ei2 + ρE1 Sample Clauses

ei2 + ρE1. For the symmetric equilibria, the first-order conditions for the respective maximization prob- lems above are a − be2s = nγE2, (7) a − be2ns = γE2, (8) 6This assumption will be relaxed further on. where E2 = ne2s +(N −n)e2ns +ρE1.7 Solving (7) and (8), we get the inter-temporal decision rule for the emissions of signatories and non-signatories, respectively e2s e = ab − aγ(N − n)(n − 1) − bnγρE1 , (9) b(b + γ(N − n + n2)) = ab + an(n − 1)γ − bγρE1 . (10) 2ns b(b + γ(N − n + n2)) In period 1, signatories decides jointly the emission levels that maximize their expected discounted net welfare. More formally, they solve max { [π (e , E ) + δEπ (e Σ , E )] = [ae b 2 γ 2 − e − (E ) ] ei1,i∈S i∈S i1 i1 1 i2 i2 2 i∈S i1 2 i1 2 1 b 2 γ 2 ¯ +nδ[ae − e − (E ) − θP (E )]}, where E2 = ne2s + (N − n)e2ns + ρE1. A non-signatory i ∈ N \ S solves 2s 2 2s 2 2 1 ei1 i1 max{[π (e , E ) + δEπ (e , E )] = [ae b 2 γ 2 i1 2 i1 2 1 − e − (E ) ] i1 i2 2ns +δ[ae − b e2 − γ (E )2 − θ¯P (E )]}, subject to: E2 = ne2s + (N − n)e2ns + ρE1. 2 2ns 2 2 1 In a symmetric equilibrium, given (7) and (8), the first-order conditions for signatories and non-signatories are respectively: ′ 1s a − be = nγE − nδ[nγE e − γ(ne + (N − n)e′ + ρ)E − θ¯P ′(E )], (11) 2ns 1 2 2s 2s 2ns 1 a − be1ns = γE1 − δ[γE2e′ − γ(ne2ns + (N − n)e′ + ρ)E2 − θ¯P ′(E1)]. (12) 2ns Using a similar reasoning as in the non-cooperative scenario, it can be shown that in period 1 and for any coalition of size n, the signatories’ emissions as well as the non-signatories’ emis- sions are lower under endogenous uncertainty in comparison with the certainty framework. But these two results do not hold in period 2. 7Condition (7) is in fact the ▇▇▇▇▇▇▇▇▇ (1954) condition for the provision of a public good within the coalition S, which states that the marginal benefit of each coalition member is equal to the sum of the marginal damages of all the coalition members.