A, snn). The first generation knows that the next consumers will follow their technology choice to benefit from the relatively large network effect. In that sense they act as leaders in this game and can choose their own most preferred network technology. Therefore, their decision problem is

Substituting the price Pi, from the zero profit condition for B (Pi1 = -n-A,) and using the positive profit condition for A (P”,, 2 A, -n) leads to the statement that A, will be adopted whenever A, +3A, SO. Reversing the inequality defines the cases in which technology B, will be adopted. The line separating the two adoption patterns A, A2 and B,B, is shown in fig. 4 by KK. We have now described the complete adoption structure under service contracts. In a wide range of parameters full standardization will occur; nonstandardization may emerge only if the technological lead changes dramatically. Whether the ability of these contracts to capture the benefits of multiple periods is sufficient to improve the allocation of technology choices has to be examined in comparison with the welfare optimal adoption pattern of section 3. The multiplicity of possible cases gives our problem a complicated appearance, but the basic result is quite simple: service contracts favor the future generation and lead to too much technical change (excess momentum). To understand this phenomenon, we take a closer look at our model by comparing the adoption outcome under service contracts with the optimal adoption (see fig. 4). In sector [l] the new generation buys technology B,, although it should form a network on the A technology. For the older generation it is still best to purchase the A technology because of the relatively large technological lead in the first period. In sectors [2] and [3] the older consumers are even forced to adopt the B technology, which is only superior in the second period, because they know that the next generation will adopt B, in any case. So they are better off accepting this technology so as to at least benefit from the network effect. If side payments were possible, the older generation could make offers (in case [3]) to persuade the next generation to choose the best common outcome, but market contracts exclude such solutions. (Sector [4] is just the reverse case of sector [3].) Analyzing the inefficiencies under service contracts, we can no longer say

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285

anything in general about too much or too little standardization. Whereas simple market contracts or update contracts always resulted in an underprovision of standards, service contracts give preferential treatment to the best future technology. This excessive technical change emerges from the asymmetry in contracts. A leading firm in the early competition can never make credible promises to lower the future price sufficiently to also win the next generation. But tomorrow’s leading supplier can already today commit itself to a price valid for both points. This contracting instrument makes it easier for him to convince even the first-period users who anticipate the future adoption and therefore are willing to forgo current benefits in favor of the network effect and the future improvements (sectors [2], [3], and [4-J). 5. Co~~tition

of the contracts

So far we have discussed different types of contracts as if each type were given exogenously. In fact, firms can choose with which contracts they compete for customers. The producers select not only their price strategy but also the type of contract. Therefore, we can analyze the conditions under which each contract is optimal for firms. Before the market game starts, each firm chooses the profit-maximizing contract given the type of contract the other firm will offer. Since no one wants to deviate any more, we have a Nash solution in contracts. If more than one such equilibrium exists, we will assume that firms focus on the one mutually preferred. We can simplify the following discussion, starting with a comparison of market and update contracts. As is known from subsection 4.2, the contracts are identical except for the range of parameters where non-discriminating market contracts were unable to allow the older generation to participate in technological progress. Update contracts allow a higher appropriability of the willingness to pay and therefore increase profits. In all other cases the firms will be indifferent to either of the two contracts and their choice must remain arbitrary in our model. This simple discussion allows us to reduce the contract competition to a comparison of service contracts with the update type only. To play this selection game, we have to calculate not only the profits for the pure solutions, i.e. both firms choose the same contract either update or service, but also the profits from the intermediate solutions, where one offers a service and the other an update contract. The derivation of market outcomes under pure update contracts and pure service contracts has been done extensively in section 4. To complete the discussion we would have to calculate the mixed cases and then play the Nash game for any possible combination. To abbreviate this lengthy procedure outlined in the previous sections, we turn immediately to the resulting allocations and types of contract depicted in fig. 5.

286

M. Thum, Nenvork

externalities,

/

Fig. 5. Allocation

I

technolo@d

progwss

121 1 update

with contract

/

competition.

Now we are able to summarize the endogenous emergence of different contract types from network effects and technical progress: if the technical lead of one technology is high in both periods, service and update contracts will equally fit the profit-maximizing calculus of firms.” Simple market contracts show up as inferior because of their lack of discriminating new and old users; the old users’ willingness to pay could not be absorbed. At the other extreme, where the technological lead changes considerably and nonstandardization occurs, the update contract dominates. It allows firms to play implicitly collusive strategies in that both firms concentrate on appropriating the purchasing power of ‘their’ generation and therefore lower the competition in the other period. Adjacent to this technological diversity case, standardization on one technology is reached through service contracts. The margin between the A, B, and t’he A,A, allocations (or between A1 B, and BIB,, respectively) is marked by the equality of profits from winning both periods or only the first (the second) one. The winner in the race for de facto “Although in the mode1 a variety of possible contracts results, real markets may sometimes only yield update contracts. If one firm alone dominates the market and the innovation effort cannot be perfectly observed, the principal-agent problem will be extremely severe and consumers will not acccept contracts of the service type.

M. Thum, Network externalities, technological progress

n

’

0). ,

287

/

of AA of BB of AA

1:

AB

2:

AB instead

;;

AA instead of BB

instead

BB instead

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allocation

with contract

competition.

standardization is only able to commit himself sufficiently to low prices with service contracts. Under update conditions, consumers know that the producers will charge them the full value of technical progress in the future, and therefore modify their adoption decision so that non-standardization would occur. l8 Lastly, it remains to compare the outcome of contract competition with the welfare optimum. The deviations from rent-maximizing allocation are plotted in fig. 6. Comparing the remaining inefficiencies to the misallocation under simple market or update contracts, we observe a considerable reduction in the parameter range of suboptimal adoption, but there is still too little standardization. This result will change to excess momentum (too much of the future leading technology is adopted) as in the case of service contracts, if the technological progress (~~-a,) goes to zero. Then the whole system of contract competition converges to the service case. Combining the 18To complete the discussion we have to explain the numbered cases (1 and 2). Standardization on the B technology will occur in any case, and the network effect is larger than the second-period lead d 2. Therefore, first-period competition also decides the second-period outcome (second-period consumers act as followers). Hence, service contracts are inferior for the B firm, because they leave more payment to the period with higher competition.

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results from the single contracts and the contract competition we can conclude that the competition of several possible contracts reduces the inefficient allocations by a considerable amount. The area of suboptimal adoption structures is clearly smaller under contract competition than under pure update or simple markets contracts (but not necessarily smaller than under service contracts). The creativity of markets improves the adoption process, but even the competition of the contracts will not fully reach the welfare optimal allocation.

6. Concluding

remarks

Summing up our previous discussion, we were able to show that the different adoption inefficiencies known from the recent literature may be caused by technological progress and network externalities if different contracts are assumed. Furthermore, the existence of the various contract types, which we observe in real markets such as those for software products, can be explained by the incentives of profit-maximizing firms. This selection of contracts through competitive behavior helps to overcome some of the severest inefficiencies with market endogenous mechanisms alone. Clearly, the possibility of an inefficient outcome always remains, but the allocative problems from the network effect are lower than, for example, in a (modified) model of Katz and Shapiro (1986a). Concerning these relatively strong inefficiency results which were outlined in the recent literature on standardization, Gilbert (1992, p. 8) therefore notes ‘that market forces might produce new institutions not addressed in these models to deal with these inefticienties’. As seen in the discussion of this paper, the allocative performance of markets improves simply by adding a simple strategic variable like the contract choice. In real markets many more of such strategies may exist, e.g. building converters.” “See, for example, Farrell and Saloner (1992) who also give a survey topics of converters and interfaces (pp. 1416).

on recent

work

on the

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Farrell, Joseph and Garth Saloner, 1992, Converters, compatibility, and the control of interfaces, Journal of Industrial Economics 40, 9-35. Gilbert, Richard J., 1992, Symposium on compatibility: Incentives and market structure, Journal of Industrial Economics 40, 1-8. Katz, Michael L. and Carl Shapiro, 1985, Network externalities, competition, and compatibility, American Economic Review 75, 424440. Katz, Michael L. and Carl Shapiro, 1986a, Technology adoption in the presence of network externalities, Journal of Political Economy 94, 822-841. Katz, Michael L. and Carl Shapiro, 1986b, Product compatibility choice in a market with technological progress, Oxford Economic Papers (Supplement) 38, 146165.