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How to Charge Lindahl Prices for IP goods
by Dietmar Detering, Ph.D.

Note: This article is in draft stage. Comments are welcome.

There can never be too many users of intellectual property (IP) goods. The costs of reproducing already-developed pharmaceuticals or media content (the marginal costs) are so low that it would be economically wasteful to exclude some potential buyers by charging prices that they would be unwilling or unable to pay. Swedish economist Eric Lindahl proved in 1919 that different prices for different people based on willingness to pay would result in optimal levels of public goods and would distribute costs in the fairest way possible. In the same way, private markets for IP goods could achieve fair and optimal results by charging as much as one is willing to pay for rights to use those goods. As a result, creators of IP goods would receive optimal incentives for the development of new, valuable goods, and everybody could afford rights to use any IP good. However, the required perfect price discrimination has been impossible to achieve.

This paper will explain the value of Lindahl-pricing for markets of IP goods and why it has been impossible to achieve in the past. It will then proceed to develop a new process that achieves Lindahl-pricing for any IP good on the expected average of all products bought by any consumer. Finally, several practical scenarios show how this new process can be implemented.

1          Why is Lindahl-Pricing of IP Goods Important?

For IP goods, the traditional rule that the price ideally equals marginal costs of production is not economically viable. The reason for this is that the initial costs of product development, design, and marketing account for the major portion of the total cost while the cost of reproduction is comparatively low. Setting prices equal to the marginal costs of these goods would prevent suppliers from recovering their product development costs.

However, setting prices above the marginal cost has several serious disadvantages. First, it excludes potential buyers only because their willingness to pay is lower than the asked price, even if their willingness to pay is still higher than the corresponding costs of reproduction. Second, microeconomic research has shown that uniform prices also result in an oversupply of product variety and an undersupply of product quality of IP goods and other so-called “differentiated goods”. In sum, (1) goods’ prices far exceed those prices that would need to be paid in a welfare optimal equilibrium, (2) consumers are severely limited in their freedom to use the existing variety of goods, and (3) products are of poor quality. (Compare, e.g., Economides 1993; Salop 1979; Waterman 1990.)

The only market-compatible way to solve the aforementioned problems is to charge perfectly differentiated prices where all buyers pay for any good exactly what it is worth to them. This way, IP goods could benefit anyone wherever and whenever the benefit of their use is higher than their costs of reproduction, meanwhile producers and creators receive sufficient revenue to cover costs and optimal incentives to develop new products. Even though this sounds as if the sellers would extract unreasonable amounts of money from buyers, this is not necessarily true. Competitors with close substitutes will undercut each other’s prices for each single buyer, leaving at least one seller with zero profit and reducing overall prices and revenue. This can leave consumers with a higher surplus than in conventional markets with uniform prices, as a simple example can prove:

The five movie theatres in a small town show only one motion picture each this month. For simplicity, we assume that – due to overcapacities – the costs of serving additional viewers is always zero to each theatre. We consider only one consumer: He perceives a different willingness to pay for each motion picture and has time to watch only three movies this month, and – for simplicity – we will ignore other months.

Figure 1a shows the conventional market with uniform prices for each buyer: The consumer faces fixed prices for each motion picture as indicated by boxes 106-110. In step 106-110, the consumer subtracts each theatre's uniform box office price from his willingness to pay for each movie (boxes 101-105) and purchases tickets to those movies that offer the highest surplus to him. Since he watches three movies, he chooses the theatres 1, 2, and 3. Boxes 114 and 115 show that the other two theatres will either render a very low ($1) or even a negative surplus to him. Calculating the overall market result in Box 116, the consumer has an aggregate willingness to pay of $27 for the three tickets, pays an aggregate price of $20, and realizes a total consumer surplus of $7.

Figure 1 a:
Conventional Market with Uniform Prices

Figure 1b considers the same setting only that this time the theatres compete for the consumer with perfect price discrimination. This time, the consumer pays a price equal to his marginal willingness to pay for any one of the movies. Looking at each movie, the consumer now knows that he would get tickets to the other four movies anyway: Price-discriminating, the theatres would undercut each other until all five have sold a ticket to the consumer, even though two theatres had to offer a price of zero because the consumer wants to see only three of the five movies. [1]

Given this new supplier behavior, the consumer calculates his marginal willingness to pay for each of the motion pictures in box 121-125. He does so by taking his willingness to pay for one movie and subtracting from it his willingness to pay for the next best movie that he would watch instead, knowing that he would have a ticket to it anyway. For example, in step 121, he calculates the difference between his willingness to pay for movie 1 and his willingness to pay for the movie he would substitute with movie 1. This movie is identified easily: Since he will watch only three movies, the movie with the fourth highest value to him (the third best alternative to movie 1) will be substituted by movie 1. Movie 4 would have the lowest value to him of those movies that he would watch in the case that he could not watch movie 1. The difference between his willingness to pay for these movies is $3, which is his marginal willingness to pay for movie 1. Correspondingly, step 122 calculates a marginal willingness to pay for movie 2 ($2) and step 123 calculates a marginal willingness to pay for movie 3 ($1). The consumer’s marginal willingness to pay for movies (4) and (5), however, is negative under these assumptions: He would already be able to see his favorite movies, and he has no desire to substitute one of them for a less desired movie. Correspondingly, he makes only a payment for each one of the other movies at the value of his marginal willingness to pay. As in box 116 of Figure 1a, box 131 of Figure 1b calculates his consumer surplus as the difference between his willingness to pay for the purchased tickets to movies 1-3 and his actual payment, showing that his consumer surplus tripled to $21.

Figure 1b:
Example of Lindahl-Pricing in a Simplified Setting

Of course, it would be easy to find some numbers for this example where uniform pricing would be more beneficial for the consumer than perfectly discriminating Lindahl-prices. However, Lindahl-pricing ensures market conditions in which IP goods are provided efficiently and at an optimal level because suppliers are only, but fully, compensated for their actual contribution to the welfare of the consumers. In turn, this ensures that consumers will retain a higher surplus even though the market volume (i.e., total revenue of the suppliers) might increase.

Unfortunately, the markets know only imperfect forms of price discrimination. Although superior to uniform pricing, all of them have serious limitations in their ability to cure the failure of markets for IP goods. There is no perfect price discrimination due to two problems. First, it would require prohibitively high transaction costs to establish a different price with each potential customer. Second, it is normally impossible to determine each buyer’s actual willingness to pay because it would be both very appealing and easy for the buyer to hide it.

2          Solution: Discount Clubs Using a Demand Revealing Process

Suppose there is a club that offers to its members rights to use a large number of different IP goods, ranging from pharmaceuticals to computer software, at the mere costs of reproduction. The monthly membership fee charged to members (less administrative costs) would go directly to the owners of the intellectual property rights in those goods and compensate them for their investments.

The problem with this type of club would be that neither its members nor the suppliers of the goods could trust it. Consumers would suspect that their monthly fees were overcompensating the producers, and each supplier would fear that the suppliers were being under-compensated for the value provided and that she herself was particularly bad off. What is required is a process that reveals all club members’ willingness to pay for each right to use a particular IP good, producing clear proof that everyone involved is being treated fairly.

Clarke's Demand Revealing Process (DRP, compare Clarke 1971) can determine a group’s aggregate willingness to pay for public goods. In a club setting, each member’s right to use an IP good at the cost of reproduction can be understood as a public good of that club. However, prior applications of the DRP have been limited to discrete or continuous decisions on the reproduction of public goods or other activities that do not depend on or affect other persons outside the voting group. For example, applications of the DRP have been able to determine whether producing a certain public good was worthwhile or not. Also, it would be able to determine the proper amount to be invested on a public good so as to maximize welfare. (Compare Tideman and Tullock 1976)

A simple example can show how the DRP would work when directly applied to the setting of a discount club buying a use right: The computer program megasoft is available in retail trade for 50 US$. Table 1 shows the willingness to pay of consumers 1-10, representing all members of the discount club. The supplier estimates the club’s total willingness to pay for the right of every member to use megasoft for free to be $100 and makes a corresponding offer to the club: If accepted, everybody can use megasoft and everybody has to pay $10.

The club then votes on the offer by using the DRP. Here, each member not only indicates which decision he favors but also how much he favors that particular outcome. Member 1, for example, has a willingness to pay of $60 and would acquire megasoft for $50 in retail trade. With the collective purchase, he would save $40 over the the retail price. Thus, he votes with this value in favor of the collective purchase. Members 2-9 behave similarly.

Of course, neither voter will want to understate her willingness to pay in favor of a particular outcome. The more willingness to pay shows up favoring one side, the more likely this side is to win. However, Table 1 also shows how the DRP ensures that voters are not going to overstate their willingness to pay either. It does so by charging a pivotal tax, the key component of Clarke’s DRP, to those voters who swing the vote with their stated willingness to pay alone. In the present example, the decision would have resultet in $60 to $55 against the acquisition of megasoft without the vote of member 1. This shows that, by participating, member 1 has swung the vote in his favor, resulting in a net loss for everybody else of $5. Paying these $5 as a pivotal tax still leaves member 1 with a net benefit of $35 (willingness to pay for outcome of $40 less the pivotal tax of $5). [2]

A voter who overstates his willingness to pay for a certain outcome, however, attempts to swing the vote even if, as a result of him swinging the vote, the net loss to all other voters is higher than his personal gain. By charging him a pivotal tax equal to the net loss of all other voters, he would be worse off since the pivotal tax exceed his benefits of swinging the vote in such cases. [3]

Table 1:
Club Member 1 Swings the Vote with Her Participation and Pays a Pivotal Tax

Club member

Willingness to pay

Vote “Pro“

Vote “Contra“

Pivotal tax















































Clearly, decision-making costs are very high in the DRP when everybody gets involved in a vote on each single offer. Yet, there are two additional problems that Lindahl-pricing of IP goods has to overcome:

(1) The likelihood that an offer will be rejected can be very high. This is because suppliers will try to get a price as high as possible but can only guess how high the club’s willingness to pay for the right to use their IP good is. In the above example, the supplier could have asked for only $50 just to make sure that his offer is being accepted, but he would have made $50 less than he actually did. He could also have tried to ask for more, perhaps $200, but the voters would have rejected that offer, leaving the supplier with no revenue at all. [4] Such an outcome means a waste of resources because the IP good in consideration already exists and should be used by anybody willing to pay its costs of reproduction.

(2) In order for an offer to be accepted, the price has to be as low or lower than the collective willingness to pay for that particular use right. However, this means that the suppliers’ proceeds are either zero because their offer got rejected or they are still lower than they should be as a fair compensation for their provided value.

Due to these problems, the suppliers revenue would be below what they should achieve with true Lindahl-pricing and consumers would remain excluded from many IP goods. The solution comes in form of a refined procudure that was initially suggested by Green and Laffont (1977) to solve other problems of the DRP: Only a representative (random) sample of the club’s members votes on any particular offer. Then, the sample’s revealed willingness to pay for the offer determines the price that all non-voters have to pay for the offered use right irrespective of their actual personal willingness to pay. However, voting sample members still are either being excluded from the use right or, if they had accepted the offer, pay the price determined before they voted. (See Figure 2)

This way, every club member who is not part of the voting sample gets the right to use the offered IP goods at costs of reproduction. Members pay a price for those rights that averages on all purchased offers and on the average of all club members the Lindahl prices for each offer, this way compensating intellectual property owners in a fair and welfare-maximizing way. Members experience exceptions from this only for those IP goods that they were voting on as part of a voting sample.

Figure 2:
Flowchart of Lindahl-Pricing of IP Goods in a Discount Club

3          Distribution of IP Goods

Owning the use rights alone will not satisfy the buyers – they will have to be able to exercise those rights as well. There are many ways to provide owners of use rights with the desired IP goods, as long as they are coupled with systems to prevent users from giving those goods to others who don’t have the corresponding use rights. Pharmaceuticals can continue to be prescribed by doctors, and either the prescribing doctors or the pharmacies are making sure that the patient has the proper use rights. Media content can be distributed either from centralized servers or in peer-to-peer networks. Network and server costs can be incorporated in network access fees or charged separately.

For many IP goods, costs of reproduction, distribution, and liability are not as negligible as those of media content. The corresponding use prices paid by owners of the use rights could be left to market competition. Other reproducers could receive licences to provide the corresponding goods at competitive prices. For example, a competition among producers of generic medicine would result in a competition for price, purity, consistency, and effectiveness of administrations of the same active substance.

4          Practical Implemantations

4.1        Cable TV Services

A practical implementation of Lindahl-pricing for IP goods could start with a cable TV service where large numbers of subscribers with an existing billing infrastructure are already available. In order to give subscribers enough time to develop a sense of value, the operator will introduce new channels or premium services for a few weeks each. After that, random voting samples decide whether they want to keep a certain new offering in exchange for an increase in monthly fees. Similarly, all the channels previously included in the bundled cable service could be offered for a demand-revealing vote by samples of subscribers.

Later, cable operators could offer access to many more kinds of IP goods this way, delivering more and more through their infrastructure to subscribers. Computer software and games, music, encyclopaedias, information databases, and electronic books are good examples, provided that copyright protection is working well to ensure non-transferability of those goods. Even use rights to pharmaceuticals could be among the offered goods. [5]

4.2        Online Music Networks, Yahoo, Real Media, AOL, MSN, and Others

Preparing or offering premium content services already, internet services can create a serious alternative to cable TV services – not only in providing audio-visiual entertainment but also in offering an infrastructure for Lindahl-pricing clubs for other IP goods. Already, millions of consumers are subscribers to such networks, paying $10 - $15 per month to receive premium content through their internet connections. Value and revenue could be vastly increased by extending the offering to anything that can be delivered online.

4.3        Government

Governments could use the presented Lindahl-pricing method to provide access to all IP goods to all citizens and fair compensation to the suppliers, too. It would be irrelevant whether the government would levy a special tax on citizens to make payments to the suppliers or whether it would pay it out of general tax income. It is only important that the government uses the described application of the DRP to determine the fair compensation for suppliers and provides access to any IP good ever produced.

5          Other Issues

In cases of hardship where members of a voting sample that rejected a use right depend on having access to it, members still would have the option of switching to another discount club that has that IP good included in the basket for new members.  Given relatively high switching costs (e.g., paperwork, fees), this option would only insignificantly reduce the incentive to vote truthfully when being a member of a voting sample.

However, if the government offers this method of Lindahl-pricing, there might be only a single “club” and switching is impossible. As an alternative, such unlucky voting members could be allowed to purchase the desired IP good through traditional uniform pricing models. Insurances or loan programs could help overcome burdens of hardship without much effect on the demand revelation.

Allowing consumers to switch or quit club membership and allowing independent clubs to freely accept, reject, and expel members will also help to form groups that are homogeneous with respect to the members’ interests in different IP goods and their abilities to pay. Two forms of competition will evolve:
(1) competition among the clubs for members with low willingness to pay who decrease the club’s aggregate willingness to pay for offers and thus decrease the prices paid; and
(2) consumers’ competition for membership in clubs with a lower aggregate willingness  than their own.
Both forms of competition jointly increase the likelihood that a consumer will be able to find a group where membership is beneficial for him/her.

This paper did not discuss how the new pricing process can benefit business, even though modern business relies heavily on IP goods in forms of computer software, information database, etc. The problem is that the total value that different business entities derive from IP goods varies much more than between individual consumers. For example, a small bakery would have gain much less from accessing the LexiNexis information network than a large lawfirm. However, an attractive and fair solution can be imagined with (1) businesses forming discount clubs separated along industry boundaries and (2) DRP voting power, pivotal taxes, and payments for use rights would be scaled along annual revenue figures.

6          Conclusion

This paper has presented a pricing method that restores properties of free markets where traditional markets fail. The resulting benefits are worth fighting for: Not only can producers receive optimal incentives to produce new and valuable IP goods, but also can every person gain unlimited access to all IP goods – whether they are for learning, healing, or entertaining. Overall, this Lindahl-pricing method can increase the wealth of entire societies by guaranteeing maximum use of the world’s information industries’ output. A fair and generous reward will be offered to the producers of quality IP goods, and there will be no need anymore for fair use fights over copyright law and bureaucratic controls of drug expenditure growth.

7          Bibliography

Clarke, Edward H. 1971. Multipart Pricing of Public Goods. Public Choice 11: 17-33.

Economides, Nicholas. 1993. Quality Variations in the Circular Model of Variety-Differentiated Products. Regional Science and Urban Economics 23: 235-257.

Green, Jerry and Jean-Jacques Laffont. 1977. Imperfect Personal Information and the Demand Revealing Process. A Sampling Approach. Public Choice 29 (2/special issue): 79-94.

Salop, Stephen C. 1979. Monopolistic Competition with Outside Goods. Bell Journal of Economics 10: 141-156.

Tideman, T. Nicolaus and Gordon Tullock. 1976. A New and Superior Process for Making Social Choices. Journal of Political Economy 84 (6): 1145-1159.

Waterman, David. 1990. Diversity and Quality of Information Products in a Monopolistically Competitive Industry. Information Economics and Policy 1989/90 (4): 291-303.

[1] Of course, this setting requires that the tickets are personal and non-transferable in order to prevent resale of unwanted tickets to other consumers with a preference for those movies.

[2] Since there is no need for the proceeds from the pivotal tax, it would be least irritating to the DRP to waste them. However, the literature shows several models that minimize undesirable side incentives for voters when the pivotal tax proceeds are being redistributed.

[3] Here, the pivotal tax is being calculated as the difference between approving and rejecting votes under exclusion of the pivotal voter, which represents the welfare loss to everybody else in the group due to the pivotal voter swinging the vote. However, the incentive to truthfully reveal one’s willingness to pay in the DRP could be achieved by calculating a pivotal tax as the difference between approving and rejecting votes under inclusion of the pivotal voter under consideration as well. This is economically less obvious, but, for a correct incentive, it is merely important that the risk of paying a pivotal tax and the tax’s magnitude is equally high when overstating one’s willingness to pay for a certain outcome. Either way, only pivotal voters pay a pivotal tax and its magnitude is anywhere between one cent and the voted value.

[4] Repeat offers (with a lower price) should be avoided because their mere possibility could encourage strategic understatements of pro-voters.

[5] However, this seems to be irrelevant as long as most people benefit from health insurance that pays any price demanded by pharmaceutical companies if the medication is needed.

Ökonomie der Medieninhalte.
Allokative Effizienz und Soziale Chancengleichheit in den Neuen Medien
© copyright 1999-2001 Dietmar Detering. All Rights Reserved.

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