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Copyright protection and hardware taxation
Information Economics and Policy 15 (2003) 467–483 www.elsevier.com / locate / econbase
Copyright protection and hardware taxation Amit Gayer a , *, Oz Shy a,b a
Department of Economics, University of Haifa, Haifa 31905, Israel b Humboldt University at Berlin, Berlin, Germany
Abstract This paper investigates the recently practiced method of taxing hardware and transferring the proceeds to software makers, or artists in general. We characterize the conditions under which the policy of compensating copyright owners for infringements on their intellectual property using hardware taxation is inefficient. 2003 Elsevier B.V. All rights reserved. Keywords: Software piracy; Hardware taxation; Intellectual property; Copyright violation JEL Classification: L86; O34
1. Introduction
1.1. Major observations and legal issues Violations of copyrighted material in general and software in particular are known as piracy. Piracy is conducted via copying for personal usage, or for commercial purposes. Copying could be utilizing analog formats, for example, dubbing audio and video cassettes, or could be digital, for example, copying computer software, DVD, or MP3 artistic works. There are many different estimates concerning the level of piracy in the various entertainment and software industries. Some argue that software piracy in the West could be between 25 and 50%, whereas it could reach 90% in the developing countries in the Far East. Clearly, the degree of piracy heavily depends on the *Corresponding author. E-mail addresses: amit [email protected] (A. Gayer), [email protected] (O. Shy). ] 0167-6245 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0167-6245(03)00023-4
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enforcement of copyright laws to eliminate markets for pirated entertainment media and for computer software. Music and software publishers often quote their ‘losses’ resulting from piracy in the billions of dollars; however, one should bear in mind that these quotes tend to be exaggerated since they are based on the false assumption that if copyright laws were strictly enforced, those who pirate would necessarily become buyers. The fast penetration of the Internet into the home and business communities further intensified the piracy of artistic titles. In addition to public and commercial mainframe computers that store computer software as freeware and shareware packages for the public to download, Napster developed software in which users can exchange music titles over the Internet. [See, www.napster.com. Napster was recently ordered to block all copyprotected music titles.] The innovation was that music titles can be downloaded not only from a particular mainframe computer, but also from hard drives of other participating users. Theoretically, the second-best solution to the piracy problem (assuming that copyright enforcement is infeasible) would be to tax those consumers who purchase pirated copies. However, taxing these consumers is equivalent to selling the software, and is therefore infeasible. This raises the question whether there exist economic methods for compensating music and software publishers for the partial loss of their intellectual property rents. The present paper investigates the effects of the imposition of tax on hardware and using the proceeds to recover the loss of profits claimed by software producers. Some countries have already implemented hardware taxes and some are planning to introduce this tax. France imposes a surcharge of 59–69 cents on each recordable medium such as on blank CDs, minidisks, and cassettes, with the intention of levying a surcharge on personal computers’ hard drives (Business Week, February 5, 2001, p.19). The proceeds of the already imposed surcharge go to royalty funds for artists. Besen and Kirby (1989) cite the Home Recording Act of 1982 introduced in the US Congress. Copyright holders would be compensated for private copying out of the royalties levied on the sale of audio and video. The same authors report that in Germany there is a levy on manufacturers and importers of recording equipment. The remuneration consists of an equitable share of the proceeds resulting from the sale of the equipment (limited to 5%). In both Austria and Germany, authors of audio-visual works have similar rights against manufacturers of blank tapes, with the amount of royalty being established by the law. The ‘thinking’ behind this mechanism is that hardware would be used for creating, copying, and storing pirated copies.
1.2. The literature and our investigation Several papers have already analyzed the effects of piracy on the demand for the legally supplied software. See, a pioneering paper by Conner and Rumelt (1991), and extensions in Shy and Thisse (1999), Shy (2000, 2001, Ch. 3), Poddar (2002,
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2003), Slive and Bernhardt (1998), and Takeyama (1994, 1997). More recently, King and Lampe (forthcoming) investigate the claims when the producer can freely choose the degree of piracy prevention. They show that allowing piracy cannot raise profits if the monopoly producer can directly price discriminate between potential-pirates and other customers. In the absence of price discrimination, they show that allowing piracy will only maximize profits when the ability to pirate is inversely related to customer willingness-to-pay. Finally, an empirical investigating showing how the increase in software piracy can boost the demand for the legal software is conducted in Givon et al. (1995). Earlier papers discussing the effects of photocopying include Besen and Kirby (1989), Johnson (1985), Liebowitz (1985), and Novos and Waldman (1984). In this paper we deliberately abstract from the ‘profitable piracy’ debate, which is extensively analyzed in the literature analyzed above. Instead, we focus our investigation on the effects of hardware taxation on the profit of a software publisher, whose software is pirated by some users. We develop a model in which the user population gain utility from software to be used on a piece of hardware. Thus, users must purchase hardware and software from different manufacturers. We calculate equilibrium prices under which the user population is divided into three groups: those who buy hardware and software, those who buy the hardware and pirate the software, and those who do not buy anything so they become nonusers. We then investigate how a tax on hardware affects the profit of the software producer under the extreme assumption that the proceeds from this tax are transferred to the software publisher, as a compensation for the partial violation of the publisher’s intellectual property right. Finally, we investigate the effects of hardware taxation on social welfare.
1.3. Organization The paper is organized as follows. Section 2 sets up a model of hardware and software producers, where consumers can either buy the software or use it illegally without paying for it. Section 3 investigates the effects of hardware taxation and the welfare consequences of this hardware tax. Section 4 investigates the effects of hardware taxation on social welfare. Section 5 proposes an alternative formulation. Section 6 introduces multiple software developers. Section 7 concludes.
2. The market for hardware, software, and piracy Consider a market composed of users who wish to utilize a certain piece of software (e.g., computer software, a music performance, a digitally stored book, or a movie). For the sake of brevity we call this title by the name software, and assume that this software is copyrighted. The software analyzed in this paper can be obtained in two ways. It can be
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purchased on conventional media such as diskettes or compact disks. Alternatively, it can be illegally copied. There are many ways in which copyrighted media can be copied, for example, it could be downloaded via the Internet, sent by e-mail, copied from diskettes, CD, DVD, or audio cassettes.
2.1. Users There is a continuum of types of potential software users indexed by x on the interval [0, 1], with density of h $ 1users per type. Thus, the total number of consumers in this market is h. Each user consumes at most one unit of this software, either by purchasing it from the store for a price p s , or by pirating it without paying p s . In addition, each user who wishes to use the software must purchase one unit of hardware (e.g., a computer, CD/ DVD player, or a cassette player) for a price of p h . The utility of each user indexed by x 0 # x # 1 is defined by
a x 1 g N 2 p h 2 p s if buys hardware and software Ux 5 b x 1 g N 2 p h if buys hardware and pirates the software 0 if does not use software and hardware def
5
(1)
The parameters a . 0 and b . 0 measure a user’s basic utility from the services provided by this software title. Thus, user-types indexed by x close to 0 are interpreted as those who gain very little from using computers and software, whereas users indexed by an x close to 1 gain the most out of using computers and software. We make the following assumption. Assumption 1. For every user x, legally purchased software yields more services than pirated software. Formally, purchased software and pirated software are vertically differentiated, i.e., a . b. The interpretation of Assumption 1 is as follows. Legally purchased software is bundled with manuals, installation software, service, as well as discounts on upgrades. In contrast, users who pirate the software may not be able to copy the manuals, may be forced to utilize complicated installation techniques, and are not entitled to obtain service and upgrades. In addition, users who do not buy the software may have hard time in locating the software, and then copying or downloading it for installation purposes. In addition, some illegal users may feel uncomfortable in using copyrighted software without paying for it. Finally, the utility function (1) implicitly assumes a correlation between the value of software and the value for non-pirated features of the software. Section 5 provides an alternative formulation which relaxes this assumption. The variable N is the endogenously determined total number of users, which is the sum of those who buy the software and those who illegally copy the software.
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The parameter g $ 0 is the network externality parameter reflecting the degree of importance of the total number of users. Therefore, if g . 0, the utility of each user is enhanced with the total number of all consumers who use this software. There are two interpretations for this assumption. In one interpretation, users gain from having more people using the same software since they can work together, say by exchanging files. A second interpretation refers to popularity or fashions where people ‘feel better’ by using products that are similar to what others consume. It is important to observe that all users, regardless of whether they are buyers or illegal users, gain from the network size. Thus, buyers benefit with an increase in the number of buyers as well as in the number of illegal users, and illegal users also benefit from an increase in the number of buyers as well as in the number of illegal users. We confine our analysis to the following parameter range. Assumption 2. The network effect parameter is bounded by the basic valuation for the software. Formally,
H
J
b b 2a ] , g , max ]; ] . 2h h 3h Assumption 2 constrains the network externality effect. Higher values of g (strong network effects) would make the software highly valuable by all consumers (type x50 in particular) thereby generating an equilibrium where all potential users become actual users even with the imposition of a revenue-maximizing tax on hardware. Lower values of g (weak network effects) would generate equilibria with only small number (or even none) of the users who pirate the software.
2.2. Users’ choice problem Let x p denote the type of consumers who are indifferent between pirating the software and not using the software at all. In view of the utility function (1), this consumer type is solved from p h 2 gN b x p 1 g N 2 p h 5 0, hence x p 5 ]]]. b
(2)
Thus, all users indexed on [0, x p ] do not use (and do not purchase) any hardware and software. Similarly, let x b denote the type of consumers who are indifferent between buying the software and pirating the software. In view of the utility function (1), this consumer type is solved from ps a x b 1 g N 2 p h 2 p s 5 b x b 1 g N 2 p h , hence x b 5 ]] a 2b
(3)
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Thus, all users indexed on [x p , x b ] pirate the software, and all users index on [x b , 1] buy the software, Therefore, the number of software buyers is h(1 2 x b ), and the total number of users who pirate the software is h(x b 2 x p ). Therefore, the aggregate number of users (i.e., the sum of buyers and illegal users) is given by
S
D
ph 2 g N h ( b 2 p h) N 5 h (1 2 x p ) 5 h 1 2 ]]] , hence N 5 ]]]. b b 2 gh
(4)
Fig. 1 illustrates how the market is divided among buyers, illegal users and nonusers.
2.3. The government Clearly, the government is unable to directly tax those who illegally copy the software since pirated copies are not purchased in any formal way. Also, it is clear that piracy cannot be reduced if the government taxes software buyers. In fact, taxing software buyers would reduce the number of buyers. Thus, the only tax mechanism available to the government is to tax the hardware purchased by each legal and an illegal software user. Let t denote the per-unit (specific) tax on hardware, and by T the total revenue collected from this tax. Then, T 5 tN.
(5)
Finally, to make our investigation complete, we assume that the purpose of this tax is to ‘compensate’ the software producer for the copyright infringement associated with piracy. Thus, we assume that the government’s sole objective is to compensate the software producer by transferring the entire revenue collected by the tax on hardware.
2.4. The hardware producer We assume that hardware is produced and sold by a single monopoly firm, and that there is no black market for hardware. Let F h denote the fixed cost borne by the hardware producer, and c h the marginal cost. With no loss of generality, we set c h 50. Therefore, the hardware producer chooses a price, p h , that solves
Fig. 1. Buyers, illegal users (pirates), and non-users.
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h( b 2 p h) max p h 5 ( p h 2 t)N 2 F h 5 ( p h 2 t) ]]] 2 F h . b 2 gh ph
473
(6)
We make the following assumption. Assumption 3. The hardware fixed cost is bounded. Formally,
h( b )2 F h , ]]]. 4( b 2 gh ) Assumption 3 ensures that the hardware producer earns positive profit. Under this assumption, the hardware producer’s profit-maximizing price is
b 1t p h 5 ]]. 2
(7)
Notice that the hardware price increases with the tax on hardware and with b which is the software-valuation parameter of a pirating user.
2.5. The software publisher There is a single monopoly software house producing a certain software package. Let F s denote the fixed cost borne by the software publisher and c s the marginal cost. With no loss of generality we set c s 50. The seller of the software chooses p s that solves
S
D
ps s s b s s ]] max p 5 p h (1 2 x ) 2 F 1 T 5 p h 1 2 2 F s 1 T. a 2b ps
(8)
There are two ways to interpret the software maker’s profit function (8). The first interpretation involves a non-strategic software developer who treats the government’s subsidy, T, as given. Such an interpretation is commonly used in the public finance literature. The second interpretation involves a strategic software developer who can indirectly ‘manipulate’ the subsidy via the price of software. However, inspecting (4) reveals that the aggregate number of users is influenced only by p h and not by p s , which means that these two interpretations yield the same results. Thus, maximizing (8), the software firm’s profit-maximizing price is then given by
a 2b h(a 2 b ) p s 5 ]], provided that F s # ]]] 1 T. 2 4
(9)
The sufficient condition in (9) implies that the fixed cost of software publishing should be either relatively small, or that the tax revenue transferred to the publisher must be sufficiently high as to cover part of the fixed costs. Therefore,
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Proposition 1. No software is developed if
H
J
h(a 2 b ) T , max F s 2 ]]], 0 . 4 That is, the software will not prevail in the case that tax revenues do not exceed the software publisher’s loss (if any).
3. Hardware taxation and the software publisher
3.1. The low fixed cost case We start our analysis by assuming that the fixed cost of the software publisher, F s , is sufficiently low (or zero) so that the publisher is not making a loss even in the absence of any subsidy. In Section 3.2 we investigate the high fixed cost case. Formally, let
h(a 2 b ) F s # ]]] 4
(10)
Substituting (7) and (9) into (4), and then also into (2) and (3), we obtain the aggregate number of users (buyers and illegal users), as well as the user types who are indifferent between not using and pirating, and between pirating and buying the software. Therefore,
h( b 2 t) N 5 ]]], 2( b 2 gh )
H
J
b 2 2gh 1 t x p 5 max 0, ]]]] , 2( b 2 gh )
1 and x b 5 ]. 2
(11)
Notice that (11) and Assumption 2 imply that when hardware is not taxed (t50) all the market is served (x p 50). Next, (11) implies that the tax revenue collected by the government is
h( b 2 t) T 5 tN 5 t ]]] 2( b 2 gh )
(12)
Substituting (7) into (6), and (9) and (12) into (8) yields the equilibrium profit levels as functions of the tax rate on hardware. Thus, 2h( b 2 t)2 (3d 2 4gh )2 p h 5 ]]]]]]] 2 F h , and (d 2 2gh )(7d 2 8gh )2 h(a 2 b ) h(a 2 b ) h( b 2 t) p s 5 ]]] 2 F s 1 T 5 ]]] 2 F s 1 t ]]] 4 4 2( b 2 gh )
(13)
We now ask what would be the hardware tax rate that maximizes government’s
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Fig. 2. Software publisher’s profit as a function of the tax on hardware.
revenue, and what would be the rate which maximizes the profit of the software developer. However, inspecting (12) and (13) reveals that these two tax rates are identical. Therefore, maximizing (12) with respect to t yields
b tˆ 5 ]. 2
(14)
Fig. 2 illustrates how the tax on hardware affects the software publisher’s profit. Fig. 2 reveals that the profit of the software publisher increases with an increase in the tax rate on hardware at low tax rates, but decreases at high tax rates. The reason is that high tax rates increase the price of hardware (see, (7)) and reduce the demand for hardware and hence for pirated software as well. The reduction in the overall demand for software dominates the increase in the tax rate thereby reducing the profit of the software publisher. The profit function, labeled as p s1 , is associated with low fixed cost F s , in which case the publisher earns a strictly positive profit even in the absence of any compensation coming from the tax revenues. In contrast, the profit function p s2 reflects relatively high fixed costs, in which case the publisher will not produce unless he receives a subsidy (financed by hardware tax revenues). We can now state the following proposition.
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Proposition 2.
(a) By setting the hardware tax rate t 5 gh, the government can eliminate piracy. However, ( b) The hardware tax rate that maximizes the (tax inclusive) profit of the software developer is below the tax rate that eliminates piracy. Proof. (a) From (11) we see that x p → x b as t → gh. (b) t 5 b / 2 , gh by Assumption 2. h
3.2. The high fixed cost case We now assume that the fixed cost of the software publisher, F s , is sufficiently high so that without a subsidy the publisher is making a loss. Formally, we reverse the condition given in (10). This case is illustrated by the lower profit curve in Fig. 2. This case is important since without any intervention the software industry would not produce any software, thereby eliminating the hardware industry as well. Therefore, this case represents the only market condition under which intervention may be justified. We now ask what should be the minimal tax rate on hardware that would guarantee normal profit for the software publisher. From (13), this tax rate is given by ]]]]]]]]]]]]] bh 2œhhhf2a ( b 2 gh ) 2 b 2 1 2bghg 2 8F s ( b 2 gh )j t˜ 5 ]]]]]]]]]]]]]]]]. (15) 2h The tax rate t˜ makes the software publisher break even, and is drawn in Fig. 2. It is easy to illustrate that an increase in the fixed cost F s would lower the profit ˜ which is the necessary tax to keep the software curve thereby increasing t, publisher breaking even.
4. Welfare analysis So far, we analyzed how the hardware tax affects the profit of the software publisher. In this section we analyze the effects of hardware taxation on social welfare. clearly, the main concern of the regulator should be how the tax on hardware affects aggregate social welfare.
4.1. The low fixed cost case Suppose that the software publisher incurs low fixed costs (if any) as given in (10). Section 4.2 below investigates the high fixed cost case.
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We define aggregate consumer surplus by the sum of the utilities of all users. Formally, xb
def
CS 5h
1
E sbx 1 gN 2 p d dx 1 h E fax 1 gN 2 p 2 p g dx h
h
xp
s
xb 2
2
3a ( b 2 gh ) 1 2b (2gh 2 t) 2 b (3g 2h 2 1 t 2 ) 1 2ght 2 ]]]]]]]]]]]]]]]] 5h 2 h p h (1 2 x p ) 8( b 2 gh )2 2 h p s (1 2 x b )
(16)
Note that (1) implies that all potential users indexed on [0, x p ) gain a utility of zero since they neither buy the software nor they pirate it. The sum of profits of the hardware and software producers is given by
ph 1ps
h
p
s
b
p
h
5 ( p 2 t)(1 2 x )h 1 p (1 2 x )h 1 th(1 2 x ) 2 F 2 F 5 p h (1 2 x p )h 1 p sh(1 2 x b ) 2 F h 2 F s .
s
(17)
Clearly, aggregate profit (17) enters as a negative sum in aggregate consumer surplus (16) since it reflects a transfer from buyers to firms. Altogether, we define the social welfare function by the sum of users’ utilities and the profits of the hardware and software firms. Formally, def
h
W(t) 5CS 1 p 1 p
s
3a ( b 2 gh )2 1 2b 2 (2gh 2 t) 2 b (3g 2h 2 1 t 2 ) 1 2ght 2 5 h ]]]]]]]]]]]]]]] 2 F h 2 F s. 8( b 2 gh )2 (18) Differentiating (18) with respect to t yields ≠ 2W h(2gh 2 b ) ≠W ]] and ] 2 5 ]]]] 2 . 0, ≠t ≠t 4( b 2 gh )
U
t 50
2 hb 2 5 ]]]]2 , 0. 4( b 2 gh )
We are now ready to state the following proposition. Proposition 3. When the fixed cost of software is low (see (10) ), the tax rate that maximizes social welfare is t 5 0. Proposition 3 demonstrates that under low software fixed costs, this tax distorts social welfare, hence this transfer of rents to the software publisher does not enhance social welfare. In what follows, we demonstrate that this is not necessary the case when the software industry bears high fixed cost.
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4.2. The high fixed cost case We now assume that the fixed cost of the software publisher, F s , is sufficiently high so that without a subsidy the publisher is making a loss. Formally, we reverse the condition given in (10). Proposition 3 demonstrated that hardware taxation reduces social welfare when the software publisher earns at least normal profit. On the other hand, Fig. 2 illustrates that under high fixed costs, the software industry will not exist unless it ˜ Therefore, is subsidized by a hardware tax rate of at least t. Proposition 4. Suppose that the fixed cost of software is high [condition (10) is reversed], and
h( b 2 t˜ )2 ]]] F # . 4( b 2 gh ) h
(19)
Then, the tax rate that maximizes social welfare is strictly positive and is given by t˜ which is defined by (15). Proposition 4 provides some rational for taxing hardware. However, this argument is valid only if piracy endangers the existence of the software industry. The Condition (19) in Proposition 4, which is taken from (13), ensures that the ˜ hardware industry is not making a loss at the optimal tax rate t.
5. An alternative formulation Our formulation so far has relied on the utility function (1) which has the property that consumers’ value for the software, as measured by the index number x, is correlated with the consumers’ marginal valuation for the extra features embedded in a legally purchased software that do not exist in the pirated version, and measured by (a 2 b )x. This correlation is extensively discussed in King and Lampe who attribute this assumption to results of ‘profitable’ piracy. In this section we briefly develop a model which does not rely on the above correlation, but, following King and Lampe, does rely on an assumption that some consumers (e.g., large companies who face high litigation costs) cannot pirate the software. We demonstrate that our conclusions regarding the use of hardware taxation remain valid when the value for software and the value for non-pirated features are not correlated. As before, N denote the endogenously determined total number of users (buyers and illegal users), p h the price of hardware purchased by all users, and p s the price of software. Let there be h p users who pirate the software and assume a density of h b of buyers indexed by x, x $ 0.
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The utility function of a consumer x who cannot pirate the software (type-b, stands for buyers) is given by def
Hg
U bx 5
N 2 ph 2 ps 2 x
0
if buys hardware and software , if does not use software and hardware
(20)
where we assume that g , 1 /h b . Let xˆ b denote a type-b consumer who is indifferent between purchasing hardware and software and not purchasing at all. The number of software buyers is then xˆ bh b . Therefore the total number of software users (buyers and illegal users combined) is N 5 h p 1 xˆ ph b . The utility function (20) implies that
gh p 2 p h 2 p s ˆx b 5 ]]]] . 1 2 gh b
(21)
The hardware firm chooses its price p h to solve
sgh bh p 1 th b 2 2h pd 2 max p h 5 ( p h 2 t)N 2 F h 5 ]]]]]] 2 F h. 9h b (1 2 gh b ) ph
(22)
The software firm chooses its price p s to solve
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D
p h s s s b b s s gh 2 p 2 p ˆ ]]]] max p 5 p x h 2 F 1 T 5 p h b 2 F s 1 T, b ps 1 2 gh
(23)
where, as before, T 5 tN is the hardware tax revenue which is transferred to the software developer in a lump-sum fashion. The unique Nash–Bertrand equilibrium is given by 2h p 1 2th b 2 gh bh p ]]]]]] p 5 3h b h
and
2gh bh p 2 th b 2 h p ]]]]]] p 5 . 3h b s
(24)
The consumer who is indifferent between buying and not using hardware and software, as well as the resulting revenue collected from hardware taxation are given by b
p
b
p
2gh h 2 th 2 h b xˆ 5 ]]]]]] b b 3h (1 2 gh )
p
b
b
p
t(2h 2 th 2 gh h ) and T 5 ]]]]]] . b 3(1 2 gh )
(25)
Finally, the equilibrium profit levels are
sgh bh p 1 th b 2 2h pd 2 p h 5 ]]]]]] 2Fh 9h bs1 2 gh bd
(26a)
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4g 2 (h b )2 (h p )2 2 gh bh p (7th b 1 4h p ) 2 t 2 (h b )2 1 h p (8th b 1 h p ) p s 5 ]]]]]]]]]]]]]]]]] 2 F s. 9h bs1 2 gh bd (26b) We now turn to analyzing the economic consequences of hardware taxation. It can be easily verified that the equilibrium profit function of the software developer, given in (26b), is strictly concave with respect to the hardware tax rate, t. Moreover, the tax rate that maximizes this profit is
h p (8 2 7gh b ) tˆ 5 ]]]] .0 4h b
(27)
by our assumption that g , 1 /h b . In fact, the profit function (26b) is fully characterized by Fig. 2 where tˆ is now given in (27) instead of (14). For range of values for F s , we can also calculate the equivalent of t˜ which is the threshold tax rate that would induce the software developer to stay in business. Clearly, in the present model Proposition 2 is irrelevant since here the h p consumers will always pirate the software. However, Propositions 3 and 4 remain valid with the same interpretation, that is, hardware tax reduces social welfare unless, it is needed to secure non-negative profit for the software developer.
6. Multiple software developers A referee pointed out an additional difficulty in implementing the hardware for the purpose of compensating multiple software developers. Suppose that the purchase of hardware must be accompanied by the purchase of s software packages, sold separately by s 5 1, 2, . . . , s software developers. In this case, the upper part of the utility function (1) becomes
O p. s
h
Ux 5 a x 1 g N 2 p 2
s
(28)
s 51
Following the same derivation as in Sections 2.4 and 2.5, except assuming that there are s software developers, the Nash–Bertrand software prices and profit levels are
a 2b p s 5 ]] s 11
(a 2 b )h and p s 5 ]]] 2 F s 1 T s , for s 5 1, 2, . . . , s, (s 1 1)2
(29)
where T s is the amount of revenue allocated from hardware taxation to software developer s. Clearly, if we require the government to maintain balanced budget, we must have o ss 51 T s 5 T. The reader can verify that for a single software developer (i.e., if s 5 1), Eq. (29) reduces to (9) and (13). The profit functions of the s software developers given in (29) demonstrate the following problems faced by the regulator.
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(a) If the regulator equally divides the tax revenue so that T s 5 T /s, then firms with lower development costs will end up with a strictly positive profit, which reflect a social waste due to the resulting reduction in the number of hardware buyers. (b) If the regulator divide the revenue unequally, software developers will inflate their development costs and report higher cost than what they actually have. (c) If software development costs are not uniform across software writers (i.e., F s ± F s 9 for some s, s9 5 1, 2, . . . , s ), it may be socially optimal to allow some software firms to reach bankruptcy. In this case, a regulator may not be needed as only low cost software will be written. All these three problems further diminish the feasibility of using hardware taxation to support copyright owners of software.
7. Discussion A tax on hardware indeed reduces the illegal use of software. But, it also reduces the entire demand for using software in general and the demand for buying software in particular, since this tax raises the consumer price of buying a system combining both hardware and software. The policy implications of our investigation is that the regulator should refrain from imposing the hardware tax unless this tax is essential for the survival of the software industry (and hence the entire hardware and software industry), and provided that the services of this industry are desirable. In terms of Fig. 2, the profit curve must have a strictly positive segment. Of course, if a subsidy is needed, a lump sum transfer directly from the government to the software publisher is superior the hardware taxation. However, governments may not be able to pursue such transfers for political reasons.
7.1. Network externality effects In this simple model, piracy is enhanced by the network externality effect. When the network parameter, g increases (within the permissible range of Assumption 2), (11) reveals that x p decreases and N increases, meaning that the piracy level is intensified. Proposition 2(a) reveals that a higher hardware tax would be needed to eliminate piracy. As it turns out, despite the fact that piracy increases when the network factor becomes more important (g increases), (13) shows that the profit of the software developer also increases. This demonstrates that in the presence of network effects an increase in the level of piracy need not reflect a decline in the profit of software developers, since the software becomes more valuable to buyers. Consequently the profit of software publisher may increase with the level of piracy.
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7.2. A look towards the future Finally, we believe that the solution for the violation of intellectual property rights will eventually come from the private sector and not from the public sector. More precisely, since surcharges and even an aggressive enforcement can achieve only a very limited success (if any), it is the technology advance which will make intellectual property rights self enforced. For the case of computer software, with an increased speed of the Internet, it is possible that most software will be installed on commercial servers and not on individuals’ hard drives. This means that file servers will be able to track down who owes and how much for the use of a particular piece of software and other type of information and entertainment products, see Varian (1995). Thus, software publishers will be able to rent software for the time it is actually used. As for digitally stored music, books, and movies, technology will soon enable publishers to rent them as well by encrypting the digital bits using self-destroying software. This software could be activated by counters allowing the specific medium to be played the number of times they are rented for. Such a mechanism was tried out on the DIVX standard which was competing with the DVD standard during the 1990s. To conclude, we believe that copyrights are more efficiently protected by the technology itself rather than by hardware taxes.
Acknowledgements We thank an anonymous referee as well as Paul Belleflamme, Avner Bar-Ilan, and Avi Weiss for most valuable suggestions and comments on earlier drafts. Part of this research was conducted while Oz Shy was visiting the Walther Rathenau Institute for Organization Theory whose hospitality is gratefully acknowledged.
References Besen, S., Kirby, S., 1989. Private copying, appropriability, and optimal copying royalties. Journal of Law and Economics 32, 255–280. Conner, K., Rumelt, R., 1991. Software piracy: an analysis of protection strategies. Management Science 37, 125–139. Givon, M., Mahajan, V., Muller, E., 1995. Software piracy: estimation of lost sales and the impact on software diffusion. Journal of Marketing 59, 29–37. Johnson, W., 1985. The economics of copying. Journal of Political Economy 93, 158–174. King, S., Lampe, R., forthcoming. Network externalities, price discrimination and profitable piracy. Information Economics and Policy. Liebowitz, S., 1985. Copying and indirect appropriability: photocopying of journals. Journal of Political Economy 93, 945–957. Novos, I., Waldman, M., 1984. The effects of increased copyright protection: an analytical approach. Journal of Political Economy 92, 236–246.
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Poddar, S., 2002. Network Externality and Software Piracy. WIDER Discussion Paper 2002 / 115. Helsinki, Finland. Poddar, S., 2003. On Software Piracy when Piracy is Costly. Working Paper, Department of Economics, National University of Singapore. Shy, O., 2000. The economics of copy protection in software and other media. In: Kahin, B., Varian, H. (Eds.), Internet Publishing and Beyond. MIT Press, Cambridge, MA, pp. 99–113, Ch. 5. Shy, O., 2001. The Economics of Network Industries. Cambridge University Press, Cambridge. Shy, O., Thisse, J., 1999. A strategic approach to software protection. Journal of Economics & Management Strategy 8, 163–190. Slive, J., Bernhardt, D., 1998. Pirated for profit. Canadian Journal of Economics 31, 886–899. Takeyama, L., 1994. The welfare implications of unauthorized reproduction of intellectual property in the presence of demand network externalities. Journal of Industrial Economics 42, 155–166. Takeyama, L., 1997. The intertemporal consequences of unauthorized reproduction of intellectual property. Journal of Law and Economics 40, 511–522. Varian, H., 1995. The information economy. Scientific American September, 161–162.
Copyright protection and hardware taxation Amit Gayer a , *, Oz Shy a,b a
Department of Economics, University of Haifa, Haifa 31905, Israel b Humboldt University at Berlin, Berlin, Germany
Abstract This paper investigates the recently practiced method of taxing hardware and transferring the proceeds to software makers, or artists in general. We characterize the conditions under which the policy of compensating copyright owners for infringements on their intellectual property using hardware taxation is inefficient. 2003 Elsevier B.V. All rights reserved. Keywords: Software piracy; Hardware taxation; Intellectual property; Copyright violation JEL Classification: L86; O34
1. Introduction
1.1. Major observations and legal issues Violations of copyrighted material in general and software in particular are known as piracy. Piracy is conducted via copying for personal usage, or for commercial purposes. Copying could be utilizing analog formats, for example, dubbing audio and video cassettes, or could be digital, for example, copying computer software, DVD, or MP3 artistic works. There are many different estimates concerning the level of piracy in the various entertainment and software industries. Some argue that software piracy in the West could be between 25 and 50%, whereas it could reach 90% in the developing countries in the Far East. Clearly, the degree of piracy heavily depends on the *Corresponding author. E-mail addresses: amit [email protected] (A. Gayer), [email protected] (O. Shy). ] 0167-6245 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0167-6245(03)00023-4
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enforcement of copyright laws to eliminate markets for pirated entertainment media and for computer software. Music and software publishers often quote their ‘losses’ resulting from piracy in the billions of dollars; however, one should bear in mind that these quotes tend to be exaggerated since they are based on the false assumption that if copyright laws were strictly enforced, those who pirate would necessarily become buyers. The fast penetration of the Internet into the home and business communities further intensified the piracy of artistic titles. In addition to public and commercial mainframe computers that store computer software as freeware and shareware packages for the public to download, Napster developed software in which users can exchange music titles over the Internet. [See, www.napster.com. Napster was recently ordered to block all copyprotected music titles.] The innovation was that music titles can be downloaded not only from a particular mainframe computer, but also from hard drives of other participating users. Theoretically, the second-best solution to the piracy problem (assuming that copyright enforcement is infeasible) would be to tax those consumers who purchase pirated copies. However, taxing these consumers is equivalent to selling the software, and is therefore infeasible. This raises the question whether there exist economic methods for compensating music and software publishers for the partial loss of their intellectual property rents. The present paper investigates the effects of the imposition of tax on hardware and using the proceeds to recover the loss of profits claimed by software producers. Some countries have already implemented hardware taxes and some are planning to introduce this tax. France imposes a surcharge of 59–69 cents on each recordable medium such as on blank CDs, minidisks, and cassettes, with the intention of levying a surcharge on personal computers’ hard drives (Business Week, February 5, 2001, p.19). The proceeds of the already imposed surcharge go to royalty funds for artists. Besen and Kirby (1989) cite the Home Recording Act of 1982 introduced in the US Congress. Copyright holders would be compensated for private copying out of the royalties levied on the sale of audio and video. The same authors report that in Germany there is a levy on manufacturers and importers of recording equipment. The remuneration consists of an equitable share of the proceeds resulting from the sale of the equipment (limited to 5%). In both Austria and Germany, authors of audio-visual works have similar rights against manufacturers of blank tapes, with the amount of royalty being established by the law. The ‘thinking’ behind this mechanism is that hardware would be used for creating, copying, and storing pirated copies.
1.2. The literature and our investigation Several papers have already analyzed the effects of piracy on the demand for the legally supplied software. See, a pioneering paper by Conner and Rumelt (1991), and extensions in Shy and Thisse (1999), Shy (2000, 2001, Ch. 3), Poddar (2002,
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2003), Slive and Bernhardt (1998), and Takeyama (1994, 1997). More recently, King and Lampe (forthcoming) investigate the claims when the producer can freely choose the degree of piracy prevention. They show that allowing piracy cannot raise profits if the monopoly producer can directly price discriminate between potential-pirates and other customers. In the absence of price discrimination, they show that allowing piracy will only maximize profits when the ability to pirate is inversely related to customer willingness-to-pay. Finally, an empirical investigating showing how the increase in software piracy can boost the demand for the legal software is conducted in Givon et al. (1995). Earlier papers discussing the effects of photocopying include Besen and Kirby (1989), Johnson (1985), Liebowitz (1985), and Novos and Waldman (1984). In this paper we deliberately abstract from the ‘profitable piracy’ debate, which is extensively analyzed in the literature analyzed above. Instead, we focus our investigation on the effects of hardware taxation on the profit of a software publisher, whose software is pirated by some users. We develop a model in which the user population gain utility from software to be used on a piece of hardware. Thus, users must purchase hardware and software from different manufacturers. We calculate equilibrium prices under which the user population is divided into three groups: those who buy hardware and software, those who buy the hardware and pirate the software, and those who do not buy anything so they become nonusers. We then investigate how a tax on hardware affects the profit of the software producer under the extreme assumption that the proceeds from this tax are transferred to the software publisher, as a compensation for the partial violation of the publisher’s intellectual property right. Finally, we investigate the effects of hardware taxation on social welfare.
1.3. Organization The paper is organized as follows. Section 2 sets up a model of hardware and software producers, where consumers can either buy the software or use it illegally without paying for it. Section 3 investigates the effects of hardware taxation and the welfare consequences of this hardware tax. Section 4 investigates the effects of hardware taxation on social welfare. Section 5 proposes an alternative formulation. Section 6 introduces multiple software developers. Section 7 concludes.
2. The market for hardware, software, and piracy Consider a market composed of users who wish to utilize a certain piece of software (e.g., computer software, a music performance, a digitally stored book, or a movie). For the sake of brevity we call this title by the name software, and assume that this software is copyrighted. The software analyzed in this paper can be obtained in two ways. It can be
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purchased on conventional media such as diskettes or compact disks. Alternatively, it can be illegally copied. There are many ways in which copyrighted media can be copied, for example, it could be downloaded via the Internet, sent by e-mail, copied from diskettes, CD, DVD, or audio cassettes.
2.1. Users There is a continuum of types of potential software users indexed by x on the interval [0, 1], with density of h $ 1users per type. Thus, the total number of consumers in this market is h. Each user consumes at most one unit of this software, either by purchasing it from the store for a price p s , or by pirating it without paying p s . In addition, each user who wishes to use the software must purchase one unit of hardware (e.g., a computer, CD/ DVD player, or a cassette player) for a price of p h . The utility of each user indexed by x 0 # x # 1 is defined by
a x 1 g N 2 p h 2 p s if buys hardware and software Ux 5 b x 1 g N 2 p h if buys hardware and pirates the software 0 if does not use software and hardware def
5
(1)
The parameters a . 0 and b . 0 measure a user’s basic utility from the services provided by this software title. Thus, user-types indexed by x close to 0 are interpreted as those who gain very little from using computers and software, whereas users indexed by an x close to 1 gain the most out of using computers and software. We make the following assumption. Assumption 1. For every user x, legally purchased software yields more services than pirated software. Formally, purchased software and pirated software are vertically differentiated, i.e., a . b. The interpretation of Assumption 1 is as follows. Legally purchased software is bundled with manuals, installation software, service, as well as discounts on upgrades. In contrast, users who pirate the software may not be able to copy the manuals, may be forced to utilize complicated installation techniques, and are not entitled to obtain service and upgrades. In addition, users who do not buy the software may have hard time in locating the software, and then copying or downloading it for installation purposes. In addition, some illegal users may feel uncomfortable in using copyrighted software without paying for it. Finally, the utility function (1) implicitly assumes a correlation between the value of software and the value for non-pirated features of the software. Section 5 provides an alternative formulation which relaxes this assumption. The variable N is the endogenously determined total number of users, which is the sum of those who buy the software and those who illegally copy the software.
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The parameter g $ 0 is the network externality parameter reflecting the degree of importance of the total number of users. Therefore, if g . 0, the utility of each user is enhanced with the total number of all consumers who use this software. There are two interpretations for this assumption. In one interpretation, users gain from having more people using the same software since they can work together, say by exchanging files. A second interpretation refers to popularity or fashions where people ‘feel better’ by using products that are similar to what others consume. It is important to observe that all users, regardless of whether they are buyers or illegal users, gain from the network size. Thus, buyers benefit with an increase in the number of buyers as well as in the number of illegal users, and illegal users also benefit from an increase in the number of buyers as well as in the number of illegal users. We confine our analysis to the following parameter range. Assumption 2. The network effect parameter is bounded by the basic valuation for the software. Formally,
H
J
b b 2a ] , g , max ]; ] . 2h h 3h Assumption 2 constrains the network externality effect. Higher values of g (strong network effects) would make the software highly valuable by all consumers (type x50 in particular) thereby generating an equilibrium where all potential users become actual users even with the imposition of a revenue-maximizing tax on hardware. Lower values of g (weak network effects) would generate equilibria with only small number (or even none) of the users who pirate the software.
2.2. Users’ choice problem Let x p denote the type of consumers who are indifferent between pirating the software and not using the software at all. In view of the utility function (1), this consumer type is solved from p h 2 gN b x p 1 g N 2 p h 5 0, hence x p 5 ]]]. b
(2)
Thus, all users indexed on [0, x p ] do not use (and do not purchase) any hardware and software. Similarly, let x b denote the type of consumers who are indifferent between buying the software and pirating the software. In view of the utility function (1), this consumer type is solved from ps a x b 1 g N 2 p h 2 p s 5 b x b 1 g N 2 p h , hence x b 5 ]] a 2b
(3)
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Thus, all users indexed on [x p , x b ] pirate the software, and all users index on [x b , 1] buy the software, Therefore, the number of software buyers is h(1 2 x b ), and the total number of users who pirate the software is h(x b 2 x p ). Therefore, the aggregate number of users (i.e., the sum of buyers and illegal users) is given by
S
D
ph 2 g N h ( b 2 p h) N 5 h (1 2 x p ) 5 h 1 2 ]]] , hence N 5 ]]]. b b 2 gh
(4)
Fig. 1 illustrates how the market is divided among buyers, illegal users and nonusers.
2.3. The government Clearly, the government is unable to directly tax those who illegally copy the software since pirated copies are not purchased in any formal way. Also, it is clear that piracy cannot be reduced if the government taxes software buyers. In fact, taxing software buyers would reduce the number of buyers. Thus, the only tax mechanism available to the government is to tax the hardware purchased by each legal and an illegal software user. Let t denote the per-unit (specific) tax on hardware, and by T the total revenue collected from this tax. Then, T 5 tN.
(5)
Finally, to make our investigation complete, we assume that the purpose of this tax is to ‘compensate’ the software producer for the copyright infringement associated with piracy. Thus, we assume that the government’s sole objective is to compensate the software producer by transferring the entire revenue collected by the tax on hardware.
2.4. The hardware producer We assume that hardware is produced and sold by a single monopoly firm, and that there is no black market for hardware. Let F h denote the fixed cost borne by the hardware producer, and c h the marginal cost. With no loss of generality, we set c h 50. Therefore, the hardware producer chooses a price, p h , that solves
Fig. 1. Buyers, illegal users (pirates), and non-users.
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h( b 2 p h) max p h 5 ( p h 2 t)N 2 F h 5 ( p h 2 t) ]]] 2 F h . b 2 gh ph
473
(6)
We make the following assumption. Assumption 3. The hardware fixed cost is bounded. Formally,
h( b )2 F h , ]]]. 4( b 2 gh ) Assumption 3 ensures that the hardware producer earns positive profit. Under this assumption, the hardware producer’s profit-maximizing price is
b 1t p h 5 ]]. 2
(7)
Notice that the hardware price increases with the tax on hardware and with b which is the software-valuation parameter of a pirating user.
2.5. The software publisher There is a single monopoly software house producing a certain software package. Let F s denote the fixed cost borne by the software publisher and c s the marginal cost. With no loss of generality we set c s 50. The seller of the software chooses p s that solves
S
D
ps s s b s s ]] max p 5 p h (1 2 x ) 2 F 1 T 5 p h 1 2 2 F s 1 T. a 2b ps
(8)
There are two ways to interpret the software maker’s profit function (8). The first interpretation involves a non-strategic software developer who treats the government’s subsidy, T, as given. Such an interpretation is commonly used in the public finance literature. The second interpretation involves a strategic software developer who can indirectly ‘manipulate’ the subsidy via the price of software. However, inspecting (4) reveals that the aggregate number of users is influenced only by p h and not by p s , which means that these two interpretations yield the same results. Thus, maximizing (8), the software firm’s profit-maximizing price is then given by
a 2b h(a 2 b ) p s 5 ]], provided that F s # ]]] 1 T. 2 4
(9)
The sufficient condition in (9) implies that the fixed cost of software publishing should be either relatively small, or that the tax revenue transferred to the publisher must be sufficiently high as to cover part of the fixed costs. Therefore,
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Proposition 1. No software is developed if
H
J
h(a 2 b ) T , max F s 2 ]]], 0 . 4 That is, the software will not prevail in the case that tax revenues do not exceed the software publisher’s loss (if any).
3. Hardware taxation and the software publisher
3.1. The low fixed cost case We start our analysis by assuming that the fixed cost of the software publisher, F s , is sufficiently low (or zero) so that the publisher is not making a loss even in the absence of any subsidy. In Section 3.2 we investigate the high fixed cost case. Formally, let
h(a 2 b ) F s # ]]] 4
(10)
Substituting (7) and (9) into (4), and then also into (2) and (3), we obtain the aggregate number of users (buyers and illegal users), as well as the user types who are indifferent between not using and pirating, and between pirating and buying the software. Therefore,
h( b 2 t) N 5 ]]], 2( b 2 gh )
H
J
b 2 2gh 1 t x p 5 max 0, ]]]] , 2( b 2 gh )
1 and x b 5 ]. 2
(11)
Notice that (11) and Assumption 2 imply that when hardware is not taxed (t50) all the market is served (x p 50). Next, (11) implies that the tax revenue collected by the government is
h( b 2 t) T 5 tN 5 t ]]] 2( b 2 gh )
(12)
Substituting (7) into (6), and (9) and (12) into (8) yields the equilibrium profit levels as functions of the tax rate on hardware. Thus, 2h( b 2 t)2 (3d 2 4gh )2 p h 5 ]]]]]]] 2 F h , and (d 2 2gh )(7d 2 8gh )2 h(a 2 b ) h(a 2 b ) h( b 2 t) p s 5 ]]] 2 F s 1 T 5 ]]] 2 F s 1 t ]]] 4 4 2( b 2 gh )
(13)
We now ask what would be the hardware tax rate that maximizes government’s
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Fig. 2. Software publisher’s profit as a function of the tax on hardware.
revenue, and what would be the rate which maximizes the profit of the software developer. However, inspecting (12) and (13) reveals that these two tax rates are identical. Therefore, maximizing (12) with respect to t yields
b tˆ 5 ]. 2
(14)
Fig. 2 illustrates how the tax on hardware affects the software publisher’s profit. Fig. 2 reveals that the profit of the software publisher increases with an increase in the tax rate on hardware at low tax rates, but decreases at high tax rates. The reason is that high tax rates increase the price of hardware (see, (7)) and reduce the demand for hardware and hence for pirated software as well. The reduction in the overall demand for software dominates the increase in the tax rate thereby reducing the profit of the software publisher. The profit function, labeled as p s1 , is associated with low fixed cost F s , in which case the publisher earns a strictly positive profit even in the absence of any compensation coming from the tax revenues. In contrast, the profit function p s2 reflects relatively high fixed costs, in which case the publisher will not produce unless he receives a subsidy (financed by hardware tax revenues). We can now state the following proposition.
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Proposition 2.
(a) By setting the hardware tax rate t 5 gh, the government can eliminate piracy. However, ( b) The hardware tax rate that maximizes the (tax inclusive) profit of the software developer is below the tax rate that eliminates piracy. Proof. (a) From (11) we see that x p → x b as t → gh. (b) t 5 b / 2 , gh by Assumption 2. h
3.2. The high fixed cost case We now assume that the fixed cost of the software publisher, F s , is sufficiently high so that without a subsidy the publisher is making a loss. Formally, we reverse the condition given in (10). This case is illustrated by the lower profit curve in Fig. 2. This case is important since without any intervention the software industry would not produce any software, thereby eliminating the hardware industry as well. Therefore, this case represents the only market condition under which intervention may be justified. We now ask what should be the minimal tax rate on hardware that would guarantee normal profit for the software publisher. From (13), this tax rate is given by ]]]]]]]]]]]]] bh 2œhhhf2a ( b 2 gh ) 2 b 2 1 2bghg 2 8F s ( b 2 gh )j t˜ 5 ]]]]]]]]]]]]]]]]. (15) 2h The tax rate t˜ makes the software publisher break even, and is drawn in Fig. 2. It is easy to illustrate that an increase in the fixed cost F s would lower the profit ˜ which is the necessary tax to keep the software curve thereby increasing t, publisher breaking even.
4. Welfare analysis So far, we analyzed how the hardware tax affects the profit of the software publisher. In this section we analyze the effects of hardware taxation on social welfare. clearly, the main concern of the regulator should be how the tax on hardware affects aggregate social welfare.
4.1. The low fixed cost case Suppose that the software publisher incurs low fixed costs (if any) as given in (10). Section 4.2 below investigates the high fixed cost case.
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We define aggregate consumer surplus by the sum of the utilities of all users. Formally, xb
def
CS 5h
1
E sbx 1 gN 2 p d dx 1 h E fax 1 gN 2 p 2 p g dx h
h
xp
s
xb 2
2
3a ( b 2 gh ) 1 2b (2gh 2 t) 2 b (3g 2h 2 1 t 2 ) 1 2ght 2 ]]]]]]]]]]]]]]]] 5h 2 h p h (1 2 x p ) 8( b 2 gh )2 2 h p s (1 2 x b )
(16)
Note that (1) implies that all potential users indexed on [0, x p ) gain a utility of zero since they neither buy the software nor they pirate it. The sum of profits of the hardware and software producers is given by
ph 1ps
h
p
s
b
p
h
5 ( p 2 t)(1 2 x )h 1 p (1 2 x )h 1 th(1 2 x ) 2 F 2 F 5 p h (1 2 x p )h 1 p sh(1 2 x b ) 2 F h 2 F s .
s
(17)
Clearly, aggregate profit (17) enters as a negative sum in aggregate consumer surplus (16) since it reflects a transfer from buyers to firms. Altogether, we define the social welfare function by the sum of users’ utilities and the profits of the hardware and software firms. Formally, def
h
W(t) 5CS 1 p 1 p
s
3a ( b 2 gh )2 1 2b 2 (2gh 2 t) 2 b (3g 2h 2 1 t 2 ) 1 2ght 2 5 h ]]]]]]]]]]]]]]] 2 F h 2 F s. 8( b 2 gh )2 (18) Differentiating (18) with respect to t yields ≠ 2W h(2gh 2 b ) ≠W ]] and ] 2 5 ]]]] 2 . 0, ≠t ≠t 4( b 2 gh )
U
t 50
2 hb 2 5 ]]]]2 , 0. 4( b 2 gh )
We are now ready to state the following proposition. Proposition 3. When the fixed cost of software is low (see (10) ), the tax rate that maximizes social welfare is t 5 0. Proposition 3 demonstrates that under low software fixed costs, this tax distorts social welfare, hence this transfer of rents to the software publisher does not enhance social welfare. In what follows, we demonstrate that this is not necessary the case when the software industry bears high fixed cost.
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4.2. The high fixed cost case We now assume that the fixed cost of the software publisher, F s , is sufficiently high so that without a subsidy the publisher is making a loss. Formally, we reverse the condition given in (10). Proposition 3 demonstrated that hardware taxation reduces social welfare when the software publisher earns at least normal profit. On the other hand, Fig. 2 illustrates that under high fixed costs, the software industry will not exist unless it ˜ Therefore, is subsidized by a hardware tax rate of at least t. Proposition 4. Suppose that the fixed cost of software is high [condition (10) is reversed], and
h( b 2 t˜ )2 ]]] F # . 4( b 2 gh ) h
(19)
Then, the tax rate that maximizes social welfare is strictly positive and is given by t˜ which is defined by (15). Proposition 4 provides some rational for taxing hardware. However, this argument is valid only if piracy endangers the existence of the software industry. The Condition (19) in Proposition 4, which is taken from (13), ensures that the ˜ hardware industry is not making a loss at the optimal tax rate t.
5. An alternative formulation Our formulation so far has relied on the utility function (1) which has the property that consumers’ value for the software, as measured by the index number x, is correlated with the consumers’ marginal valuation for the extra features embedded in a legally purchased software that do not exist in the pirated version, and measured by (a 2 b )x. This correlation is extensively discussed in King and Lampe who attribute this assumption to results of ‘profitable’ piracy. In this section we briefly develop a model which does not rely on the above correlation, but, following King and Lampe, does rely on an assumption that some consumers (e.g., large companies who face high litigation costs) cannot pirate the software. We demonstrate that our conclusions regarding the use of hardware taxation remain valid when the value for software and the value for non-pirated features are not correlated. As before, N denote the endogenously determined total number of users (buyers and illegal users), p h the price of hardware purchased by all users, and p s the price of software. Let there be h p users who pirate the software and assume a density of h b of buyers indexed by x, x $ 0.
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The utility function of a consumer x who cannot pirate the software (type-b, stands for buyers) is given by def
Hg
U bx 5
N 2 ph 2 ps 2 x
0
if buys hardware and software , if does not use software and hardware
(20)
where we assume that g , 1 /h b . Let xˆ b denote a type-b consumer who is indifferent between purchasing hardware and software and not purchasing at all. The number of software buyers is then xˆ bh b . Therefore the total number of software users (buyers and illegal users combined) is N 5 h p 1 xˆ ph b . The utility function (20) implies that
gh p 2 p h 2 p s ˆx b 5 ]]]] . 1 2 gh b
(21)
The hardware firm chooses its price p h to solve
sgh bh p 1 th b 2 2h pd 2 max p h 5 ( p h 2 t)N 2 F h 5 ]]]]]] 2 F h. 9h b (1 2 gh b ) ph
(22)
The software firm chooses its price p s to solve
S
D
p h s s s b b s s gh 2 p 2 p ˆ ]]]] max p 5 p x h 2 F 1 T 5 p h b 2 F s 1 T, b ps 1 2 gh
(23)
where, as before, T 5 tN is the hardware tax revenue which is transferred to the software developer in a lump-sum fashion. The unique Nash–Bertrand equilibrium is given by 2h p 1 2th b 2 gh bh p ]]]]]] p 5 3h b h
and
2gh bh p 2 th b 2 h p ]]]]]] p 5 . 3h b s
(24)
The consumer who is indifferent between buying and not using hardware and software, as well as the resulting revenue collected from hardware taxation are given by b
p
b
p
2gh h 2 th 2 h b xˆ 5 ]]]]]] b b 3h (1 2 gh )
p
b
b
p
t(2h 2 th 2 gh h ) and T 5 ]]]]]] . b 3(1 2 gh )
(25)
Finally, the equilibrium profit levels are
sgh bh p 1 th b 2 2h pd 2 p h 5 ]]]]]] 2Fh 9h bs1 2 gh bd
(26a)
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4g 2 (h b )2 (h p )2 2 gh bh p (7th b 1 4h p ) 2 t 2 (h b )2 1 h p (8th b 1 h p ) p s 5 ]]]]]]]]]]]]]]]]] 2 F s. 9h bs1 2 gh bd (26b) We now turn to analyzing the economic consequences of hardware taxation. It can be easily verified that the equilibrium profit function of the software developer, given in (26b), is strictly concave with respect to the hardware tax rate, t. Moreover, the tax rate that maximizes this profit is
h p (8 2 7gh b ) tˆ 5 ]]]] .0 4h b
(27)
by our assumption that g , 1 /h b . In fact, the profit function (26b) is fully characterized by Fig. 2 where tˆ is now given in (27) instead of (14). For range of values for F s , we can also calculate the equivalent of t˜ which is the threshold tax rate that would induce the software developer to stay in business. Clearly, in the present model Proposition 2 is irrelevant since here the h p consumers will always pirate the software. However, Propositions 3 and 4 remain valid with the same interpretation, that is, hardware tax reduces social welfare unless, it is needed to secure non-negative profit for the software developer.
6. Multiple software developers A referee pointed out an additional difficulty in implementing the hardware for the purpose of compensating multiple software developers. Suppose that the purchase of hardware must be accompanied by the purchase of s software packages, sold separately by s 5 1, 2, . . . , s software developers. In this case, the upper part of the utility function (1) becomes
O p. s
h
Ux 5 a x 1 g N 2 p 2
s
(28)
s 51
Following the same derivation as in Sections 2.4 and 2.5, except assuming that there are s software developers, the Nash–Bertrand software prices and profit levels are
a 2b p s 5 ]] s 11
(a 2 b )h and p s 5 ]]] 2 F s 1 T s , for s 5 1, 2, . . . , s, (s 1 1)2
(29)
where T s is the amount of revenue allocated from hardware taxation to software developer s. Clearly, if we require the government to maintain balanced budget, we must have o ss 51 T s 5 T. The reader can verify that for a single software developer (i.e., if s 5 1), Eq. (29) reduces to (9) and (13). The profit functions of the s software developers given in (29) demonstrate the following problems faced by the regulator.
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(a) If the regulator equally divides the tax revenue so that T s 5 T /s, then firms with lower development costs will end up with a strictly positive profit, which reflect a social waste due to the resulting reduction in the number of hardware buyers. (b) If the regulator divide the revenue unequally, software developers will inflate their development costs and report higher cost than what they actually have. (c) If software development costs are not uniform across software writers (i.e., F s ± F s 9 for some s, s9 5 1, 2, . . . , s ), it may be socially optimal to allow some software firms to reach bankruptcy. In this case, a regulator may not be needed as only low cost software will be written. All these three problems further diminish the feasibility of using hardware taxation to support copyright owners of software.
7. Discussion A tax on hardware indeed reduces the illegal use of software. But, it also reduces the entire demand for using software in general and the demand for buying software in particular, since this tax raises the consumer price of buying a system combining both hardware and software. The policy implications of our investigation is that the regulator should refrain from imposing the hardware tax unless this tax is essential for the survival of the software industry (and hence the entire hardware and software industry), and provided that the services of this industry are desirable. In terms of Fig. 2, the profit curve must have a strictly positive segment. Of course, if a subsidy is needed, a lump sum transfer directly from the government to the software publisher is superior the hardware taxation. However, governments may not be able to pursue such transfers for political reasons.
7.1. Network externality effects In this simple model, piracy is enhanced by the network externality effect. When the network parameter, g increases (within the permissible range of Assumption 2), (11) reveals that x p decreases and N increases, meaning that the piracy level is intensified. Proposition 2(a) reveals that a higher hardware tax would be needed to eliminate piracy. As it turns out, despite the fact that piracy increases when the network factor becomes more important (g increases), (13) shows that the profit of the software developer also increases. This demonstrates that in the presence of network effects an increase in the level of piracy need not reflect a decline in the profit of software developers, since the software becomes more valuable to buyers. Consequently the profit of software publisher may increase with the level of piracy.
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7.2. A look towards the future Finally, we believe that the solution for the violation of intellectual property rights will eventually come from the private sector and not from the public sector. More precisely, since surcharges and even an aggressive enforcement can achieve only a very limited success (if any), it is the technology advance which will make intellectual property rights self enforced. For the case of computer software, with an increased speed of the Internet, it is possible that most software will be installed on commercial servers and not on individuals’ hard drives. This means that file servers will be able to track down who owes and how much for the use of a particular piece of software and other type of information and entertainment products, see Varian (1995). Thus, software publishers will be able to rent software for the time it is actually used. As for digitally stored music, books, and movies, technology will soon enable publishers to rent them as well by encrypting the digital bits using self-destroying software. This software could be activated by counters allowing the specific medium to be played the number of times they are rented for. Such a mechanism was tried out on the DIVX standard which was competing with the DVD standard during the 1990s. To conclude, we believe that copyrights are more efficiently protected by the technology itself rather than by hardware taxes.
Acknowledgements We thank an anonymous referee as well as Paul Belleflamme, Avner Bar-Ilan, and Avi Weiss for most valuable suggestions and comments on earlier drafts. Part of this research was conducted while Oz Shy was visiting the Walther Rathenau Institute for Organization Theory whose hospitality is gratefully acknowledged.
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