the antagonism of push and pull strategies, and the current funding campaigns to fight orphan...

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The antagonism of push and pull strategies, and the current funding campaigns to ght orphan diseases Patrick Leoni * Euromed Management, Department of Economics, Domaine de Luminy, 13288 Marseille, France article info Article history: Available online 25 November 2010 Keywords: Push and pull mechanisms Orphan diseases Optimal policies Developing countries Public good abstract We argue that an increase in investments in R&D for innovative treatments to eradicate neglected diseases in developing countries leads to a rational decrease in investments in available treatment technologies. In a formal model where the government of a developing country seeks to optimally allocate public resources, we show that the higher the odds of appearance of an innovative treatment, as occurring when investments in R&D increase, the lower the optimal provision of current treatments and other health expenditures. We also show that this phenomenon is aggravated when the opportunity cost of investments in current treatments increases. This implies that welfare in developing countries deteriorates as innovative treat- ments are more likely to become available. We also describe an insurance scheme that remedies these issues, and that leads to Pareto-optimal allocations regardless of the investment level in R&D for innovative treatments. Ó 2010 Elsevier Ltd. All rights reserved. Introduction Many diseases such as HIV/AIDS, malaria and tuberculosis have a high prevalence in poor countries. Treatments exist for many of them, but their cost is prohibitive and their effectiveness can largely be improved. Despite large international aid, most of the cost of eradicating these pandemic with available treatments remain on poor countries (see UNAIDS, 2005). In a broader context, Philipson, Jena, and Mechoulan (2010) argues that the worlds willingness to pay for better global health in developing countries is as much as 2 percent of total domestic health spending in these countries. Large nancial efforts are nonetheless allocated in developed countries to make available innovative and cheaper treatments for these diseases; in particular, Push and Pull Mechanisms described later aim at restoring incentives for private pharmaceutical compa- nies to initiate R&D in innovative treatments. A typical example is the worldwide effort to develop a therapeutic vaccine against HIV/AIDS (see Klausner et al., 2003). We argue that these mechanisms alone, and without an insur- ance mechanism described here, are antagonistic with the current campaigns in developing countries aimed at fostering the delivery of available treatments. In particular, we show that an increase in investments in Push/Pull Mechanisms leads to a temporary decrease in welfare in developing countries because of a resulting rational reduction in patientscoverage. Moreover, we show that this paradoxical reduction increases as the opportunity cost of current investments increases, as it is typical with severe budget shortfalls. The availability of securities as in Leoni and Luchini (in press), for instance, restores incentives to invest in available treatments, regardless of the nancial efforts put into Push/Pull Mechanisms. On top of describing these securities, Leoni and Luchini (in press) analyze the welfare improvement in developing countries resulting from their availability, regardless of the odds of appearance of innovative treatments. We extend this analysis by pointing out that optimal investments in available treatments are strongly decreasing in investments in Push/Pull Mechanisms, and that opportunity costs of current investments is an aggravating factor to this phenomenon. Therefore, we argue that the availability of the insurance scheme above becomes increasingly important to compensate for welfare losses as the obsolescence of current investments becomes more imminent and budget shortfalls increase. These ndings are consistent with standard results in optimal investments as in Dixit and Pindyck (1994, Chap. 1e 7) . The fact that a likely rapid obsolescence leads to lower health investments is consistent with some recent observations in the case of HIV/AIDS, even if a direct causality is not yet established. In 2005 for instance, UNAIDS (2005) p.11 reports that some Sub-Saharan countries were in measure to rationally increase their AIDS-related expenditures but failed to do so despite high prevalence; these sovereign decisions occurred during the R&D phases of a therapeutic vaccine both by Merck and the Pasteur Institute. No such behavior was reported after the failure of these two ventures, even if we strongly emphasize that many other explanations are possible. * Tel.: þ33 4 68 50 68 11. E-mail address: [email protected]. Contents lists available at ScienceDirect Social Science & Medicine journal homepage: www.elsevier.com/locate/socscimed 0277-9536/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.socscimed.2010.10.031 Social Science & Medicine 72 (2011) 202e205

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Page 1: The antagonism of push and pull strategies, and the current funding campaigns to fight orphan diseases

lable at ScienceDirect

Social Science & Medicine 72 (2011) 202e205

Contents lists avai

Social Science & Medicine

journal homepage: www.elsevier .com/locate/socscimed

The antagonism of push and pull strategies, and the current funding campaignsto fight orphan diseases

Patrick Leoni*

Euromed Management, Department of Economics, Domaine de Luminy, 13288 Marseille, France

a r t i c l e i n f o

Article history:Available online 25 November 2010

Keywords:Push and pull mechanismsOrphan diseasesOptimal policiesDeveloping countriesPublic good

* Tel.: þ33 4 68 50 68 11.E-mail address: patrick.leoni@euromed-managem

0277-9536/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.socscimed.2010.10.031

a b s t r a c t

We argue that an increase in investments in R&D for innovative treatments to eradicate neglected diseasesin developing countries leads to a rational decrease in investments in available treatment technologies. Ina formalmodelwhere the government of a developing country seeks to optimally allocate public resources,we show that the higher the odds of appearance of an innovative treatment, as occurringwhen investmentsin R&D increase, the lower the optimal provision of current treatments and other health expenditures. Wealso show that this phenomenon is aggravated when the opportunity cost of investments in currenttreatments increases. This implies that welfare in developing countries deteriorates as innovative treat-ments are more likely to become available. We also describe an insurance scheme that remedies theseissues, and that leads to Pareto-optimal allocations regardless of the investment level in R&D for innovativetreatments.

� 2010 Elsevier Ltd. All rights reserved.

Introduction

Many diseases such as HIV/AIDS, malaria and tuberculosis havea high prevalence in poor countries. Treatments exist for many ofthem, but their cost is prohibitive and their effectiveness can largelybe improved. Despite large international aid, most of the cost oferadicating these pandemic with available treatments remain onpoor countries (see UNAIDS, 2005). In a broader context, Philipson,Jena, and Mechoulan (2010) argues that the world’s willingness topay for better global health in developing countries is as much as 2percent of total domestic health spending in these countries.

Large financial efforts are nonetheless allocated in developedcountries to make available innovative and cheaper treatments forthese diseases; in particular, Push and Pull Mechanisms describedlater aim at restoring incentives for private pharmaceutical compa-nies to initiate R&D in innovative treatments. A typical example is theworldwide effort to develop a therapeutic vaccine against HIV/AIDS(see Klausner et al., 2003).

We argue that these mechanisms alone, and without an insur-ance mechanism described here, are antagonistic with the currentcampaigns in developing countries aimedat fostering thedeliveryofavailable treatments. In particular, we show that an increase ininvestments in Push/PullMechanisms leads to a temporarydecreasein welfare in developing countries because of a resulting rationalreduction in patients’ coverage. Moreover, we show that this

ent.com.

All rights reserved.

paradoxical reduction increases as the opportunity cost of currentinvestments increases, as it is typical with severe budget shortfalls.The availability of securities as in Leoni and Luchini (in press), forinstance, restores incentives to invest in available treatments,regardless of the financial efforts put into Push/Pull Mechanisms.

On top of describing these securities, Leoni and Luchini (in press)analyze the welfare improvement in developing countries resultingfrom their availability, regardless of the odds of appearance ofinnovative treatments. We extend this analysis by pointing out thatoptimal investments in available treatments are strongly decreasingin investments in Push/PullMechanisms, and that opportunity costsof current investments is an aggravating factor to this phenomenon.Therefore, we argue that the availability of the insurance schemeabove becomes increasingly important to compensate for welfarelosses as the obsolescence of current investments becomes moreimminent and budget shortfalls increase. These findings areconsistent with standard results in optimal investments as in Dixitand Pindyck (1994, Chap. 1e7) .

The fact that a likely rapid obsolescence leads to lower healthinvestments is consistent with some recent observations in the caseof HIV/AIDS, even if a direct causality is not yet established. In 2005for instance, UNAIDS (2005) p.11 reports that some Sub-Saharancountries were in measure to rationally increase their AIDS-relatedexpenditures but failed to do so despite high prevalence; thesesovereigndecisions occurredduring theR&Dphasesof a therapeuticvaccine both by Merck and the Pasteur Institute. No such behaviorwas reported after the failure of these two ventures, even if westrongly emphasize that many other explanations are possible.

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P. Leoni / Social Science & Medicine 72 (2011) 202e205 203

The paper is organized as follows. We first give concreteexamples of Push/Pull Mechanisms and an overview of currentfunding campaigns worldwide with available treatments; we thenexplain and document the antagonism created by these efforts;concluding remarks are then presented; finally, the formal modeland the proofs are given in the Appendix.

Push/Pull Mechanisms and international aid

There are specific deterrents for a private pharmaceuticalcompany to invest in R&D for diseases found in developing coun-tries. The risk of failure is high in many cases (a therapeutic AIDSvaccine for instance), the market is not profitable enough becausemost of the infections are in poor countries, and there is a history ofbreaking patents at least for HIV/AIDS. At the same time, innovativetreatments are critically needed in developing countries to containand then to eradicate these diseases, and private companies are themost likely to develop them (Webber & Kremer, 2001). In the caseof HIV/AIDS, the new technology capable of challenging the manydrugs patents already in place is a therapeutic vaccine, which coulddelay the need for current treatments such as ARV drugs for severalyears at a low cost (see Klausner et al., 2003, and Wei et al., 2004).

There are difficult medical challenges to overcome when devel-oping such innovative treatments. Push Mechanisms tackle thesepitfalls, by reducing the cost of R&D failure and facilitating wide-spread dissemination of scientific knowledge. Push Mechanismshave in part focused on developing research grants to universitiesand on increasing knowledge transfer at international level.A typical example is the International AIDS Vaccine Initiative (IAVI,2004), which has already worked with academia and industry tolaunch 4 vaccine development partnerships in Sub-Saharan Africa.Other examples of push strategies involve tax credits to commercialcompanies seriously undertaking vaccine development, whosepurpose is to transfer the cost of failure to society as a whole.

Pull Mechanisms foster the commercialization phase, which isdeficient because of low market return and high risk of loosingpatent’s rights. Themost commonpullmechanism in theU.S. is a taxcredit on sales to organizations officially designated for the deliveryto patients in developing countries. Another particularly promisingpull mechanism is an Advance Market Commitment (or AMC), asdescribed in Berndt et al. (2007) and Towse and Kettler (2005) forinstance. Other interesting attempts are transferable patent exten-sions,whichallowanextensiononanother existingpatentwhen thecurrent patent is broken, and a transferable priority regulatoryreview with direct consequence to speed access to highly valuedtreatments (see Ridley, Grabowski, & Moe, 2006).

Independently of these initiatives, there are many programs atinternational level aimed at fostering investments in currenttreatment technologies. Among these initiatives, we point out the‘3 by 5’ initiative that was an ambitious project launched in 2003 byUNAIDS. The GFATM also received U.S.$ 9 billion in 2001 to coor-dinate prevention, care and treatment worldwide mostly againstHIV/AIDS but also against other orphan diseases (in a broad sense,which a strong emphasis in diseases with high incidence indeveloping countries). Roughly U.S.$ 2.5 billion have been investedin HIV programs, and treated 220,000 patients between 2001 and2005 (Lamptey, Johnson, & Khan, 2006). A thirdmajor initiativewasthe launch in 2003 of the U.S. President’s Emergency Plan For AIDSRelief. This plan spanned 5 years and was endowed with U.S.$ 15billion to fight HIV/AIDS beyond U.S. borders.

The relative importance of this foreign aid may have significantspill-over effects on domestic expenditures, such as fungibility andcrowding-out effects. Feyzioglu, Swaroop, and Zhu (2005) andAgosin andMachado (2005) report no significantempirical evidenceof these effects at macro-economic level in developing and

emerging countries, both for direct aid and foreign investment.A similar study for health expenditures is nonetheless missing.

The antagonism and a solution

The identification of the antagonism between Push/Pull Mech-anisms and these funding campaigns, and a possible solution toremedy it, is a central element of optimal public policies in devel-oping countries affected bywidespread pandemic. Themain reasonis that current campaigns targeted at deliveringavailable treatmentsare funded both by international agencies, developed countries, andalso foremost by developing countries. UNAIDS (2005) reports that,during the period 2004e2007, roughly one-third of the overallburden worldwide to treat HIV-patients with available treatmentswas born bysomeof the poorest countries in theworld. Inparticular,Hickley (2003) argues that slightly less than 1% of overall nationalexpenditures of SouthAfrica in 2005was allocated toHIV/AIDS only.The basic insight of the antagonism is described next, whereas theformal point is developed in the Appendix.

Consider a government in developing countries, facing the deci-sionof investing largeamountof resources to treataparticulardiseasewith available treatments in a situation of major budget shortfalls.A critical aspect of these investments is that a significant part will beforegone when an upgrade occurs because of the introduction of aninnovative treatment, as documented next for the case of HIV/AIDS.

Managerial costs, also called Program Level Costs, are the mostnatural sunk costs and clearly lost when upgrading. These costsinclude monitoring and evaluation of current delivery policies, stafftraining, supervision of personnel and patients tracking. UnitedNationsestimatesassert that suchcosts amounted toUS$1.236billionin 2006, US$ 1.095 billion in 2007 andUS$ 1.281 billion for all 135 lowand middle income countries (UNAIDS, 2005). In South Africa forinstance, these costs roughlyamount to8%of theglobal investment inARV treatment program (Cleary et al., 2005). Even if these losses arenot direct monetary losses, the opportunity cost they trigger isenormous for developing countries in situation of severe budgetshortfalls, and thismust beencompassed inanyoptimal public policy.

Other severe losses when upgrading are on the drug productionside. ARV drugs are often produced in developing countries, forinstance in Brazil and India, where the patents have been broken.The nature of ARV treatments makes any reshuffling of these plantstoo expensive because of rigid manufacturing plans and costlyregulatory requirements (Shah, 2004).

The risk faced by developing countries is about the date ofobsolescence of these current investments. The longer the currentinvestments remain in place, the higher the return and benefits tosociety as a whole. We next see how the uncertainty about the timethese losses occur distorts optimal decisions to invest now inavailable treatments technologies.

The optimal decision of investing now in current treatmenttechnologies is based on the comparison between the return of theinvestments on the one hand, and the overall social cost of theinvestments on theother. The social costs of these investments oughtto include theopportunity costofmoney; that is, the cost of not usingthis money for other necessary social needs such as building schoolsand roads. The decision to invest now is optimal when the expectedsocial benefits exceed the expected social costs, where the expecta-tion encompasses the random time of obsolescence of currentinvestments. This method is standard in Economics, and it is studiedin related setting in Dixit and Pindyck (1994).

Since the time of appearance is random, it is rational to use theexpected time of appearance when making the above comparison.When better information becomes available over time, the estimatorof the expected appearance time becomes more accurate, leading inturn tomore reliable risk assessment. In our setting, the efficiency of

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Push and Pull Mechanisms directly affects the odds of a vaccineappearance, and thus directly affects the investment decision. Theoptimal delay to invest to the date when this estimator becomesaccurate enough to guarantee enough social return on investments.

This reduction in investment is typical of an uninsurable risk,where the losses are takenwithout any possibility of compensation.The design of an artificial insurance capable of hedging the risk ofpremature obsolescence is thus essential to restore economicincentives to increase the optimal provision of current treatments,while awaiting the appearance of better treatments.

We now describe a set of financial securities tackling the invest-ment problems above. These securities take the form of derivativeswith payment contingent on the appearance (or not) of a successfulinnovative treatment, to be issued both by insurance companies andinternational agencies with the idea of “securityzing” a broadinsurance contract. Consider two securities, with same horizon (orpayment time), which stipulate the same of amount of moneywhena pre-specified and well-defined innovative treatment becomesavailable or not before this horizon. The security paying off whenappearance is demanded by developing countries for the reasonsabove,whereas the securitypayingoffwhennonewproduct appearsis demanded by pharmaceutical companies to compensate for therisk of failure in the R&D.

Further specifications are necessary to remove some moralhazardswhen trading these products, and toprice them fairly. Thesedetails are given in Leoni and Luchini (in press); moreover, it isshown there that the introduction of these financial productsincrease social welfare by providing full insurance coverage both todeveloping countries and to pharmaceutical companies.

Conclusion

We have explained and documented the antagonism betweencurrent funding campaigns to fight diseases in developing coun-tries and the worldwide efforts to promote the appearance ofinnovative treatments. We exhibit the strong negative correlationbetween investments in Push/Pull Mechanisms and investments inavailable treatments, as well as the role of opportunity costs ofcurrent investments in aggravating this pattern. As a direct corol-lary, our analysis shows that social welfare in developing countriesdeteriorates as the likelihood of the introduction of an innovativetreatment increases, because of correlated rational drops in currenthealth expenditures.

Therefore, we argue that the availability of the insurancescheme above becomes increasingly important to compensate forwelfare losses as the obsolescence of current investments becomesmore imminent and budget shortfalls increase. An insurancescheme as in Leoni and Luchini (in press) remedies these issues,regardless of the investments in Pull/Push Mechanisms.

Acknowledgments

I am indebted to K. Arrow, A. Dixit, A. Kirman and manyparticipants to various universities and institutions where thepaper has been presented. A. Birch, the editor, and three anony-mous referees also provided very useful comments.

A. Appendix. The model

We now formalize the idea that an increase in the odds ofa future vaccine appearance, as occurs when Push and Pull Mech-anisms are actively implemented, lowers the optimal provision ofcurrent treatments. We also show that this phenomenon is aggra-vated when the opportunity cost of investments in current treat-ments increases, where an increase in opportunity cost is defined

as a lowered marginal utility of the funds invested. Our model isa simple and standard problem of optimal allocation of resources bya government, although it captures the most relevant economicissues at stake.

In our framework, the government of a developing country allo-cates resources to enhance national consumption, provision ofproduction of current treatments and other unrelated public healthexpenditures for a given level of endowments (which includeagivenlevel of international subsidies). There are two periods (t ¼ 0 andt ¼ 1), and a given population of infected patients in period 0. Abenevolent government is in charge of treating the patients. Everyinfectedagentmustreceivemedicaltreatmentinperiod1,orelsediesduring this period. Potentially, there are two forms ofmedical treat-ment that guarantee the survival of the infectedpatient. Thefirst oneis a pill of ARV drug, with the assumption that technical knowledgeexists inperiod0tostartproductioninperiod1.Thealternativetothistreatment isa therapeuticvaccine(oranyother innovationoutdatingexisting treatments) available in period 1 with positive probabilitydescribed next.

The vaccine is developed in period 0 by an agency independentof the government. In period 1, it becomes common knowledgewhether the development campaign started in period 0 issuccessful. If the vaccine is available in period 1, the agency (such asthe GFATM or a similar body) funds a distribution campaign to treatthe infected population.We assume that a vaccine appears in period1with exogenous probability a> 0. This probability can be regardedas the odds of success in the clinical trial started in period 0.

We now describe the government decision problem. There isone consumption good available in every period, which can beregarded as capital at hand. The government receives an exogenousendowment w0 > 0 of this consumption good in period 0. Thisendowment is the only source of revenue in this period, and it canbe regarded as capital available from fiscal revenues, paymentsfrom previous investments or international subsidies. Thegovernment can turn the consumption good into ARV treatmentsand unrelated health expenditures in a way described later, or canalso consume it directly. Immediate consumption can also beinterpreted as the provision of other public goods such as roads orschools. The government thus faces a problem of optimal allocationof resources between national consumption, treatment of theinfected population and the provision of other health expenditures.

In period 1, the government has an endowment of consumptiongood w1 > 0 if the vaccine is available, and w2 > 0 otherwise. Weassume that w1 is significantly smaller than w2 because the lossescaused by the decline in international subsidies described earlier. Inparticular, this drop in endowment gives stronger incentives to thegovernment to hedge against this fluctuation. Let c0 denote theamount of consumption good consumed in period 0, and let c1(resp. c2) denote the amount of consumption good consumed inperiod 1 if the vaccine is available (resp. if not available).

The government is thus in charge of producing ARV treatmentsand other health expenditures, called health good. These areproduced in period 0, and are distributed at no cost to the pop-ulation in period 1. For sake of simplicity, we assume that for anyamount of consumption good c � 0, the government uses a one-to-one technology to produce a measure h of health expenditures. Thegovernment also uses a one-to-one technology to produce ARVtreatments. A measure T of ARV treatment has two components,one component h' that can be turned into other health good if thevaccine appears, and a component d that is AIDS specific and is lostif a vaccine appears. The component d will be called treatments. Tosimplify the analysis, we assume that the component g' isembedded into the provision of the health good h. If the vaccine isavailable, it is distributed to the population at no cost to thegovernment by the agency.

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The utility derived by the government from a sequence(c0,c1,c2,d,h) is given by the welfare function

Uðc0; c1; c2;d;hÞ ¼ uðc0Þ þ ba½vðhÞ� þ bð1� aÞ½vðhÞ þ VðdÞ�(1)

where b > 0 is an intertemporal discount factor, and where thefunctions u,v and V are all strictly increasing, strictly concave,twice-continuously differentiable and satisfy the Inada conditions.The function V measures the specific emphasis on treating theinfected population regardless of possible losses, we assume thatV($)¼ gf($), where g˛ð0;1Þ is a constant that represents the relativesocial weight the government puts on unrecoverable losses. Thelower g, the lower the social benefits that the government getsfrom treating the infected patients. The constant g can naturally beregarded as a measure of the opportunity cost of money of unre-coverable losses in case of a vaccine appearance, in the sense thatthe lower g the lower themarginal utility of additional investmentsin treatments and thus the higher the opportunity cost of money.The function u (resp. v) measures the utility derived fromconsumption good (resp. public good). The functions V and v candepend on the level of infected population, political priorities orother demands for health expenditures.

We now describe the budget constraints faced by the govern-ment. The budget constraint in period 0 is given by

c0 þ g þ d � w0; and c0; g; d � 0: (2)

The following result analyzes the optimal provision of healthgood and AIDS treatments as the likelihood of a vaccine appearanceincreases.

Proposition 1. Assume that no insurance can be purchased. Theoptimal provisions d* and h* decrease as a increases.

Proposition 1 states that, in absence of transition mechanism,the optimal provision of health good and AIDS treatments decreaseas the vaccine becomes more and more likely to appear. The intu-ition is given in the Introduction, and the result is also consistentwith those in Dixit and Pindyck (1994, Ch. 7e11), although ourframework is better fitted for the AIDS problem at stake.

We next analyze how the optimal provision of treatments andhealth good is affected when the opportunity cost of money ofunrecoverable losses increases, and without the possibility toinsure.

Proposition 2. For every a, the optimal provisions d* and h*decrease as g decreases.

Proposition 2 states that, regardless of the investments in Pull/Pull Mechanisms, both the optimal provision of health good andAIDS treatments decrease as the opportunity cost of money ofunrecoverable losses increases (this is equivalent to a decrease in g

as explained earlier). The intuition of this result is explained in theIntroduction. The result is consistent with the reluctance to investin ARV treatments as reported in UNAIDS (2005). This issue istypical of countries' situation of shortfall of public resources, wherethe amount of money foregone in AIDS investments puts a severestrain on other necessary public expenditures.

B. Appendix. Proofs

We now prove Propositions 1 and 2. The proofs start byanalyzing the optimization problem faced by the government.

Since the utility functions are strictly increasing, the budgetconstraints in Eq. (2) must be binding. After rearranging terms, thisimplies that the program faced by the government comes down tomaximizing the expression

uðw0 � d� hÞ þ bð1� aÞVðdÞ þ bvðhÞ; (3)

with respect to the variables (d,h,q). We first notice that, by theInada conditions, the solution variables ðd;hÞ to the above programmust be strictly positive. Taking the first order conditions, andusing the price relation given in Proposition A, we obtain thefollowing equilibrium relations:

u0ðw0 � d� hÞ ¼ bv0ðhÞ; and (4)

u0ðw0 � d� hÞ ¼ bð1� aÞV 0ðhÞ (5)

Rearranging the above equations, we obtain that

v0ðhÞ ¼ ð1� aÞV 0ðdÞ (6)

We now prove Proposition 1. By Eq. (6), the optimal h increasesas d increases, and conversely, because both u and V0 are decreasingby assumption. To prove the result, we proceed by way of contra-diction. By the previous remark, it is enough to consider thefollowing case to reach a contradiction: there exist optimal (h1,d1)corresponding to a1 and optimal (h2,d2) corresponding to a2 suchthat a1 > a2 and (h1,d1) > (h2,d2). Under this case, consider now Eq.(4) applied to (h2,d2) and a2. By the previous remarks, we have that

u0ðw0 � d1 � h1Þiu0ðw0 � d2 � h2Þ ¼ bv0ðh2Þ > bv0ðh1Þ; (7)

which directly implies that

u0ðw0 � d1 � h1Þibv0ðh1Þ: (8)

Eq. (8) contradicts the fact that (h1,d1) is an optimal allocation,and thus must satisfy Eq. (4) with equality. This is a contradiction,and the proof is now complete.

The proof of Proposition 2 follows the same lines, after recog-nizing that V0($) ¼ gf 0($).

References

Agosin, M., & Machado, R. (2005). Foreign investment in developing countries: doesit crowd in domestic investment? Oxford Development Studies, 33, 149e162.

Berndt, E., et al. (2007). Advancemarket commitments for vaccines against neglecteddiseases: estimating costs and effectiveness. Health Economics, 16, 491e511.

Cleary, S., et al. (2005). Financing antiretroviral treatment and primary health careservices. In P. Ijumba, & P. Barron (Eds.), South African health review. Durban:Health Systems Trust.

Dixit, A., & Pindyck, R. (1994). Investment under uncertainty. PrincetonUniversity Press.Feyzioglu, T., Swaroop, V., & Zhu, M. (2005). A panel data analysis of the fungibility

of foreign aid. World Bank Economic Review, 12, 29e58.Hickley, A. (2003). Public expenditure on HIV/AIDS in South Africa: analysis of

allocations and funding mechanisms in national and provincial budgets.Proceedings of the International AIDS Economics Network Meeting, .

IAVI. (2004). Accelerating global efforts in AIDS vaccine research and development.International AIDS Vaccine Initiative. (Technical report. Scientific Blue Print).

Klausner, R. D., et al. (2003). The need for a global HIV vaccine enterprise. Science,300, 2036e2039.

Lamptey, P., Johnson, J., & Khan, M. (2006). The global challenge of HIV and AIDS.Population Bulletin, 6, 1e24, (University of Stellenbosch).

Leoni, P., & Luchini, S. Designing the financial tools to promote universal access toAIDS care. Journal of Health Economics, in press.

Philipson, P., & Jena, A., & Mechoulan, S. (2010). Global health and economic effi-ciency. Working paper.

Ridley, D., Grabowski, H., & Moe, J. (2006). Developing drugs for developingcountries. Health Affairs, 25, 313e324.

Shah, N. (2004). Pharmaceutical supply chains: key issues and strategies for opti-mization. Computers and Chemical Engineering, 28, 929e941.

Towse, A., & Kettler, H. (2005). Advance price or purchase commitments to createmarkets for treatments for diseases of poverty: lessons from three policies.Bulletin of the World Health Organization, 83, 301e307.

UNAIDS. (2005, June). Resource needs for an expanded response to aids in low andmiddle income countries. Geneva: Joint United Nations Programme on HIV/Aids.(Technical report).

Webber, D., & Kremer, M. (2001). Perspectives on simulating industrial research anddevelopment for neglected infectious diseases. Bulletin of the World HealthOrganization, 79, 735e741.

Wei, L., et al. (2004). Therapeutic dendritic cell vaccine for chronic HIV-1 infection.Nature Medicine, 10, 1359e1365.