Economics
Letters
43 (1993)
Ol65-1765/93/$06.00
0
Network
analysis
Steinar
*
Department of Economics,
Received
17 May 1993
Accepted
29 June
Science
Publishers
B.V. All rights
reserved
or pay-per-view?
A welfare
Holden
59
59-64
1993 Elsevier
University of Oslo,
Box llXL5 Blindern.
0317 Oslo. Norway
1993
Abstract
The
welfare
pay-per-view
effects
television
of pay-per-view
admits
third-degree
television
and
advertising-supported
price discrimination
networks
and may involve
a large
are compared.
It is shown
loss of consumer
that
surplus.
1. Introduction
Technological
progress is usually associated with the introduction
of new or better products.
Technological
progress then generates revenues for the firms as far as consumers are willing to pay
for the new or better products.
However, technological
progress may also mean new methods of
paying for old products. Pay-per-view
(PPV) is a case in point. The Tyson-Ruddock
WC boxing
match on 18 March 1991 appeared
on PPV. At that time 16m American
households
were
connected
to the system and of these just over lm households ordered the fight, for $35 each (The
Economist,
23 March 1991). The total revenues were $36m which, according to The Economist,
was far more than the networks could ever have hoped to raise from advertising.
The TysonRuddock match is not an exception,
many other popular events are now broadcast on PPV only.
PPV does not change the production
function;
the TV programs
that can be made are no
different
from what could be made before. The innovation
is that new technology
makes it
possible to let only the people who pay be able to view a specific program. In this paper I compare
and show that the introduction
of PPV has large
PPV with advertising-supported
networks.
welfare-reducing
effects. This is in spite of the fact that the introduction
of PPV increases GDP,
and thus is measured
as economic growth.
The motivation
for the paper is to illustrate
a few points in a simple fashion. No attempt at
generality
is made.
* I am grateful to the United States Reference
Center for providing me with information
and to Nils-Henrik
von der Fehr for useful comments
on an earlier version.
about
pay-per-view
television,
60
S. Holden I Economics Letters 43 (1993) 59-64
2. PPV and network
Consider the broadcasting
of a specific WC boxing match. Under PPV, the seller is assumed to
charge a uniform price, q, for viewing the match. 1 Households
will pay for and view the match if
and only if their willingness to pay, u, is greater than or equal to q. The demand function for the
boxing match is
>
x = D(q)
(1)
where x is the number of households
that have a willingness to pay for the match greater than q,
and thus pay for the match.
If the match is broadcast by a network, the households
may view the match without paying.
However,
they have to accept interruption
of commercial
breaks during the match. Such breaks
may reduce the utility of the viewers. Let a(A)denote the perceived cost of viewing the match if
the amount of advertising
is A. [a(A)
clearly varies among individuals,
but this is neglected
for
simplicity.]
It seems reasonable
to assume that a(A)is convex, and increasing
in A. The number
of households
that view the match if it is broadcast by a network is now
x =
D+(A)).
(2)
We first consider the case in which the match is broadcast
by a network.
The revenues
of the
network from advertising depend on the amount of advertising
and the number of households
that
view the match. (I neglect uncertainty
in the analysis, so there is no distinction
between expected
and actual number of viewers.) Let the net revenues of the network be
R=R(x,A),
where R is strictly
determined
by
concave
(3)
and strictly
increasing
in both arguments.
The amount
A = argmax R(x,A),subject to x = D(a(A))
.
The optimal
amount
R,(x*,
of advertising,
R,(x*,A*)=O,
is
(4)
A*, is given by the first-order
A*)D’(a*)a’(A*)+
of advertising
condition
(5)
x * = D(u(A*))
and a(A*).
Now consider the PPV system. In addition
where
to the costs of broadcasting,
a PPV company
has
costs associated with collecting payment from the viewers. For simplicity, these costs are assumed
to depend linearly on the number of viewers, so that the costs of the PPV companies
are
C(x) = Q + cx ,
Q, c > 0 .
(6)
Under PPV, the price will be set so that only a fraction of the viewers that would like to see the
match are actually willing to pay the chosen price. This opens up the possibility of also sending a
‘low-quality’
version, in order to earn some revenue from the households
that do not buy the
version is usually sent later, when the news content
has
original
version. ’ The low-quality
I I neglect any fixed costs of being connected to a PPV channel. This simplifies
where the households
with sufficient willingness to pay already are connected
would clearly make PPV less attractive
in welfare terms.
’ This is an example of third-degree
price discrimination,
cf. Tirole (1988).
the analysis, and corresponds
to a situation
to a PPV channel. Incorporating
such costs
S. Holden
I Economics
61
Letters 4.3 (1993) 59-64
disappeared.
I assume that the PPV channel does not charge any price for viewing this low-quality
version
(for example,
because the willingness
to pay is too low compared
with the costs of
collecting payment).
The low-quality
version thus only generates
revenue through advertising.
If a household
has willingness
to pay, u, for the original version,
then I assume that the
willingness
to pay for the low-quality
version (gross of any perceived costs of advertising)
is CYU,
where (YE (0, 1). For simplicity, I let (Y be exogenous,
although in reality CYclearly depends on the
specification
of the low-quality
version.
Households
will only pay for the first version of the match if this gives higher utility than to wait
for the low-quality
version with advertising
A, that is, if
u-qzau-a(A).
(7)
[In equilibrium
we must have that for all households
Rearranging
(7) yields
u 2 [q -a(A)]/@
The number
of households
Wq,
we also have u - q > 0.1
- a) .
(8)
It follows from (8) that the number of households
low-quality
version has advertising
A is
F(q, A) = Nq
for which (7) holds,
- G>l/(l
that view the first version
at price q when
- (.y>>
that view the low-quality
(9)
version
is then
- F(q, A) >
A) = W(A)la)
the
(10)
that is, the ‘gross’ number
of households
that want to see the low-quality
version
[where
u 2 a(A)/a]
minus the number
of households
that have already seen the first version
(for
simplicity,
it is assumed
that nobody
wants to see the match twice, possibly
because
some
households
have already recorded the first version on video tape).
The PPV channel determines
q and A simultaneously
by
max GT= (q - c)F(q,
The first-order
conditions
A) + R(H(q,
A), A) - Q .
(11)
may be written
(12)
(13)
Let up = u(AP) be the perceived costs of advertising
in the low-quality
the PPV are illustrated
in Figs. 1 and 2. The Marshallian
consumer
broadcast
on network is
version.
surplus
The network and
’ if the match is
(14)
while the consumer
‘See
Tirole (1988,
surplus
on PPV is
pp. 7-12) for a discussion on the use of consumer surplus
S. Holden
62
I Economics Letters 4.3 (1993) 59-64
9 ?
Consumer surplus
$
q-a
l-a
Consumer surplus
9
ah-4
l-a
a(A)
L_
_.. .~ _
D(a)
D(q)
Fig. 2. Pay-per-view.
Fig. 1. Network.
(15)
where the two first terms are the consumer surplus of the households
that view the first version,
while the last two terms are the consumer surplus of the households
that view the second version.
For the households,
the introduction
of PPV has three effects. First, for the households
with a
willingness
to pay that,fulfills
(8) (so that they buy the first version), PPV involves an additional
cost of viewing the program,
q. Although the PPV may send the first version without advertising
(which is assumed here), it seems reasonable
to assume that q > a(A*) so that PPV involves a
reduction
in the consumer
surplus for these households.
Secondly,
households
with a lower
willingness
to pay, that do not buy the first version, experience
a reduction
in consumer
surplus
because the utility of viewing the second version is lower than the utility of viewing the first
version. Thirdly, the amount of advertising chosen in the second version of PPV will in general be
different from the amount of advertising
under network. Here there are two opposing effects. On
the one hand, the PPV has an incentive to have more advertising,
because the more advertising
in
the second version,
the lower the consumer
surplus from seeing this version,
and the more
households
will choose to buy the first version. On the other hand, households
have a lower utility
so that with too many commercials,
a large part of the
from viewing the second version,
households
will choose not to view at all.
To illustrate
these effects, consider two numerical
examples,
one with constant
elasticity of
demand and one with a linear demand curve. Under constant elasticity of demand I also assume
that there is a maximum willingness
to pay, 4 (which does not affect the reduction
in consumer
surplus), so that the demand function is of the form x = Kq-” for q 5 tj and x = 0 otherwise.
For
on network is
simplicity,
I also set aA = up = a. The consumer surplus if the match is broadcast
Q
I
II
Kv-E dv = _&(u-t+’
while the consumer
surplus
on PPV is
_ q-E+l),
(16)
S. Holden
I Economtcs
Lrttm
4_l (199.Z) S-64
63
Kv-” dv +
49 - a)
i
which
is equal
l-a
-+o).
(17)
to
Consider
the Tyson-Ruddock
match which was seen by about lm households,
at a price $35.
Assume that the maximum willingness to pay is 4 = $200. Furthermore,
let the perceived costs of
advertising,
a = $1 (both under network and in the second version of PPV), and assume that the
utility of viewing the second version is half of the utility of viewing the first version,
cy = 0.5.
Assume also that if the match had been broadcast only at network,
it would have been seen by
1OOm households.
Thus, from 1OOm = Ku-‘, and u = 1, we obtain K = 1OOm. From (9) we find
that lm = K ((35-I)/(1
- 0.5)))‘;. and inserting for K we obtain E = 1.1. From (16) and (18) it
follows that the total consumer
surplus when the match is broadcast
at network is $411m, while
the consumer
surplus under PPV is $206m. The loss in consumer
surplus under PPV is thus
411-206 = $205m. On comparison,
the revenues of the match under PPV are only $35m.
With linear demand,
demand is D(q) = K,, - K, q. As above, we assume the perceived cost of
advertising
a = 1, and the reduction
in utility of the second version, (Y = 0.5. Now we assume that
if the match had been broadcast on network, it would have been seen by 50m households.
From
5O=K,,-K,u=K,,-K,
and l=K,,-K,(q-u)/(l-a)=K,,-K,
68, we obtain K,,=50.731,
K, = 0.731 and thus the maximum willingness
to pay i = 69.4 (given by K,, - K,q = 0). Straightforward calculations
using (14) and (15) (or simpler,
calculate
the areas of the triangles
and
squares in Figs. 1 and 2) give us the consumer
surplus under network as $1,71Om, whereas the
consumer
surplus under PPV is $842m. In this case the reduction
in consumer
surplus
is
$1710m-$842m
= $868m. Thus, under linear demand the reduction
in consumer
surplus is much
larger than under constant elasticity of demand, which reflects the fact that under linear demand
there are many more households
with a quite large willingness
to pay.
3. What about the revenues?
According
to The Economist, 23 March 1991, the introduction
of PPV raises the revenues from
WC matches considerably.
This yields a potential for big profits for the PPV companies.
However,
in the United States today there are several PPV companies
that compete for the TV-rights of the
matches. This will increase the price for the TV-rights. If we consider the bidding for TV-rights of
one match in isolation,
then the unique Nash equilibrium
price is equal to the net profits the
winner of the TV-rights can expect to make from broadcasting
the match. In this case the seller of
the TV-rights obtain the whole rise in profits due to the introduction
of PPV. On the other hand,
the number
of PPV companies
is limited and there is an endless stream of new matches.
The
theory of repeated games with infinite horizon [see, for example, Tirole, 19SS)] has taught us that
this gives scope for collusion among the PPV companies.
Yet in practice the extent of collusion
64
S. Holden
I Economics
Letters
43 (1993) 59-64
appears limited. According to Business Week, 2 September
1991, the Holyfield vs. Foreman match
in April 1991 gave revenues
of $55m. Of these, the PPV company
Time Warner paid $20 to
promote
the bout, more than $20m to the fighters and $5m to local cable companies.
Time
Warner, say its executives ‘made a few million’ on the match. (On the other hand, Time Warner
has lost money on its new series of smaller-time
fights, Business Week, 2 September
1991.)
These figures suggest that it is the fighters who obtain the lion’s share of the increase
in
revenues.
But this cannot be the end of the argument.
First, although the income distribution
usually is neglected in analyses of economic efficiency, it is tempting to make an exception here.
Comparing
the utilities of different individuals
is very problematic
from a theoretical
point of
view. On the other hand, it seems to me fairly uncontroversial
that the increase in utility E.
Holyfield or G. Foreman obtain from their share of $20m cannot be 20 million times the utility of
an extra dollar for an average household.
Secondly, even neglecting income distribution,
the analysis must include the effort the fighters
have made to be in the position to fight WC matches. Posner (1975) shows that all monopoly rents
may be dissipated in the costs of a contest between firms to become a monopolist
[see also Tirole
(1988)]. In the present setting, this would be the case if there is free entry of equally talented
youths (so that the expected utility of participating
in the contest of becoming World Champion
is
zero), and if the effort has no socially valuable by-products.
4. Concluding
remarks
The main motivation
of this paper is to illustrate how the introduction
of PPV television
will
have a large negative impact on consumer surplus. Two rough numerical examples gave reductions
in the consumer surplus from sending one WC match in boxing on PPV of $205m under constant
elasticity of demand and $868m under linear demand. Obviously,
these figures cannot be taken as
more than rough illustrations
of the possible size of the efficiency loss. Yet they should indicate
that the problem is worthy of further research.
The comparison
between PPV and advertising-supported
network is based on an analysis of an
event that would be broadcast under both systems (a WC boxing match). This neglects the fact
that PPV makes it possible to finance programs that could not be financed within a system with
advertising.
A total analysis of whether the introduction
of PPV is welfare reducing
would of
course have to include this aspect.
The paper also illustrates a more general point. Technological
progress is, as emphasized
in the
recent literature
on endogenous
growth, often the result of conscious effort to make profits. But,
as the introduction
of PPV television
illustrates,
the rise in profits may not reflect a rise in
the increase
in profits may arise precisely
because
willingness
to pay. On the contrary,
technological
progress enables the producer to capture a larger share of the consumer
surplus.
References
Power,
Tirole.
R.. 1975, The social cost of monopoly
and regulation,
Journal of Political Economy
J., 1988, The theory of industrial organization
(MIT Press, Cambridge,
MA).
83, 807-827.