Copyright Collectives and
Contracts: An Economic Theory
Perspective
Richard Watt (University of Canterbury and SERCI)
 Efficiency of collective management of copyright
 Standard theory is based on transaction costs
 Also, collectives are normally assumed to undertake 3 roles
 Licensing access to users
 Distributing royalty income to members
 Enforcing against infringement
 I will add a further rationale to the transaction costs one for
the efficiency of collective management, and I will
concentrate upon the second and first roles to add a new
role – that of risk management and insurance.
 This will be done by looking at the sorts of contracts that
copyright collectives undertake, first among the members
themselves, and second between the collective and users.
Copyright collectives as syndicates
 An optimal risk-sharing problem in economics is when:
 Given a risky payoff X and m agents, divide X into (risky) shares xi
i=1,…,m, such that ∑xi=X, with xi being acceptable for agent i,
i=1,…,m.
 A group of such risk sharers is normally called a “syndicate”.
 This is quite a good description of what a copyright collective is
and does; a group of agents (copyright holders) together
generate a risky payoff (royalty income from licensing of the
repertory), which they must share among themselves
(distribution of royalty income) in such a way that is
acceptable to all.
 The sharing rule is a contract between syndicate members.
Main issues to contemplate
 How should the sharing rule be constructed?
 To what extent is it true that the decisions taken by the
syndicate (for example, on repertory bundling, and repertory
pricing) are in fact optimal for the syndicate members
individually?
 The first question is about efficient risk sharing. It has been
extensively tackled in the economic theory literature, and there
are several important aspects that should serve as a guide for
copyright collectives.
 The second question is asking when the syndicate is able to be
thought of as a representative agent. Again, this has been
answered in the economic theory literature.
 The two issues are very closely related.
Efficient risk sharing
 In any Pareto efficient solution to a risk sharing problem, the
contracted sharing rule, x = (x1,…,xm), should be such that it is
impossible to alter x in such a way that at least one member is
made better off without making any other individual worse off.
 While a rather simple requirement, this leads to very concrete
and important restrictions upon how sharing should take place.
 The first implication of an efficient sharing rule is the “mutuality
principle”
 In each state of nature each syndicate member should receive a
payoff that depends only on the level of aggregate surplus to be
shared in that state of nature.
 So a member’s income cannot depend upon that particular
member’s realisation, or upon the aggregate income in any
other state of nature.
 So, concretely, monitoring individual use in order to pay each
member according to how much use was made of his/her
copyrights is not Pareto efficient.
 Doing that only shifts risk back onto the individual members,
when that risk can be better shared among all of the group.
 So how should income be shared?
 Essentially we would start by adding a second restriction to the
sharing rule – that it be individually rational, i.e. that it satisfies
a participation constraint for each member.
 And then, presumably, the final sharing rule would be found by
a bargaining process.
A focal contract – linear sharing
 Many “real world” sharing rules are linear functions of the
aggregate surplus; xi,j = ci + aiXj , where the ai are independent
of state j aggregate wealth, Xj .
 This is only a feature of an efficient sharing rule when all of the
syndicate members have “equi-cautious” utility functions of
the same HARA (hyperbolic absolute risk aversion) class.
 Outside of this case, efficient sharing is likely to be non-linear.
 The HARA class contains most standard utility functions (power
utility or CRRA including logarithmic utility, and negative
exponential utility or CARA, among others).
 So if, for example, all members were equally risk averse with
CRRA utility functions, then the sharing rule should be linear.
Sharing aggregate risk
 Pareto efficiency also gives us a rule for sharing aggregate risk,
that is, for sharing any differences in the aggregate surplus
over different realisations of it.
 Wilson (1968) showed that aggregate risk should be shared in
inverse proportion to an individual’s Arrow-Pratt level of risk
aversion (or, if you prefer, proportionally to his/her risk
tolerance).
 Note again that this sharing rule is independent of actual
outcomes of individual copyright lotteries (as per the mutuality
principle). It only depends on risk bearing preferences.
The effect of the Law of Large
Numbers (LoLN)
 Risk sharing within a syndicate also gives us a nice way of
determining the optimal size of the syndicate.
 This may be important for the current debate on whether
digitisation implies that collective management is no longer as
efficient as it may once have been.
 A syndicate that engages in efficient risk sharing does two
things – it pools risks, and it shares (or spreads) risks.
 From the LoLN, risk pooling leads to a situation in which the
average of the aggregate outcome becomes less and less risky
the more risks are added, so long as the risks themselves are
independent.
 Given that, the more members there are, assuming that risk
sharing does indeed take place, the more favourable can be the
risk bearing situation of each member.
 But not only is the addition of new members valuable for each
existing member individually, it also works to the benefit of the
entire syndicate.
 This can be most easily seen under the assumption that each
work is iid, with expected value μ and variance σ². Assume the
syndicate has n>1 members.
 From LoLN, the average aggregate surplus of the syndicate has
expected value μ and variance σ²/n. So the syndicate can pay
each member the average surplus, and then each member
would be better off than acting alone (by having the same
expected value at a lower variance).
 Thus each member would be willing to pay a strictly positive
amount of money, p(n), to join the syndicate.
 The syndicate as a whole can earn a positive payoff of
P(n)=n×p(n). Note that P(n) is increasing with n.
Perfect risk sharing
 That the syndicate should have as many members as possible
can be seen in another way.
 If each (identical) member is paid the average aggregate
surplus, then they do still each carry some risk. But what if the
syndicate paid them the expected value of their work, μ, for
sure?
 That would be the very best that we could possibly do for the
members – a risk-free payoff with no loss in expected value, i.e.
it is ‘perfect’ risk sharing.
 But then the syndicate as a whole suffers a risk – the aggregate
surplus will sometimes be greater than the total payout, nμ,
and othertimes less. That risk needs to be financed.
 But the larger is n, the LoLN implies that the lower is this risk,
so the lower is the need for costly financing of it.
 In short, the addition of members serves to eliminate a costly
element – risk itself – both at the individual and the aggregate
level.
 And this advantage is greater the greater is n.
 In that way, the LoLN implies that the optimal syndicate size is
as large as possible.
 And note that this has nothing at all to do with transaction
costs, only risk pooling and risk sharing.
 It holds as an implication whenever there is risk, and it is all the
stronger the more risk there is.
 However, the more the assumption of iid risks is violated, the
more the potential risk savings in the aggregate may be diluted.
Optimal syndicate size and
digitisation
 If we can accept that the digital environment increases the
variance of the payoffs for an individual work (makes very
high outcomes possible – perhaps due to the increased size of
the market, makes very low ones possible as well – perhaps
due to piracy), then the LoLN would predict that the optimal
size of the syndicate should be all the larger, as there is a
greater need for risk management with the increased risk.
 This contrasts with some literature which argues that
digitisation reduces transaction costs, and thus serves to
reduce the optimal size of copyright collectives.
Adding a decision rule
 Things are complicated a little when the syndicate must make a
decision that will affect the (random) aggregate variable (total
royalty income). For example, the decision to only market a
blanket license, and the decision as to the price at which it will
be licensed.
 In this case, it becomes important that the syndicate’s
preferences also represent those of its members.
 As it happens, the sufficient condition for this to happen is
exactly the same as for the sharing rule to be linear – all
syndicate members must have equi-cautious utility functions in
the same HARA class.
Contracts between a CMO syndicate
and repertory users
 The other area in which contracts are an issue for a copyright
collective is in the relationship with users.
 There, the contracts essentially boil down to exactly what is
licensed, and at what price.
 I will not deal with pricing, but rather the more interesting issue
of aggregation of the repertory into a single unit which is
licensed under a blanket license.
 Is it always efficient for a CMO to restrict its offer to blanket
licensing of the entire repertory, rather than licensing of subsets of the repertory, and perhaps under more restrictive
licensing contracts?
 The answer is maybe. And if it is efficient, then it is for similar
reasons as to why it is efficient to aggregate members into a
single CMO in the first place.
The economics of bundling
 As a general conclusion, the literature on the economics of
bundling tells us that bundling of information goods is both
economically efficient and profit enhancing for the owners of
the bundled goods (copyright holders), because it reduces the
heterogeneity in user willingness to pay for individual titles (a
bundle allows a sale at the average, rather than the minimum,
willingness to pay).
 E.g. two users and two works. User A values work 1 at $10 and
work 2 at $20. User B values work 1 at $20 and work 2 at $10. If
the works are not bundled, then they can be licensed at $10
each, which would give revenue of $40 (both users buy a
license for both works). Or at $20 each, which also gives
revenue of $40 (each user buys a license for only one work).
But if they are bundled and licensed at $30, then both users buy
a license for the bundle, and revenue is $60.
 So indeed, in principle, it is worthwhile for a CMO to only offer
a license to the entire repertory, rather than offering
disaggregated options.
 This benefit can be shared with users by price regulation, or by
bi-lateral negotiation.
 Nevertheless, in the same way as the result on aggregation of
members, the benefits from bundling repertory may be
weakened if there are external effects over works.
 Also, the benefits are weakened by the possible presence of
observable differences between users (of the same sort that
would normally lead to price discrimination), that can provide
scope for specialist bundles (subsets of the repertory) to be
offered.
 The gains from aggregation of copyright holders into a single
CMO, and the gains from aggregation of repertory into a single
product, are both based on the Law of Large Numbers (LoLN).
 For CMO membership, the LoLN implies that adding members
allows the average aggregate surplus to have a lower variance at
the same expected value. Thus adding members gives clear risk
saving advantages.
 For blanket licensing, the LoLN implies that the average valuation
of users of the bundle will be increasingly concentrated near the
mean valuation as more goods are added to the bundle. Thus
adding works allows pricing at the average rather than minimum
willingness to pay.
 Notwithstanding that, bundling is more efficient the lower are
the marginal costs of production, and less efficient the lower
are the marginal costs of delivery.
 So digitisation has an ambiguous effect on the optimal bundle
size.
Concluding comments
 Copyright collectives may form not only for reasons related to
transaction costs.
 They are also an optimal response to a demand for risk-management
and insurance by copyright holders.
 This, in turn, is what drives the configuration of the contracts
between the individual members and the collective.
 We have discussed the following general results related to the
contractual environment of copyright collectives:
 Efficient risk sharing contracts imply that each member’s payoff should
not depend upon his/her final contribution to aggregate surplus.
 The more members can be attracted to the collective, in principle the
greater are the benefits that each realises. And this also can be translated
into greater benefits for the collective as a whole.
 If the digital revolution serves to increase the risk of each individual work,
then the rationale for forming a collective is all the stronger.
 When the collective must take a decision that affects the
aggregate surplus, then that decision is optimal under the
condition that each of the members has equi-cautious utility of
the same HARA class. In this case (and assuming efficient risk
sharing) the collective as a whole is validly a representative
individual for the members, and the contracts signed by the
collective would be optimal for the members as well.
 Bundling of the repertory into a single licensing unit is, in
principle, optimal for the collective (i.e. it allows for greater
profits). Of course these profits can be shared with users by
regulating the price of access.