1. Technology Agreements with Heterogeneous Countries
Michael Hoel, University of Oslo, Norway
Aart de Zeeuw, Tilburg University, Netherlands

2. IEAs International Environmental Agreements
Emission reductions (e.g. Kyoto Protocol)
“Stable” coalitions small (Barrett)
free-rider incentives dominate incentives to cooperate
“k.b just above c”, k is size of coalition
Technology agreement?
R&D plus spillovers, three stages
Asymmetry (total abatement instead of only size!)
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3. Model N countries Same abatement potential, normalized to 1
Different valuations of abatement vi, i = 1,2,…,N
The coalition decides on total R&D M
Costs of abatement c(M) decreasing function of total R&D M
Countries that abate or not can be different from countries that are in or out of the coalition!
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4. More specific
Countries with higher valuations than costs abate: number of countries is denoted by m(M)
Benefit W(k) to the coalition of size k of one country abating is the sum of the larger valuations up to vk
Total benefit to the coalition is m(M)W(k)
Total costs to the coalition are R&D costs M plus abatement costs k.c(M) or m(M).c(M)
V(k) just above 0 determines the stable size (?)
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5. Sensitivities
If the cost function c(M) shifts up, it can be shown that V(k) increases, so that the stable size k* may increase
If the valuations vi increase, W(k) and m(M) increase, so that V(k) increases and the stable size k* may decrease
How does M change?
How does total abatement change?
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6. Two types of countries Valuations: h and l, h > l
number of h-countries: n
R&D levels: M1 < M2, c(M1) = h, c(M2) = l
Partial abatement P, full abatement F
For k ≤ n, only h-countries in coalition
For k > n, h-countries and l-countries in coalition
V(k) = max[VF(k), VP(k)]
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11. Sensitivities
If the cost function c(M) shifts up, so that M1 and M2 increase by the same amount, kF and kP will both increase but kP more because VP is flatter, so that a shift may occur from partial to full abatement
Shifts between partial and full abatement
Determine kF and kP
Only h-countries: kF, kP ≤ n
Pivotal n*
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14. Partial to full abatement
Sufficiently low M2
not too costly to get every country abating
Sufficiently low n! (n < n1)
otherwise partial abatement is sufficiently interesting
But also sufficiently high n (n > n0) because for n = 0 all the l-countries must be willing to invest M2, that is M2 < N(N - 1)l
Full abatement does not occur if n0 > n1 and n < N
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16. Example N = 20, h = 2, l = 1, c(M) = γ/M, M1 = γ/h, M2 = γ/l
γ = 250: n1 = 10.8: full abatement 20 for n ≤ 10
γ = 500: n0 = 5, n1 = 10.5, full abatement in between
l = 1.5: full abatement on [0, 15.4]
l-countries want to cover investment costs M2
h = 3: full abatement on [3, 7.4]
Higher low l valuations is good but higher high h valuations is not so good
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17. Conclusion Technology (R&D) agreements Asymmetry in valuations
Countries abate if R&D is sufficiently high
Membership of coalition means contributing to R&D
Stable coalition implies full abatement if M2 and n are sufficiently low
Higher l increases but higher h decreases the range of full abatement
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