Abstract
It is well-known that the private provision of public goods results generally in collective underprovision. The same situation seems plausible in the case of combating HIV/AIDS. The desire to intervene effectively has been addressed by a lot of international negotiations. A landmark in international efforts is the Declaration of Commitment on HIV/AIDS (UN 2001). It was adopted at the United Nations General Assembly Special Session in June 2001 (Department of HIV/AIDS Family and Community Health 2003, p. 10). For the first time governments from 189 states gathered to discuss a specific health problem. The Declaration describes the HIV/AIDS epidemic and its effects as well as desired interventions. Basic priorities are educating people, especially the youth; stopping mother-child-transmission; providing treatment to all those who are infected; developing an AIDS vaccine or a cure and alleviating the impacts of HIV/AIDS. Although specific time-bound targets exist for each of those aims, these agreements are not legally binding. Governments cannot be compelled to keep their promises since an enforcing authority is missing. Since autonomous governments primarily consider their national benefits, they fail to take positive cross-border effects into account. As a consequence, an efficient transnational provision level of health measures cannot be provided (Kremer 2006, p. 26; Kaul 2002, p. 27). However, this conclusion is based on the very strong assumption that the sum of individual efforts at the national level equals the global effort. The condition of a summation technology is not valid for every health-promoting public good as we know from Chap. 2.
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- 1.
A more general description of suboptimality based on insufficient incentives can be found in Olsen (1965).
- 2.
For concreteness, governments act on behalf of their citizens.
- 3.
The subsequent analyses concentrate on these three health interventions and thus measures like collecting data for transnational health statistics and developing second-drug lines against HIV also mentioned in Chap. 2 will not be discussed. We explain in Sect. 3.1 why we focus on the three key health-promoting public goods.
- 4.
A simple but successful strategy is Tit-for-Tat which has got attention after the publications of Axelrod (1980a, b). Axelrod invited game theorists to design strategies which do not fail in repeated games. To identify the most successful proposal, a computer competition was simulated in which each submission was tested. Tit-for-Tat which was submitted by Rapoport won. The idea is to cooperate in the first round if the choices of the other are unknown. In the subsequent rounds, previous cooperation is rewarded by cooperation and opportunistic behaviour is answered by becoming opportunistic.
- 5.
Kremer (2006, pp. 34–37) suggests the implementation of a large-scale purchase commitment programme financed by the World Bank to encourage R&D in vaccine research.
- 6.
If private firms do not compete in HIV vaccine research, patent-race games seem less appropriate. Multiple firms spend resources on R&D until one of them makes a discovery. The firm that innovates first will obtain a patent while all other firms will gain nothing.
- 7.
For simplicity the utility function does not include externalities caused by implemented health interventions. For example, the discovery and supply of an HIV vaccine could reduce the provision of curative health activities like treatment with antiretroviral drugs since an infection with HIV could be prevented.
- 8.
For concreteness, a country cannot receive benefits. We suppose that countries possess benevolent governments that act on behalf of their citizens who gain from health measures. Because we have assumed identical individuals, the utility function of a representative individual is represented.
- 9.
A similar figure can be found in Cornes and Sandler (1996, p. 146).
- 10.
This assumption is known as a zero conjecture variation in that sense that each agent regards the behaviour of the other agents as independent of its own (Cornes and Sandler 1984b, p. 371).
- 11.
An analytical investigation of the existence of a Nash equilibrium can be found in Bergstrom et al. (1986, pp. 32–34).
- 12.
This depiction follows the figure in Hirshleifer (1983, p. 375).
- 13.
For the standard result see Hirshleifer (1983, pp. 375–376) as well as Cornes and Sandler (1996, pp. 155–158).
- 14.
The contract curve represents all Pareto-efficient allocations given the price p and the income levels \( {I_i}\ \)for \( i = 1,2 \).
- 15.
The right-hand side of (3.12) is equivalent to the marginal costs MC which are identical for each country \( (M{C_1} = M{C_2}) \).
- 16.
A similar argument can be found in Ihori (2005).
- 17.
- 18.
This is due to the fact that the second constraint also needs to be fulfilled.
- 19.
- 20.
Reaction curves can be derived as in the benchmark case. However, in the previous analysis we have modified \( {G_{ - i}} \) to receive a reaction curve.
- 21.
Country 1 can reduce its contribution to the public good and can utilise an increasing part of income for private consumption in point A compared to \( B' \).
- 22.
As noted by Hirshleifer (1983, p. 376), the \( 45^\circ \)-line where \( {g_1} = {g_2} \) plays an important role. Country 1 (2) will never provide prophylactic health measures outside of the range \( {g_1} \leqslant {g_2} \) \( ({g_2} \leqslant {g_1}) \). This results from the weakest-link technology.
- 23.
The right-hand side of (3.19) is equivalent to the sum of both countries’ marginal costs \( M{C_1} + M{C_2} \).
- 24.
This is the case which is explained by Hirshleifer (1983).
- 25.
An alternative way of analysing allocative implications of a best-shot aggregation technology can be found in Cornes and Hartley (2007a, pp. 1701–1704). In contrast to the approach of a best response function, they use a replacement function expressing an agent i’s best response as a function of the overall public good provision level G and not of the sum of the best replies of all other agents. For a further characterisation of individual and aggregated replacement functions see Cornes and Hartley (2006) as well as Cornes and Hartley (2007b).
- 26.
This depiction follows the figure in Sonntag (2009a).
- 27.
IAVI is the world’s largest organisation focussing on the development of an AIDS vaccine.
- 28.
- 29.
A detailed discussion under which circumstances financial support has to be given to research institutions in the developing world can be found in Chap. 4.
- 30.
The right-hand side of (3.36) will equal country 1's marginal costs \( M{C_1} \) if country 2 is a non-contributor. Hence, there is a difference compared with the summation case where \( M{C_1} = M{C_2} = MR{S_1} + MR{S_2} \).
- 31.
By contrast, in patent races competition in R&D may lead to excessive expenditures on R&D relative to the social optimum where the marginal social return equals the marginal cost. One rationale may be rent-seeking to secure patent protection ahead of other firms. A detailed analysis of the consequences of R&D competition can be found in Dasgupta and Stiglitz (1980).
- 32.
A detailed derivation of allocative decisions by taking intergenerative spillovers into account can be found in Sandler (1978).
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Sonntag, D. (2010). Profiling the Provision Status of Health-Promoting Public Goods Against AIDS. In: AIDS and Aid. Contributions to Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2419-3_3
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