Discussion Paper Series No.226
Would global patent protection be too weak without
international coordination?

Edwin L.-C. LAI

Research Department,
Federal Reserve Bank of Dallas

August2008

The Discussion Papers are a series of research papers in their draft
form, circulated to encourage discussion and comment. Citation anduse of such a paper should take account of its provisional character.
In some cases, a written consent of the author may be required.

Would global patent protection be too weak without
international coordination?
∗

Edwin L.-C. Lai†First Draft: November 2005
This Draft: August 27, 2008

Abstract
I extend the Grossman and Lai (2004) model to answer the question, “Would global
patent protection be too weak without international coordination?” by introducing firmbiased government preferences and trade barriers in the model. I make use of the estimates of the firm-bias parameter from the political economy literature to proxy forthe degree of governments’ firm-bias. Then I calculate the range of trade barriers thatis suﬃcient to give rise to under-protection of patents in the global system without international policy coordination in IPR protection. I make the judgement that the true
trade barrier between countries very likely falls within this range of under-protection.
Therefore, I conclude that there was probably under-protection of patents without international policy coordination in IPR protection. It means that the free-rider problem
with a large number of independent players overrides the eﬀects of firm-bias and tradebarriers, giving rise to too low a rate of innovation in the world. Allowing for the possibility that countries discriminate against foreign firms in Nash equilibrium does not change
this conclusion. The problem can possibly be corrected by international coordination in
intellectual property rights (IPR) protection.
Keywords: Intellectual property rights, TRIPS, innovation
JEL Classification Number: F1, O31, O34––––—† Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl St., Dallas, TX
75201, USA. Phone: (214) 922-6941; Fax (214)922-5194; Email: Edwin.L.Lai@gmail.com∗ I would like to thank Costas Syropoulos, participants in seminar in Michigan State
University, AEA Annual Meeting 2006 and Otago Workshop in International Economics
2006 for helpful comments. The work in this paper has been supported by the Research
Grants Council of Hong Kong, China (Project no. CityU 1476/05H) and City Universityof Hong Kong.

1Introduction

The global intellectual property rights (IPR) protection system was given a boost by
the implementation of the TRIPS agreement (Agreement on Trade-Related Aspects ofIntellectual Property Rights), which started a gradual process of IPR harmonizationin 1995. This agreement eﬀectively requires the strengthening of patent protection ofmost countries, and forces the world IPR protection policies towards harmonization(albeit a partial one). There have been nothing nearly as powerful as TRIPS in its
geographic coverage and its ability to enforce rulings, not least because of the large
number of countries involved and the credibility of the threat of punishment throughtrade retaliation. Given the tremendous repercussions of such a coordinated increase in
the strengths of IPR protection, it is fair to ask whether TRIPS is really a solution toa global coordination problem. It is clear that TRIPS has distributive eﬀect between
countries.1 However, the more important question is whether global IPR protection was
too weak before TRIPS. If it was, then TRIPS can potentially be welfare-improving fromthe global point of view, and its inclusion in global trade talks would potentially facilitate
negotiations on liberalization of other sectors/areas. For example, if less developed
countries (LDCs) lose from TRIPS and developed countries (DCs) gain from TRIPS, but
the latter’s gains outweigh the former’s losses, then it can be mutually beneficial for the
LDCs to accept harmonization of IPR standards with the DCs in exchange for the DCs’opening their markets for labor-intensive manufacturing goods or agricultural products
from the LDCs. However, if global patent protection was already too strong before
TRIPS, then no such synergy exists between talks on trade-related IPR negotiations
and other issues/areas of global trade talks.
There is no doubt that some countries attempted to coordinate their IPR policies
somewhat even before TRIPS, but empirical studies have shown that even as late as 1990,
market sizes and innovative capabilities significantly aﬀect variation in the strengths of1

McCalman (2001) has shown that the US was by far the largest beneficiary, followed by Germany

and France as distant second and third beneficiaries. On the other hand, the greatest loser was Canada,followed by Brazil and UK.

1patent protection across the world, as predicted by non-cooperative game theory.2 So, I
start with the working assumption that the world was in a non-cooperative equilibrium
before TRIPS, and then ask, Would global patent protection be too weak when left toindividual governments to decide its own level of protection?
To answer this question, we need to (a) have a theory that explains how global
patent protection was determined in a non-cooperative equilibrium; (b) have a theory
that explains how the optimal global patent protection is determined; and (c) develop a
suﬃcient condition for global under-protection (or over-protection) of IPR. In order toanswer (c), we need to explain how a global system of patent protection aﬀects incentives to innovate and how it creates distortions (deadweight losses). Therefore, we needto answer (a) and (b) first. To do so, I modify and extend a model by Grossman andLai (2004). In Section 2, I shall re-state their theory in a succinct form. Then, I develop an extension that allows us to more realistically evaluate whether non-cooperativeequilibrium gives rise to under-protection of IPR.
In the basic model of Grossman and Lai (2004), countries play a Nash game in setting
the strengths of patent protection. The best response function of a country’s government is obtained by setting the strength of patent protection that equates the marginal
costs (deadweight loss due to longer duration of monopoly pricing) and marginal benefits (increased incentives of innovation) of extending protection, given the strengthsof protection of other countries. Each country conveys positive externalities to foreigncountries as it extends patent protection, since it increases profits of foreign firms in
the home market, and increases consumer surplus of foreign consumers due to induced
innovations. As a result, there is under-protection of patent rights in Nash equilibrium
relative to the global optimum. In fact, the degree of under-protection in Nash equilibrium increases with the number of independent decision-makers in the patent-setting
game.
However, two factors prevents us from directly applying Grossman and Lai’s (2004)
basic model to answer the question posed in the title of this paper: “Would global patent
protection be too weak without international coordination?”. First is that governments
2See, for example, Ginarte and Park (1997) and Maskus (2000a).

2

may put extra weight on profits as opposed to consumer surplus (e.g. due to firm lobbying). When governments put more weight on profits, the marginal cost of patent protection decreases since deadweight loss is smaller. Therefore, patent protection in Nashequilibrium is stronger. I shall call this firm-biased preferences of governments. Second
is the existence of trade barriers. When a firm has only a fraction of the penetration
rate in a foreign market as compared to the domestic market (e.g. due to transportation
cost and other trade costs), the positive international externalities of patent protection
is diminished. Both factors tend to diminish the degree of under-protection in Nashequilibrium relative to the global optimum. If these forces are strong enough, there
may even be over-protection of patents in Nash equilibrium. Therefore, whether or notthere was under-protection of patents in the non-cooperative equilibrium is an empiricalquestion. In this paper, I incorporate these two features in an extension of the basic
Grossman and Lai (2004) model and derive a suﬃcient condition for under-protection ofpatent in the global economy. I then calibrate the model using the firm-bias parameter
estimated from the empirical literature and then finding out how small the trade barriers
have to be in order for there to be under-protection of patents in Nash equilibrium.
In the basic model, we can find a functional relationship between the global strengthof patent protection and global welfare. The same strength of global patent protection
creates the same amount of total deadweight losses (what I call static losses) and aggregate flow of new diﬀerentiated goods (what I call dynamic gains) in each period. Aslong as the global strength of patent protection is the same, global welfare is the same,
regardless of the combination of individual countries’ strengths of patent protection.
Therefore, the global optimum is a continuum of combinations of national strengths ofpatent protection that maximize global welfare. However, this will not be true in theextended model. In the more general model with trade barriers, there does not exista scalar measure of the global strength of patent protection such that there is a functional relationship between the global strength of protection and global welfare. Despite
this problem, I am able to calculate a suﬃcient condition under which, starting fromNash equilibrium, global welfare must increase with increases in the strengths of protection in all countries. When this condition is satisfied, we can conclude that there is3

under-protection in global IPR protection.
The key results of the extended model are: 1. There is only one single combination, not a continuum, of national strengths of patent protection that maximizes global
welfare. 2. Externalities still exist, but their magnitude decreases with trade barriers. Therefore, the degree of under-protection decreases with trade barriers. 3. The
degree of under-protection decreases with the firm-bias of governments. 4. Based on
the estimates of the firm-bias parameter from the political economy literature, and ourjudgement of the plausible magnitude of trade barrier, I conclude that under-protectionof global patent protection in the non-cooperative equilibrium is very likely.
Some argue that without an international agreement, countries have incentives todiscriminate against foreign firms by oﬀering lower patent protection to them. In otherwords, there is no observance of national treatment in Nash equilibrium. I accountfor this fact later in the paper. It is found that the condition for under-protection in
Nash equilibrium is less stringent than in the case with observance of national treatment
in Nash equilibrium. Therefore, allowing for non-observance of the national treatment
principle in equilibrium strengthens the argument that there is under-protection without
international coordination.
In section 2, I recap the essence of the basic model of Grossman and Lai (2004).
In section 3, I extend the basic model to incorporate firm-bias and trade barriers. In
section 4, I account for the fact that countries can discriminate against foreign firms in
Nash equilibrium. Finally, I conclude in section 5.

2

A basic theory of international protection of IPR

The theory described in this section basically draws from Grossman and Lai (2004).

2.1

Noncooperative Patent Protection

In this section, I study the national incentives for protection of intellectual property ina world economy with imitation and trade. We derive the Nash equilibria of a game inwhich two countries set their patent policies simultaneously and noncooperatively. The
4

countries are distinguished by their wage rates, their market sizes, and their stocks ofhuman capital. The last of these proxies for their diﬀerent capacities for R&D. We shallterm the countries “North” and “South,” in keeping with our desire to understand thetensions that surrounded the tightening of intellectual property rights (IPR) protectionin the developing countries in the last decade. Keith E. Maskus (2000a, ch.3) has
documented an increase in innovative activity in poor and middle-income countries suchas Brazil, Korea, and China, so our model of relations between trading partners withpositive but diﬀerent abilities to conduct R&D may be apt for studying the incentives for
IPR protection in a world of trade between such nations and the developed economies.3
But our model may apply more broadly to relations between any groups of countries
that have diﬀerent wages and diﬀerent capacities for research. Such diﬀerences exist,
albeit to a lesser extent than between North and South, in the comparison of countries
in Northern and Southern Europe, or the comparison of the United States and Canada.
We do not mean the labels North and South to rule out the application of our analysis
to these other sorts of relationships.

2.1.1

The Global IPR Regime

Consumers in the two countries share identical preferences. In each country, the representative consumer maximizes the intertemporal utility function. The instantaneous
utility of a consumer in country j is given by
Z nS (z)+nN (z)uj (z) = yj (z) +h[xj (i, z)]di,(1)0where yj (z) is consumption of the homogeneous good by a typical resident of country j attime z, xj (i, z) is consumption of the ith diﬀerentiated product by a resident of country
j at time z, and nj (z) is the number of diﬀerentiated varieties previously invented incountry j that remain economically viable at time z. There are MN consumers in the
North and MS consumers in the South. While we do not place any restrictions on the3

He also shows the extent to which patent applications in countries like Mexico, Brazil, Korea,

Malaysia, Indonesia and Singapore are dominated by foreign firms, a feature of the data that figuresin our analysis.

5relative sizes of the two markets at this juncture, we shall be most interested in the casewhere MN > MS .4 It does not matter for our analysis whether consumers can borrowand lend internationally or not.
In country j, it takes aj units of labor to produce one unit of the homogeneous
good or to produce one unit of any variety of the diﬀerentiated product. New goods
are invented in each region according to φj = F (Hj , LRj /aj ) = A (LRj /aj )b Hj1−b , where
Hj is an input whose quantity determines the innovative capability of country j, LRj is
the labor devoted to R&D there. We assume that aN < aS , which means that labor is
uniformly more productive in the North than in the South. We also assume that thenumeraire good is produced in positive quantities in both countries, so that wj = 1/aj
for j = S, N, and hence wN /wS = aS /aN > 1. Define T = (1 − e−ρτ )/ρ, where τ is the
product life of a diﬀerentiated good.
We now describe the IPR regime. In each country, there is national treatment in the
granting of patent rights. Under national treatment, the government of country j aﬀords
the same protection Ωj = ω j Tj to all inventors of diﬀerentiated products regardless of
their national origins, where ω j is the probability that a patent is enforced in country j(or the fraction of country j’s market where a patent is enforced) at any moment in time,
Tj = (1 − e−ρτ j )/ρ, and τ j is the length of the patents granted by country j. In otherwords, we assume that foreign firms and domestic firms have equal standing in applying
for patents in any country and that all patents are subject to the same enforcement
provisions. National treatment is required by TRIPS and it characterized the laws thatwere in place in most countries even before this agreement.5 In our model, a patent
is an exclusive right to make, sell, use, or import a product for a fixed period of time4

We remind the reader that market size is meant to capture not the population of a country, butrather the scale of its demand for innovative products.
5
National treatment is required by the Paris Convention for the Protection of Industrial Property, to which 127 countries subscribed by the end of 1994 and 164 countries subscribe today (seehttp://www.wipo.org/treaties/ip/paris/index.html).

There were, however, allegations from firms in

the United States and elsewhere that prior to the signing of TRIPS in 1994, nondiscriminatory laws
did not always mean nondiscriminatory practice. See Suzanne Scotchmer (2004) for an analysis of the
incentives that countries have to apply national treatment in the absence of an enforcible agreement.

6

(see Maskus, 2000a, p.36). This means that, when good i is under patent protection
in country j, no firm other than the patent holder or one designated by it may legally
produce the good in country j for domestic sale or for export, nor may the good belegally imported into country j from an unauthorized producer outside the country. We
also rule out parallel imports – unauthorized imports of good i that were produced by
the patent holder or its designee, but that were sold to a third party outside country j.6
When parallel imports are prevented, patent holders can practice price discrimination
across national markets.
We solve the Nash game in which the governments set their patent policies once-andfor-all at time 0. These patents apply only to goods invented after time 0; goods invented
beforehand continue to receive the protections aﬀorded at their times of invention. So
long as the governments cannot remove protections that were previously granted, theeconomy has no state variables that bear on its choice of optimal patent policies at
a given moment in time.

This means that the Nash equilibrium in once-and-for-all

patents is also a sub-game perfect equilibrium in the infinitely repeated game in which
the governments can change their patent policies periodically, or even continuously. Of
course, the repeated game may have other equilibria in which the governments base theircurrent policies on the history of prior actions. We do not investigate such equilibria
with tacit cooperation here, but rather postpone our discussion of cooperation until alater section.
Let us describe, for given patent strengths ΩN and ΩS , the life cycle of a typicaldiﬀerentiated product. During an initial phase after the product is introduced, theinventor holds an active patent in both countries which is only partially enforced. The
patent holder earns an expected flow of profits of ω N MN π from sales in the Northern
6

The treatment of parallel imports under TRIPs remains a matter of legal controversy. Countries

continue to diﬀer in their rules for territorial exhaustion of IPRs. Some countries, like Australia andJapan, practice international exhaustion, whereby the restrictive rights granted by a patent end withthe first sale of the good anywhere in the world. Other countries or regions, like the United States andthe European Union, practice national or regional exhaustion, whereby patent rights end only with thefirst sale within the country or region. Under such rules, patent holders can prevent parallel trade. See
Maskus (2000b) for further discussion.

7

market and an expected flow of profits of ω S MS π from sales in the Southern market,
where π is earnings per consumer for a monopoly selling a typical brand. Notice thatmonopoly profits per consumer are the same for sales in both markets, because consumers
share identical preferences. Also, they do not depend on where a good was invented orwhere it is produced, because the productivity gap between the countries exactly oﬀsets
the wage diﬀerential. Each Northern consumer realizes a flow of expected surplus ofω N Cm + (1 − ωN )Cc from his purchases of the good, where Cm is the surplus that a
consumer derives from purchases of a good produced at a cost of wj aj = 1 and soldat the monopoly price pm and Cc is the surplus he derives from a product sold for thecompetitive price of pc = 1. Similarly, a Southern consumer realizes an expected flow of
consumer surplus of ω S Cm + (1 − ω S )Cc from his purchases of the good.
After a while, the patent will expire in one country. For concreteness, let’s say that
this happens first in the South. Then the good will be legally imitated by competitive
firms producing there, for sales in the local (Southern) market. The imitators will not,however, be able to sell the good legally in the North, because the live patent there, if
enforced, aﬀords protection from such infringing imports. When the patent expires in
the South, the price of the good falls permanently to wS aS = 1, and the original inventor
ceases to realize profits in that market. The flow of consumer surplus in the South rises
to MS Cc .
Eventually, the inventor’s patent expires in the North. Then the Northern market
can be served completely by competitive firms producing in either location. At this time,
the price of the good in the North falls to pc = 1 and households there begin to enjoy thehigher flow of consumer surplus MN Cc . The original inventor loses his remaining sourceof monopoly income. Finally, after a period of length τ̄ has elapsed from the moment of
invention, the good becomes obsolete and all flows of consumer surplus cease.

2.1.2

The Best Response Functions

Consider the choice of patent policies ΩN and ΩS that will take eﬀect at time 0 andapply to goods invented thereafter. The expressions for the aggregate welfare in country8

i, discounted to time 0, is given by
Wi (0) = Λi0 += Λi0 +¤
wi Li ri Hi Mi (φS + φN ) £++Ωi Cm + (T̄ − Ωi )Ccρρρ¤wi (Li − LRi ) Mi (φS + φN ) £+Ωi Cm + (T̄ − Ωi )Ccρρ
φ+ i π (MS ΩS + MN ΩN ) , for i = S, N,ρ(2)where Λi0 is the fixed amount of discounted surplus that consumers in country i derivefrom goods that were invented before time 0. The second equality arises from the factthat there is zero profit for each firm, so that ri Hi +wi LRi = φi v = φi π (MS ΩS + MN ΩN ),where v = (MS ΩS + MN ΩN )π is the value of a new patent.
We are now ready to derive the best response functions for the two governments.
The best response expresses the strength of patent protection that maximizes a country’s
aggregate welfare as a function of the given patent policy of its trading partner. Consider
the choice of ΩS by the government of the South. This country bears two costs fromstrengthening its patent protection slightly. First, it expands the fraction of goods
previously invented in the South on which the country suﬀers a static deadweight loss of
MS (Cc − Cm − π). Second, it augments the fraction of goods previously invented in the
North on which its consumers realize surplus of MS Cm instead of MS Cc . Notice thatthe profits earned by Northern producers in the South are not an oﬀset to this latter
marginal cost, because they accrue to patent holders in the North. The marginal benefit
that comes to the South from strengthening its patent protection reflects the increased
incentive that Northern and Southern firms have to engage in R&D. If the welfaremaximizing ΩS is positive and less than T̄ , then the marginal benefit per consumer ofincreasing ΩS must match the marginal cost, which implies
φS (Cc − Cm − π) + φN (Cc − Cm ) =£¤γ S φS + γ N φN
MS π Cm ΩS + Cc (T̄ − ΩS ) ,v(3)

where γ j is the responsiveness of innovation in region j to changes in the value of apatent (in elasticity form), i.e.

φ∂φj
= γ j vj .
∂v

Similarly, in the North, the marginal benefit of strengthening patent protection mustmatch the marginal cost at any interior point on the best response curve. The marginal
9

cost in the North is diﬀerent from that in the South, because the North’s national
income includes the profits earned by Northern patent holders but not those earned bySouthern patent holders. The marginal benefit diﬀers too, because the eﬀectiveness ofpatent policy as a tool for promoting innovation varies according to the importance of acountry’s market in the aggregate profits of potential innovators and because the surplus
from a typical product over its lifetime depends upon a country’s patent regime. The
condition for the best response of the North, analogous to (3) above, is
φS (Cc − Cm ) + φN (Cc − Cm − π) =£¤γ S φS + γ N φN
MN π Cm ΩN + Cc (T̄ − ΩN ) . (4)v

Noting that γ S = γ N = γ, 7 the two best response functions can be written similarly
as

∙
¸
Mi Ωi
T̄ − Ωi
Cc − Cm − μi π = γ
Cm + Cc () for i = S, N ,MS ΩS + MN ΩNΩi(5)where μi = φi /(φS + φN ) is the share of world innovation that takes place in country
i. Moreover, μi = Hi /(HS + HN ) for this research technology. Thus, both μi and γ are
independent of the patent policies in the Cobb-Douglas case. It follows from (5) thatthe best response functions are linear and downward sloping in this case, and that thebest response function for the South is steeper than that for the North, when the two
are drawn in (ΩS , ΩN ) space.
Thus, the patent policies of the two countries are strategic substitutes. To understand the strategic interdependence between the governments in choosing their policies,
consider the choice of patent protection by the South. Suppose the North were tostrengthen its patent protection; i.e., to increase ΩN . This would shrink the fractionof total discounted profits that an innovator earns in the South and so, ceteris paribus,
reduce the responsiveness of global innovation to patent policy in the South. Moreover,the increase in ΩN would draw labor into R&D in the North and South. If β < 0, the7

The fact that the two supply elasticities γ S and γ N are equal despite the diﬀerences in humancapital endowments, in employment, and in labor productivity is a property of the Cobb-Douglas
research technology. It follows from the observation thatγi =bfor all i(1 − b)10

elasticity of innovation with respect to patent value would fall. The South would findthat its market is relatively less important to potential innovators and that these innovators are less responsive to its patent policy. For both reasons, the marginal benefit
to the South of strengthening its patent protection would fall and so the government
would respond to the increase in ΩN with a reduction in patent length or an easing ofenforcement.
It is easy to show using (5) that the best response curve for the South must have aslope that is everywhere greater in absolute value than MS /MN , while the best response
curve for the North must have a slope that is everywhere smaller in absolute value than
MS /MN .8 It follows that the curve for the South must be steeper than that for the
North at any point of intersection. This guarantees uniqueness of the Nash equilibriumand ensures stability of the policy setting game.
We summarize the most important findings in this section as follows.
Proposition 1 Let the research technology be φj = A (LRj /aj )b Hj1−b in country i, for
i = S, N. Since the two patent policies are strategic substitutes in both countries, there
exists a unique and stable Nash equilibrium of the policy setting game.
8

We have not discussed the shape of the best response functions where they hit the axes or where

the constraint that Ωi ≤ T̄ begins to bind. The best-response curve of the South becomes vertical if ithits the vertical axis at a point below ΩN = T̄ . It also becomes vertical if the South’s best response isT̄ for some positive value of ΩN . Similarly, the best-response curve for the North becomes horizontal

if either it hits the horizontal axis before ΩS = T̄ or if the North’s best response is T̄ for some positive
value of ΩS . Thus, the best response curve for the South must be steeper than that for the North atany point of intersection, even if these additional segments of the best response functions are taken into
account.

11

2.2

International Patent Agreements

In this section, we study international patent agreements.9 We begin by characterizing
the combinations of patent policies that are jointly eﬃcient for the two countries.10
Then we compare the Nash equilibrium outcomes with the eﬃcient policies, to identify
changes in the patent regime that ought to be eﬀected by an international treaty. Finally,
we address the issue of policy harmonization.

By that point, we will have seen that

harmonization is neither necessary nor suﬃcient for global eﬃciency. We proceed toinvestigate the distributional properties of an agreement calling for harmonized patent
policies and ask whether both countries would benefit from such an agreement in theabsence of some form of direct compensation.
2.2.1

Eﬃcient Patent Regimes

We shall begin by showing that the sum of the welfare levels of the two countries depends
only on a measure Q of the overall protection aﬀorded by the international patent
system. This means that the same aggregate world welfare level can be achieved with
diﬀerent combinations of ΩS and ΩN that imply the same overall level of protection.
One particular level of Q–call it Q∗ –maximizes the sum of the countries’ welfare levels.
For a wide range of distributions of world welfare, eﬃciency is achieved by setting theindividual patent policies so that the overall index of patent protection is Q∗ .
In particular, let Q = MS ΩS + MN ΩN . This measure of global patent protection
weighs the degree of patent protection in each country by the size of the country’s market.
A firm that earns a flow of expected profits of ω S MS π for a period of length τ S in theSouth and a flow of expected profits of ω N MN π for a period of τ N in the North earns
9

See also McCalman (2002), who discusses globally eﬃcient patent policies in his two-country ex-tension of the Nordhaus (1969) model. Lai and Qiu (2003) consider whether the joint welfare of thetwo countries would be increased if the South were to extend its patents so as to be equal in length to
those chosen by the North in a Nash equilibrium.
10
Ours is a constrained eﬃciency, because we assume that innovation must be done privately and thatpatents are the only policies available to encourage R&D. We do not, for example, allow the governments
to introduce R&D subsidies, which if feasible, might allow them to achieve a given rate of innovation
with weaker patents and less deadweight loss.

12

a total discounted sum of expected profits equal to Qπ. Thus, Q governs the allocationof resources to R&D in each country, regardless of the particular combination of patent
policies in the separate countries.
Consider the choice of patent policies ΩN and ΩS that will take eﬀect at time 0 andapply to goods invented thereafter. Summing the welfare expressions in (2) for i = S
and i = N, we find that
ρ [WS (0) + WN (0)] = ρ (ΛS0 + ΛN0 ) + wS (LS − LRS ) + wN (LN − LRN )+ (MS + MN ) T̄ (φS + φN )Cc − Q (φS + φN ) (Cc − Cm − π)(6)

Since vS = vN = πQ, LRS and LRN are functions of Q.11 The same is true of φS and
φN . It follows that diﬀerent combinations of ΩS and ΩN that yield the same value of Q
also yield the same level of aggregate world welfare.12
If international transfer payments are feasible, then a globally eﬃcient patent regime
must have MS ΩS + MN ΩN = Q∗ , where Q∗ is the value of Q that maximizes the righthand side of (6).13 Notice that a range of eﬃcient outcomes can be achieved without theneed for any international transfers. By appropriate choice of ΩN and ΩS , the countries
can be given any welfare levels on the eﬃciency frontier between that which they would
achieve if ΩS = 0 and ΩN = Q∗ /MN and that which they would achieve if ΩS = Q∗ /MSand ΩN = 0.14
11

In country i, the allocation of labor to research is determined by
πQFL (LRi /ai , Hi ) = 1/ai .

12This result is anticipated by a similar one in McCalman (2002), who studied eﬃcient patent agree-ments in a partial equilibrium model of cost-reducing innovation by a single, global monopolist.
13
The first-order condition for maximizing ρ[WS (0) + WN (0)] implies½∙¸¾(MS + MN )T̄ − Q∗
Cc − Cm − π = γ Cm + Cc.
Q∗
The second-order condition is satisfied at Q = Q∗ when β ≤ 1/2.
14This statement ignores the ceiling on patent lengths imposed by the finite economic life of differentiated products.

A more precise statement is that a range of distributions of maximal world

welfare can be achieved by varying ΩS between ΩS = max{0, (Q∗ − MN T̄ )/MS } and min{Q∗ /MS , T̄ }13

Although aggregate world welfare does not vary with the national policies ω i andτ i as long as MS ΩS + MN ΩN = Q∗ , the countries fare diﬀerently under the alternative
combinations of policies that can be used to achieve global eﬃciency unless compensatingtransfers take place. In particular, the welfare of the North increases and that of theSouth decreases as ΩS is increased and ΩN is decreased in such a way as to keep theweighted sum constant.

It follows that, absent any international transfer payments,

the countries have a strong conflict of interest over the terms of an international patentagreement.

2.2.2

Pareto-Improving Patent Agreements

How do the eﬃcient combinations of patent policies compare to the policies that emerge
in a noncooperative equilibrium? The answer to this question – which informs us about
the likely features of a negotiated patent agreement – is illustrated in Figure 1. The
figure depicts the best response functions and the eﬃcient policy combinations on thesame diagram.
In the figure, the eﬃcient policy combinations are depicted by the line QQ.15 We
show this line being situated to the right of the SS curve and above the NN curve, which
is a general feature of our model. The reasons are clear. Starting from a point on theSouth’s best response function, a marginal strengthening of IPR protection in the South
increases world welfare. Such a change in Southern policies has only a second-order eﬀect
on welfare in the South, but it conveys two positive externalities to the North. First, it
provides extra monopoly profits to Northern innovators, which contributes to aggregate
income there. Second, it enhances the incentives for R&D, inducing an increase in both
φS and φN . The extra product diversity that results from this R&D creates additional
surplus for Northern consumers.
¡¢
while varying ΩN between ΩN = min{Q∗ /MN , T̄ } and max{0, Q∗ − MS T̄ /MN } in such a way thatMS ΩS + MN ΩN = Q∗ .
15
If international transfer payments are infeasible, the set of Pareto eﬃcient policy combinations

includes the segment of the vertical axis above its intersection with QQ and extending as far as thepoint (0, T̄ ) and the segment of the horizontal axis to the right of its intersection with QQ and extending
to (T̄ , 0).

14

ΤΝ
Q
45Ñ
S

Ì

N

H

E
Ì

Q

0

N

S

ΤS

Figure 1: Comparison of Nash Equilibrium and an Eﬃcient Patent Regime
By the same token, a marginal increase in the strength of Northern patent protection
from a point along NN increases world welfare. Such a change in policy enhances profit
income for Southern firms and encourages additional innovation in both countries. It
follows, of course, that the QQ line must lie outside the Nash equilibrium. We record
our finding in
Proposition 2 Let (ΩS , ΩN ) be an interior equilibrium in the noncooperative policy
game and let (Ω∗S , Ω∗N ) be any eﬃcient combination of patent policies. Then MS Ω∗S +MN Ω∗N > MS ΩS + MN ΩN .
The proposition implies that, starting from any interior Nash equilibrium, an eﬃcientpatent treaty must strengthen patent protection in at least one country. It also implies that the treaty will strengthen global incentives for R&D and induce more rapid
innovation in both countries.

15

2.3

Patent Policy with Many Countries

In this section, we extend our analysis to a trading world with many countries. Our
main finding is that adding countries exacerbates the free-rider problem that plagues
the noncooperative policy equilibrium. Small countries are inclined to allow others toprovide the incentives for innovation so as to avoid the deadweight losses in their homemarkets. In the limit, as the number of countries grows large and each one is small
in relation to the world economy, the unique Nash equilibrium has universal patentsof strength zero. Then, a patent treaty is critical for creating incentives for private
innovation.
We assume that there are J countries, and that country i has market size Mi , humancapital endowment Hi , and labor productivity 1/ai . The research technology in country
i is φi = F (Hi , LRi /ai ) = A (LRi /aj )b Hi1−b . All consumers share the preferences givenin (1).
Suppose that there is no cooperation between nations in setting their patent policies.
In country i, either Ωi = 0 and the marginal cost of providing the first bit of patent
protection exceeds the marginal benefit, Ωi = T̄ and the marginal benefit of providing
the last bit of patent protection exceeds the marginal cost, or 0 < Ωi < T̄ and themarginal benefit of strengthening patent protection equals the marginal cost. Equality
between marginal benefit and marginal cost implies
Cc − Cm − μi π =where Q =equilibrium.

P

j Mj ΩjMi
γ[Ωi Cm + Cc (T̄ − Ωi )] ,Q

(7)measures the strength of global patent protection in the Nash

Observe first that as μi → 0, the left-hand side of (7) approaches Cc − Cm ; a small
country captures virtually none of the monopoly profits from innovative products, so
the marginal cost of a patent per consumer and product is the diﬀerence between thecompetitive and monopoly levels of consumer surplus. But as Mi → 0, the right-handside of (7) approaches zero, because a small country provides innovators with virtuallynone of their global profits and so worldwide innovation is hardly responsive to a change

16

in such a country’s patent policy. It follows that a small country will set its index ofpatent protection equal to zero in a Nash equilibrium.
If all countries choose positive patent strengths that are less than T̄ , equation (7)holds for every i. Then we can sum (7) across the J countries, which gives
³P
´ ⎤
⎡
T̄
Cc
M
j
j
⎦.
J (Cc − Cm ) − π = γ ⎣Cm − Cc +Q

(8)Then, for a given size of the world market, Q depends only on the number of countries J

and not on the distribution of consumers and human capital across countries. Moreover,the greater is the number of countries, the weaker are the global incentives for innovation in a noncooperative equilibrium. As the number of countries grows large (holding
constant the size of the world market), the aggregate incentives for innovation approachzero.16 Evidently, the free-rider problem becomes increasingly severe as the number of
independent decision makers in the world economy expands.
Finally, note that the requirements for global eﬃciency do not depend on the numberof countries. Again, the sum of all national welfare levels is a function of the aggregate
world incentive for innovation. This sum is maximized when
³P
´ ⎤
⎡
Cc
M
j T̄
j
⎦.
Cc − Cm − π = γ ⎣Cm − Cc +Q∗

(9)Thus, if international compensation is possible, an eﬃcient global patent treaty willP
have j Mj Ωj = Q∗ , where Q∗ is solved from (9). Notice that Q∗ must exceed Q, theaggregate patent protection in the Nash equilibrium. Even if international compensation
P
is not feasible, an eﬃcient agreement will have j Mj Ωj = Q∗ for a range of distributionsof world welfare.
16

Suppose Q were to approach a finite number as J → ∞. Then γ would approach a finite number

as well, and the right-hand side of (8) would be finite. But the left-hand side of (8) approaches infinity
as J → ∞.

17

3

Extended model with trade barriers and firm-bias

The conclusion that global IPR protection is too weak in the absence of international
agreement can be met with skeptism. Many people point to the strong pharmaceuticallobbies in Washington to justify why they think global patent protection before TRIPS
must have been already too strong rather than too weak. Moreover, the existence oftrade barriers weakens the international spillovers that one nation confers on foreigncountries when it strengthens domestic IPR protection. Therefore, I address here two
key simplifications of the basic model: that governments put equal weights on consumer
welfare and firm profits and that there are no trade barriers. In reality, governments
are often biased in favor of domestic firms and trade barriers are non-trivial. Omittingthese factors can bias the conclusion that global IPR protection is too weak in the noncooperative equilibrium. Obviously, whether the conclusion of the basic model can beoverturned depends on how large are the magnitudes of these two eﬀects. The analyticaltask is to find out what values of firm-biasedness and trade barriers can sustain theoriginal conclusion that there is under-protection of IPR in Nash equilibrium, and thenjudge whether these values are plausible.
Let y be the probability that an invention by a domestic firm is sold in a foreign
market (call it the “import penetration rate”). This is an inverse measure of foreign
trade barriers. Let 1 + a be the weight a government puts on domestic profits whena weight of one is put on domestic consumer surplus in its objective function. The
parameter a measures the firm-bias of governments. Note that this approach of assigning
additional exogenous weight to firms as opposed to consumers is similar to what is doneby Bagwell and Staiger (2002). They essentially put a weight of 1 + a on firms in thegovernment’s objective function, which they treat as a reduced form derived from theanalysis of a political-economy equilibrium a la Grossman and Helpman (1994). Let vi
be the expected value of a patent of an invention by a firm in country i. Therefore,ihPvi = π
.
(yM
Ω
)
+
M
Ω
k
k
i
i
k6=i
It is useful to consider a multi-country setting, as the number of independent decision-

making governments plays a crucial role in whether there is under-protection of IP in
18

Nash equilibrium. Let there be J countries in the set N of countries in the world. In a
multi-country setting, the best-response function of country i is

y

Ã
X
j6=i

φj

!

(Cc − Cm ) + φi (Cc − Cm ) − φi (1 + a) π

!
Ã
X φj
φ
y 2 πMi fi + γ i πMi fi
γ
=
vj
vi
j6=i

(10)

where fi ≡ Cc T − (Cc − Cm ) Ωi is the present discounted value of per-person consumer
surplus derived from a diﬀerentiated good over its product life. The left-hand side of theabove equation is, in fact, the marginal cost per consumer in country i of strengthening
IPR there. The first term is the loss in consumer surplus attributed to inventions fromfirms outside country i; the second term is the loss of consumer surplus attributed toinventions from country i; and the third term is the oﬀsetting of the losses of consumer
surplus by gains in profits of firms in country i. The right-hand side is the marginal
benefit per consumer in country i. The first term is the increase in consumer welfare
in country i due to increases in flows of innovations from firms outside country i; thesecond term is the increase in consumer welfare in country i due to the increase in flowof innovation from country i. If I define the left-hand side as MCi (a) and the righti (a)hand side as MBi , then M1i ∂W= MBi − MCi (a), where Wi (a) is the Government i’s∂Ωiobjective function. (Hereinafter, I put an argument ‘a’ after the name of a function if
firm-bias aﬀects the value of the function.)
It can be easily shown that the first-order condition for global welfare maximization
with respect to the choice of Ωi is given by!
ÃX
MCi (a) + πaφi − yπ
φj =
j6=i

Ã
!
X X φjX φ
y 2 πMk fk +MBi +γ
γ k yπMk fk
vj
vk
k6=i
j6=k
k6=i

(11)

The left-hand side of this equation is the marginal global cost borne by each consumer
in country i of strengthening IPR protection in that country. The second term is the19welfare that will not be taken into account when IPR protection in country i is chosen
to maximize global welfare instead of to maximize government i’s firm-biased objective(therefore it is an addition to marginal cost); the third term reduces the global marginal
cost as it takes into account the increases in profits of firms outside of country i. The
right-hand side is the marginal global benefit (per consumer in country i) of strengthening
IPR there. The second term and the third term are both increases in welfare of consumers
outside of country i. The second term is due to faster foreign innovations, while the third
term is due to faster domestic innovations. (“foreign” and “domestic” here are relative
to each country outside of country i.) The cross-border externalities of IPR protection
are captured by the third term on the left hand side plus the second and third terms on
the right hand side. It is apparent that since an increase in trade barriers (a decreasein y) leads to less international spillovers, the likelihood of under-protection of IPR in
equilibrium is lower. Likewise, an increase in firm-bias (an increase in a) reduces the gap
between marginal global benefit and marginal national benefit, making under-protectionof IPR less likely.
Let us define the left hand side of the first order condition above as MCiw and thewright hand side of the equation as MBiw . It follows that M1i ∂W= MBiw − MCiw , where∂Ωi

W w is world welfare (without bias towards firm profits).

In the basic model, we can find a functional relationship between the global strengthof patent protection and global welfare. The same strength of global patent protection
creates the same amount of total deadweight losses (what I call static losses) and aggregate flow of new diﬀerentiated goods (what I call dynamic gains) in each period. Aslong as the global strength of patent protection is the same, global welfare is the same,
regardless of the combination of individual countries’ strengths of patent protection.
Therefore, the global optimum is a continuum of combinations of national strengths ofpatent protection that maximize global welfare. However, this will not be true in thisextended model. In this more general model with trade barriers, there does not exista scalar measure of the global strength of patent protection such that there is a functional relationship between the global strength of protection and global welfare. Despite
this problem, I am able to calculate a suﬃcient condition for global under-protection of20

patents, as shown below.
I define under-protection as a situation when, starting from Nash equilibrium, global
welfare increases as a result of some positive changes in all {Ωi }i∈N (where the magnitudes of increase are not necessarily equal). The point of the analysis is to come up© ªwith a suﬃcient condition under which, starting from Nash equilibrium ΩEi i∈N , somecoordinated increases in IPR protection of all countries is globally welfare-improving.

Note that an increase in the strength of protection in all countries raises the valuesof all patents. This increases the global deadweight losses, but gives a boost to therate of innovation. To simplify the analysis, I focus on changes in {Ωi }i∈N such that
Mi dΩi = dΩ for all i. I want to find a suﬃcient condition under which such changes
lead to an increase in global welfare. In other words, I seek a condition under which themarginal global benefit outweighs the marginal global cost.
i (a)Bear in mind that equation (10) is equivalent to M1i ∂W= 0, and equation (11)∂Ωiw

is equivalent to M1i ∂W= 0. Summing the left-hand side and the right-hand side of∂Ωiequations (10) over all i as well as both sides of (11) over all i, and comparing the two
ensuing equations, it can be shown that(J − 1) y > a(12)is a suﬃcient condition under which, starting from Nash equilibrium, small increases inwdΩΩi such that dΩi = M
is globally welfare-improving, i.e. dW> 0. The proof is givendΩi

below (and the appendix).
First I prove the following lemma:
Lemma 1. A suﬃcient condition for under-protection of IPR in Nash equilibrium isX
X ∂W (a)1 ∂W w
1i> 0 for all {Ωi }i∈N such that= 0.
Mi ∂ΩiMi ∂Ωii

i

Proof. A suﬃcient condition for under-protection is
X 1 ∂W wi

Mi ∂Ωi> 0 in Nash equilibrium© EªΩi i∈N© ª> 0 implies that if we increase each Ωi in ΩE
i i∈N
´ ³P
´
³P
w
w
∂W
1 ∂W
dΩ > 0. Thatsuch that Mi dΩi = dΩ ∀i, then dW w =i ∂Ωi dΩi =i Mi ∂Ωi
This is true becauseP

1 ∂W wi Mi ∂Ωi

21

M

dΩi
is, global welfare increases as each Ωi increases slightly such that dΩ= Mji for all i 6= j.
j

i (a)
=0
This clearly indicates under-protection at Nash equilibrium. Moreover, since ∂W∂Ωi
P 1 ∂Wi (a)for all i in Nash equilibrium, i Mi ∂Ωi = 0 includes the Nash equilibrium as a specialcase. ¥To understand Lemma 1 better, let us consider a two-country case. First refer toFigure 2 for an idea of the relationship between Nash equilibrium and global optimum.
In that diagram, point E is the Nash equilibrium while point G is the global optimum.
BRF-S and BRF-N are the best response functions of South and North respectively.
w

w

Point G is at the intersection of the curves ∂W= 0 and ∂W= 0, which are not shown.
∂ΩS
∂ΩN
MS
Note that the slopes of the iso-global-welfare lines W w = W are always equal to M
at
N
w

w

their intersection with the line M1S ∂W+ M1N ∂W
= 0. This is because, along W w = W ,
∂ΩS
∂ΩN
´
³ w
w
w
w
dΩN
= − ∂W/ ∂W . But at any point on the curve M1S ∂W+ M1N ∂W
= 0, we havedΩS∂ΩS ∂ΩN
∂ΩS
∂ΩN
³ w
´
w
MS
− ∂W
=M
/ ∂W
. Consequently, it is not hard to see that starting from any point∂ΩS ∂ΩNN

on the iso-global-welfare line to the left of GG, any small increase in ΩS and ΩN suchMS
N
that dΩ=Mwould increase W w . In the context of Figure 2, a necessary and suﬃcientdΩSN

condition for there to be under-protection in Nash equilibrium is that point E is to theleft of the curve GG.17 Lemma 1 says that the suﬃcient condition for point E to be on
the left of GG is thatÃ!
X 1 ∂W w
X 1 ∂Wi (a)> 0 for all {Ωi }i∈N that satisfy= 0.
Mi ∂ΩiMi ∂Ωiiiw

w

Figure 3 shows the relationship between the curves M1S ∂W+ M1N ∂W
= 0 (GG)
∂ΩS
∂ΩN
S (a)
N (a)
and M1S ∂W+ M1N ∂W
= 0 (EE). The curves FOC-S and FOC-N are the first order∂ΩS∂ΩN

conditions for maximization of global welfare with respect to the choice of ΩS and ΩN
respectively. In the context of Figure 3, the above condition is equivalent to saying thatthe curve EE is to the left of curve GG. If this condition is satisfied, at any point thatlies on EE (including the Nash equilibrium point E), any small change in ΩS and ΩNw

w

such that MS dΩS = MN dΩN would increase global welfare, since M1S ∂W+ M1N ∂W
> 0.
∂ΩS
∂ΩN
17

Note that if point E is to the right of GG, then any simultaneous small decrease of ΩS and ΩNMSwNsuch that dΩdΩS = MN would increase W .

22

Proposition 3 below basically provides a suﬃcient condition for the EE to be on the leftof GG.
Therefore, our next step is to prove the following proposition:
Proposition 3. A suﬃcient condition for under-protection of IPR in Nash equilibrium
when there are trade barriers and firm-bias is (J − 1) y > a.
Proof. See the appendix.
Lemma 1 provides a suﬃcient condition for under-protection in the sense that startingfrom each Ωi being at the Nash equilibrium level, small increases in {Ωi }i∈N such that
dΩi
dΩj

M

= Mji for all i 6= j leads to an increase in global welfare. Proposition 3 says that(J − 1) y > a is a suﬃcient condition for lemma 1 to hold. Therefore, it is exactly thecondition we are looking for. To check that this is a reasonable condition, note thatin the special case of the basic model, when there are two countries (J = 2), y = 1
and a = 0, the condition is satisfied. Moreover, it accords with the intuition that thefree-rider problem gets more serious when there are more countries playing the patentsetting game, for a larger J leads to more under-protection. It also is consistent with
the notions that trade barriers weaken the cross-border externality of IPR protection,
because a smaller y leads to less under-protection, and that stronger government bias
towards patent-holding firms tends to strengthen patents, for a larger a leads to lessunder-protection.18
What is a reasonable value for a? In the political-economy literature (Grossman andHelpman 1994; Maggi and Goldberg 1999), researchers have tried to estimate the weightthe U.S. government puts on campaign contributions when it puts a weight of unity on
welfare. They rarely come up with a number more than 0.5. Since this is a preference
parameter, it should be the same in the context of patent protection. Suppose there is apatent lobby, and suppose there is no consumer lobby, nor is there lobbying from other18

As an additional check, one can examine the symmetric case where Mi = Mj and Hi = Hj for all

i 6= j. It can be shown that the same suﬃcient condition is obtained.

23

sectors of the economy. Based on these suppositions, the appendix shows that the value
the government puts on campaign contributions is exactly the same as a in our model.
What is a reasonable value for J? This is the number of independent government
decision-makers in the patent-setting game. Thus, it is the number of countries in theworld that consume and trade patent-sensitive goods, and that adopt neither zero nor
full patent protection. To be conservative, let J = 5.
When a = 0.5 and J = 5, a suﬃcient condition for the Nash equilibrium to beunder-protecting patents is y > 0.1. I believe that this condition is likely to be satisfied
for most products. So, based on this rough calculation, I conclude that global patent
protection in the absence of international coordination is probably too weak.
Some people argue that the set of globally optimal levels of patent protection shouldtake into account the politically-augmented objective function of each national government, as these functions reflect the preferences of each government, which represents eachcountry in international coordination eﬀorts. If maximizing the sum of the politicallyaugmented objective functions is the goal of international coordination, then the firstorder condition (11) becomesMCi (a) − yπ

Ã
X
j6=i

φj

!

=

Ã
!
X X φjX φ
y 2 πMk fk +MBi +γ
γ k yπMk fk
v
vk
j
k6=i
j6=k
k6=i
In this case, it is clear that there is under-protection of patents in each country, as
the marginal global cost is lower while the marginal global benefit is higher. There isunambiguous positive cross-border externalities as the profits of foreign firms and theincreases consumer surplus of foreign consumers due to induced innovations are not taken
into account as Ωi increases, just like in the basic model. The spillovers are smaller inthis case, as there are trade barriers.

24

4

No National Treatment in Nash Equilibrium

One may argue that in a non-cooperative equilibrium, there is no incentive for a country
to oﬀer national treatment. One response to this criticism is that, before the TRIPS
Agreement was signed and implemented, many countries were already members of WIPO
and the Berne and Paris Conventions. These treaties required their members to adopt
national treatment. A critique of this response is that these treaties were so loosely enforced that countries did not really abide by that commitment. Does the main conclusionthat there is under-protection continue to hold if I relax the assumption of national treatment? It turns out that the answer is, “yes”. Moreover, the results in the basic model,such as: A larger country has incentives to oﬀer more IPR protection, and the positive
cross-border externalities of strengthening domestic IPR protection, continue to exist.
I first compute the Nash equilibrium. I continue to assume the existence of tradebarriers and firm-bias. Let Ωkj be the strength of protection oﬀered by country k on
goods invented by country j, where k, j = N . The value of a patent of a good invented³´
P
in country j is therefore given by vj = π Mj Ωjj + k6=j yMk Ωkj = πQj where Qj ≡P
Mj Ωjj + k6=j yMk Ωkj is the global patent protection provided to each diﬀerentiatedgood developed in country j. Focusing on the protection of goods invented by countryj, the best-response function of that country gives the optimal choice of Ωjj given thateach country i (where i 6= j) chooses Ωij . That function is(Cc − Cm ) − (1 + a) π =γMj fjj
P;
Mj Ωjj + k6=j yMk Ωkj(13)

where fjj ≡ Cc T −(Cc − Cm ) Ωjj ; while the best-response function of country i, selecting
its best choice of Ωij given that country j chooses Ωjj and each country k in the rest of
the world (where k 6= i, j) chooses Ωkj , isCc − Cm =γyMi fijP
Mj Ωjj + k6=j yMk Ωkj(There are J − 1 such equation)(14)

where fij ≡ Cc T − (Cc − Cm ) Ωij .

Note that the innovative capability of a country does not aﬀect its equilibrium
strength of IPR protection when countries can optimally choose to oﬀer diﬀerential
25

treatments to domestic and foreign firms. If one adds equations (13) and the J − 1equations (14) for all i 6= j, we have

Ã
!
#
"
_
X
γ
J (Cc − Cm ) − (1 + a) π =× T CcMk − (Cc − Cm ) Qj
Qj
k∈N

(15)

Therefore, the global patent protection Qj provided to all diﬀerentiated goods are thesame regardless of where they are developed. As vj = πQj , the equilibrium value of apatent is independent of where the good is invented. Since vi = vj for all i 6= j, we caninfer from (13) that a country with a larger domestic market tends to protect the IPR ofdomestically-invented goods more than one with a smaller domestic market. Moreover,(14) implies that a country with a larger domestic market tends to protect the IPR offoreign-invented goods more than one with a smaller domestic market. Finally, if wecompare the best response function for the choice of Ωjj with that for the choice of Ωji ,we can easily infer that a country always protects domestically invented goods morethan it does foreign-invented ones (i.e., Ωjj > Ωji for i 6= j).
The globally eﬃcient combinations of Ωjj and Ωij for all i 6= j, on the other hand,are determined by the following equation³´Pγ Mj fjj + i6=j yMi fijP
Cc − Cm − π =Mj Ωjj + i6=j yMi Ωij
Ã
!
#
"
_
X
γ
=
× T CcMk − (Cc − Cm ) Qj
Qj
k∈N

(16)

Like in the basic model, instead of being unique, there is a continuum of globally optimal
combination of levels of patent protection. Considering the two-country case, it is clearthat harmonization (in the sense that Ωii = Ωjj ) is certainly not suﬃcient for global
eﬃciency. Neither is it necessary, since Qj can be at the eﬃciency level with Ωij smalland Ωjj large, or with Ωij large but Ωjj small. Similarly, Ωii can be either large orsmall to attain global eﬃciency. Therefore, there is no need for Ωii = Ωjj to reachglobal eﬃciency. Along similar lines, it is easy to see that national treatment is neither
necessary nor suﬃcient for global eﬃciency.
Comparing equations (15) and (16) can give us a suﬃcient condition for global underprotection in Nash equilibrium. We state the result in the following proposition.
26

Proposition 4. A suﬃcient condition for under-protection when there are trade barriers, firm-bias and no requirement of national treatment in Nash equilibrium is J −1 > a.
Proof. Unlike in the case where national treatment is observed in Nash equilibrium,
the strength of global patent protection is the same regardless of the combination ofindividual countries’ strengths of patent protection. This is like in the basic model. To
compare the equilibrium global strength of patent protection with the globally optimal
one, we simply compare equations (15) and (16). It is easy to see that the necessary
and suﬃcient condition for global under-protection of patents is
J (Cc − Cm ) − (1 + a) π > Cc − Cm − π⇐⇒(J − 1) (Cc − Cm ) > aπ=⇒

J − 1 > a since Cc − Cm > π¥This is a less stringent condition than (12).19 Interestingly, the condition is independent of y.
To conclude, the non-observance of national treatment in non-cooperative equilibrium will make it even more likely that there is under-protection of patents in the global
economy.

5

Conclusion

I extend the Grossman and Lai (2004) model to answer the question, “Would global
patent protection be too weak without international coordination?” by introducing firmbiased government preferences and trade barriers in the model. I make use of the estimates of a parameter from the political economy literature to proxy for the degree of19

If we assume that a and y are both country-specific so that in general aj 6= ak and yj 6= yk for

j 6= k, then the suﬃcient condition for under-protection becomesJ − 1 > aj
This, again, is a less stringent condition than (12).

27governments’ firm-bias. Then I calculate the range of trade barriers that is suﬃcient
to give rise to under-protection of patents in the global system without international
policy coordination in IPR protection. I make the judgement that the true trade barrier between countries very likely falls within this range of under-protection. Therefore,
I conclude that there was probably under-protection of patents without international
policy coordination in IPR protection. It means that the free-rider problem with alarge number of independent players overrides the eﬀects of firm-bias and trade barriers,
giving rise to too low a rate of innovation in the world. Allowing for the possibility
that countries discriminate against foreign firms in Nash equilibrium does not change
this conclusion. The problem can possibly be corrected by international coordination in
intellectual property rights (IPR) protection.

28

References[1] Deardorﬀ, Alan V. “Welfare Eﬀects of Global Patent Protection.” Economica, February 1992, 59 (issue 233), pp. 35-51.
[2] Ginarte, Juan C. and Park, Walter G. “Determinants of Patent Rights: A CrossNational Study.” Research Policy, October 1997, 26(3), pp. 283-301.
[3] Grossman, G. M. and E. Helpman (1994). Protection for sale. American Economic
Review 84, 833—850.
[4] Grossman, Gene M. and Lai, Edwin L.-C. (2004), “International Protection ofIntellectual Property,” American Economic Review 94 (5), 1635-1653.
[5] Helpman, Elhanan “Innovation, Imitation, and Intellectual Property Rights.”
Econometrica, November 1993, 61(6), pp. 1247-1280.
[6] Lai, Edwin L.-C. “Theory of International Policy Coordination in Protection of
Ideas,” in Keith E. Maskus (ed.) Intellectual Property, Growth and Trade, vol. 2 ofthe series Frontiers of Economics and Globalization, Elsevier, 2008.
[7] Lai, Edwin L.-C. and Qiu, Larry D. “The North’s Intellectual Property Rights
Standard for the South?” Journal of International Economics, January 2003, 59(1),pp. 183-209.
[8] Maggi, Giovanni and Pinelope Goldberg (1999). Protection for Sale: An EmpiricalInvestigation. American Economic Review 89, 1135-55.
[9] Maskus, Keith E. Intellectual Property Rights in the Global Economy, Washington
D.C.: The Institute for International Economics, 2000a.
[10] Maskus, Keith E. “Parallel Imports.” The World Economy, September 2000b, 23(9),pp. 1269-1284

29

[11] McCalman, Phillip “Reaping What you Sow: An Empirical Analysis of International Patent Harmonization.” Journal of International Economics, October 2001,
55(1), pp. 161-185.
[12] McCalman, Phillip “National Patents, Innovation and International Agreements.”
Journal of International Trade and Economic Development, March 2002, 11(1), pp.
1-14.
[13] Scotchmer, Suzanne “The Political Economy of Intellectual Property Treaties.”
Journal of Law, Economics, and Organization, 2004, 20 (2), pp.415-437.

30

AppendixA

The firm-bias parameter and political economy

In this appendix, we try to justify using the parameter estimated from the political
economy literature (in particular lobbying as per Grossman and Helpman 1994) as aproxy for the firm-bias parameter a in our model. We analyze lobbying when there are
two or more countries, which trade freely with each other and set their national patent
policies non-cooperatively. We introduce the “rest of the world” to a generic country j.
For ease of exposition, we only focus on the case with free trade, i.e. y = 1. The casewith y < 1 has the same expressions for the marginal cost, which is the focus of what
we want to show here. Therefore, there is no loss generality by assuming y = 1 here.
The setup in this appendix is based on what we presented in Section 2. Here, we extend the model by considering the possibility that interest groups lobby the government
to set policy in their favor. In particular, the IPR industry has a strong self-interest in
obtaining extensive IPR protection. We follow the recent “protection for sale” literature20 in modelling the interaction between the IPR-lobby and the government. Thatis, we set up a lobbying game that is based on the menu auction approach of Bernheim
and Whinston (1986): In such a game, the IPR lobby submits a contribution schedule
CIP (τ ) to the policy-maker who then chooses the optimal patent length τ .
Let us start with a closed economy. The IPR-lobby represents the interests of theowners of human capital H that, in the Grossman-Lai model, is employed exclusively
in the production of new designs of diﬀerentiated goods. Defining r as the returns tohuman capital, the income of these capital owners is rH, which is the residual of therevenue from IPR-sensitive products minus the labor costs necessary to produce them:rH = MφπΩ − wLR ,(17)

where M is the number of consumers, φ is the flow of new inventions, π is the instantaneous profit per product, Ω ≡ (1 − e−ρτ /ρ) is the present discounted value of a flow of20

See the seminal contribution by Grossman and Helpman (1994) that represents the starting pointof this literature.

31

one dollar during the patent life τ of the product, w is wage, and LR the labor employedin the R&D sector. In this appendix, we assume that patents are perfectly enforced sothat patent length completely captures the degree of patent protection. The IPR lobby
thus faces the following gross pay-oﬀ function:
WIP =

rH
MφπΩ − wLR=,ρρ

which is the discounted present value of its flow of profits. Note that we consider neither
a labor union nor a consumer lobby. Workers in this framework are paid their marginal
product and thus have no surplus to lobby and we could not find any empirical evidence
for the role of consumers’ interests.
Taking into account the contribution schedule of the IPR-lobby, it is the governmentthat will set policy. Its objective function takes the following form:
W (a) = W (0) + aCIP (τ ) .

(18)

As usual in the “protection for sale” literature, the government’s objective is a weighted
sum of social welfare and contributions. The first term represents social welfare and canbe written more explicitly as follows:
W (0) =MφπΩ − wLR Mφ[Cm Ω + Cc (T − Ω)]
+
.
ρ
ρ

_

where T ≡ (1 − e−ρ τ /ρ) is the present discounted value of a flow of one dollar during_

the economic lifetime τ of the product. The second term in equation (18) represents theinfluence of the lobbying contribution and a indicates the importance of this channel.
Now let us consider an open economy with free trade. In an open economy, thepatent-lobby in each country j now seeks to maximize the following objective function:jWIP=φj (Ωj Mj + Ω−j M−j )π wj LR,j−ρρThe set {−j} represents the rest of the world, which consists of more than one country.
In that case, all variables with a subscript “−j” are vectors that represent the values ofthe variable of the rest of the world, with the number of rows equal to the number ofcountries in the rest of the world. Note the additional middle term in the above equation32

represents the profits from the foreign market. Next, let us redefine Wj (0), which now
contains several foreign terms:
Wj (0) =wj (Lj − LRj ) φj (Ωj Mj + Ω−j M−j )π++ρρ(φj + φ−j )Ωj Mj Cm (φj + φ−j )Mj (T − Ωj )Cc+
ρρ

As in the closed economy case, the government in country j maximizes a weighted sumof (appropriately modified) social welfare Wj (0) plus the contributions it is oﬀered:jW j (a) = Wj (0) + aCIP
(τ j )We use the menu auction approach of Bernheim and Whinston (1986), in particular,
conditions 2 and 3 of (their) Lemma 2:jii) τ 0 ∈ arg maxτ j Wj (0) + aCIP
(τ j )jjj(τ j ) + WIP− CIP(τ j )
iii) τ 0 ∈ arg maxτ j Wj (0) + a CIP
j
Using in addition the standard assumption that the contribution schedule CIP(τ j ) is

diﬀerentiable, we can combine ii) and iii) as follows:j∂WIP∂Wj (0)
+a
=0
∂τ j
∂τ j

The resulting best-response function of country j’s government can be written as:
φj (Cc − Cm ) − (1 + a)φj π + φ−j (Cc − Cm ) =£¤γ j φj + γ −j φ−j
Mj π Cm Ωj + Cc (T̄ − Ωj )v

where v is the value of a global patent. Note the similarity with equations (3) and (4),with additional weight given to the IPR-sensitive sector’s profits. In our model, thisextra weight arises as the result of lobbying.
Taking into account the property that γ j = γ −j = γ under a Cobb-Douglas innovation function, the following best response function implicitly defines the Nash equilibrium:
Mj ΩjCc − Cm − (1 + a)μj π = γ
Mj Ωj + M−j Ω−j33µ¶T̄j − Ωj
Cm + Cc,Ωj(19)

where μj ≡ φj /(φj + φ−j ) is the share of world innovation originating in country j. Notethe similarity with equation (5).

B

Proof of Proposition 3

i (a)From (10), we know that along the curve M1i ∂W
= 0,
∂Ωi

"

y

X
j

#

φj + (1 − y) φi (Cc − Cm ) − φi (1 + a) π

!
#
" Ã
X y
1
πMi fi + φi πMi fi
φj
= γ y
v
vi
j
j6=i
#
" Ã
!
X
X
γ
<
y
φj y πMi fi + φi πMi fi since πyQ < vj ∀j, where Q ≡
Mk Ωk
πyQ
j6=i
k
!
#
" Ã
X
¡
¢
γ
y2
=
φj πMi fi + φi 1 − y 2 πMi fi
πyQj
Summing over i, we know the following must be true along the curve
(

yJ

<

Ã
X
"

j

γ
y2
πyQ

φj

!

Ã
X
j

+

Ã
X

φj

j

!

)

(1 − y) (Cc − Cm ) −

Ã
X
j

φj

P

!

1 ∂Wi (a)i Mi ∂Ωi = 0:

(1 + a) π

! Ã
!
!#
Ã
X
X
¡
¢
φj π
Mi fi + 1 − y 2 π
φi Mi fi
i

(20)

i

i (a)
Recall that equation (10) is equivalent to M1i ∂W= 0 while (11) is equivalent∂Ωiw

to M1i ∂W= 0. We have established in Lemma 1 that a suﬃcient condition for under∂Ωi³P´
P
1 ∂W wi (a)protection is> 0 for all combinations of {Ωi }i∈N that satisfy i M1i ∂W=
i Mi ∂Ωi∂Ωi
0. From equations (10) and (11), we know this condition is equivalent to
(
!)
Ã
X
X
πaφi − yπ
φj
i

j6=i

(
Ã
!
)
X X X φjX φk2
y πMk fk +<γγ yπMk fk
vj
vk
i
k6=i
j6=k
k6=i

for all combinations of {Ωi }i∈N that satisfy

P

34

1 ∂Wi (a)i Mi ∂Ωi = 0.

(21)

The above inequality is equivalent toπ (a + y)

Ã
X
i

φi

!

− yπJ

Ã
X
j

φj

!

!
Ã
!
Ã
!
Ã
X
X φ
X φj
(J − 1)< y2π
γ
Mk fk + y (1 − y) π (J − 1)
γ k Mk fk
v
vk
j
j
k
k
for all combinations of {Ωi }i∈N that satisfy

P

1 ∂Wi (a)i Mi ∂Ωi = 0.

Since πQ > vj ∀j, a suﬃcient condition for the above is
(
Ã
!
Ã
!)
X
X
θ2 (a + y)φi − yJφjiγ<πQ (Cc − Cm )

"

"Ã
X

γ (J − 1)y2=
Q (Cc − Cm )

φj

j

Ã
X

!

j

y 2 π (J − 1)ÃXk+y (1 − y) π (J − 1)
φj

j

!Ã
X
k

for all combinations of {Ωi }i∈N that satisfy
Recall equation (20), and define

Mk fk

P

!

Mk fk

!

Ã
X

φk Mk fkk

+ y (1 − y)

!#

Ã
X
k

φk Mk fk!#

(22)

1 ∂Wi (a)i Mi ∂Ωi = 0.

³P ´ PP2y2
j φj (i Mi fi ) + (1 − y ) (i φi Mi fi )
Ψ ≡ ³P ´ P
.
P
(
y2
φ
M
f
)
+
y
(1
−
y)
(
φ
M
f
)
k k
j j
k
k k k k³P ´ PP
1
We know 1 < Ψ < y1 sincej φj (k Mk fk ) >k φk Mk fk . So, Ψ > y. Therefore,

35

based on the definition of Ψ above, we have, alongP

1 ∂Wi (a)i Mi ∂Ωi = 0,

!Ã
!
Ã
!#
" Ã
X
X
X
γ
y2
φj
Mk fk + y (1 − y)φk Mk fk
Q (Cc − Cm )
j
k
k
Ã
!Ã
!
!#
" Ã
X
X
¡
¢ X
γ
1
=
y2
φj
Mi fi + 1 − y 2
φi Mi fiΨQ
Cc − Cm
j
i
i
!Ã
!
!#
" Ã
Ã
X
X
X
¡
¢
1
γ
1
y2
>y
> y
φj
Mi fi + 1 − y 2
φi Mi fiasQ
Cc − Cm
Ψ
j
i
i
( Ã
! Ã
!
Ã
!
)
X
X
X
> y 2 yJφj +φj (1 − y) −φj (1 + a) θ2 according to (20)jjjUsing the above inequality to substitute for
h ³P ´ P
i
P
γ
2
y
(
φ
M
f
)
+
y
(1
−
y)
(
φ
M
f
)
in (22), we get a suﬃcient
i
i
i
i
j j
i
i i
Q(Cc −Cm )condition for there to be under-protection in Nash equilibrium as
(
Ã
!
Ã
!)
X
X
θ2 (a + y)φi − yJφj(< y 2 (J − 1) yJ

i

Ã
X
j

φj

!

j

+

Ã
X
j

φj

!

(1 − y) −

Ã
X
j

φj

!

(1 + a) θ2which is equivalent toθ2 [(a + y) − Jy] < y 2 (J − 1) [Jy + (1 − y) − (1 + a) θ2 ]a suﬃcient condition of which is(a + y) − Jy < y 2 (J − 1) [Jy − (a + y)] since θ2 < 1
which is equivalent to(J − 1) y > awhich is the same as (12). ¥36)

Slope = M S / M N

ΩN

Ww =W

GG

G
45 degrees
S

Figure 2

N

Slope = M S / M N
E∂WS ( a )=0∂Ω S

1 ∂W w
1 ∂W w+=0
M S ∂Ω S M N ∂Ω N

BRF-S

N
0
S

∂WN ( a )
=0
∂Ω N

BRF-N

ΩS

ΩN
∂WS ( a )
=0
∂Ω S

BRF-S
45 degrees

1 ∂WS ( a )1 ∂WN ( a )+=0
M S ∂Ω S
M N ∂Ω N

GG

G∂WN ( a )
=0
∂Ω N

BRF-N
E
∂W w
= 0 FOC-N∂Ω N

EE

1 ∂W w
1 ∂W w+=0
M S ∂Ω S M N ∂Ω N

∂W w
= 0 FOC-S∂Ω S

Figure 3
ΩS