Appendix: Proofs

which establishes (32).

Indeed, the fact that λ(γ∏; B) < λ < λ(y_L; B) means that τ ∈ P(a_L; λ), whereas τ ∈ P(σ∏; λ). The rest of the claim follows from the fact σ₂ ∈ T(τ; M), since M > R(τ,σ_b).

Claim 2. After the political shift in C1, (r,σg) is the only steady state for that coun­try.

First, since λ' > λ(y_L; B) > λ(γ∏; B) we now have τ ∈ P; λ') and τ ∈ P(σ∏; λ'), so there is no steady state with policy τ. Moreover, since M < R{τ^,σf) we have σ₂ ∈ T(τ; M), so the only possible equilibrium is (r_, σ∏). It is indeed an equi­librium, as M < R(r_, σ∏) means that σ∏ ∈ T(τ; M), while λ(γ∏; B) < λ' means that τ ∈ P(σ∏; λ').

Claim 3. After C1 has switched to the technology σ∏, so that C₂ faces the technology frontier m, the only steady state for C2 is ( τ, σ∏).

First the fact m < R(τ, σf) < R(τ, σf) implies that (τ, σf) is no longer a technological equilibrium, and a fortiori neither is (τ, σf).

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