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

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!) 31 December 2018 2

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! 31 December 2018 3

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 (?) 31 December 2018 4

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? 31 December 2018 5

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)] 31 December 2018 6

31 December 2018 7

31 December 2018 8

31 December 2018 9

31 December 2018 10

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* 31 December 2018 11

31 December 2018 12

31 December 2018 13

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 31 December 2018 14

31 December 2018 15

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 31 December 2018 16

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 31 December 2018 17