Spatial frequency of unstable eigenfunction of the core-periphery model incorporating differentiated agriculture with transport cost

Both the paper and the candidate derive the same sign conclusions at the two extremes: high-β stability under the no–black-hole condition and low-β stability when α>0. However, the paper’s Theorem 2 states an explicit eigenvalue limit with an incorrect constant factor, inconsistent with λ=1/(2πr) and its own appendix computation of Ωn; the correct eigenvalue limit is −γωB/((σ−1)σ), not −γrωB/((σ−1)σ). The candidate’s solution computes the exact high-β limit Ω∞=−(2πrω/(σ−1))Δ (Δ=σ(1−μ)−1) and the correct low-β eigenvalue limit by multiplying with λ, fixing the paper’s factor error and strengthening Theorem 1 by giving the exact limit. See eqs. (26)–(30) and Theorems 1–2 in the paper for context , and the appendix derivations including eq. (36) and the low-β limit of Ωn ; λ=1/(2πr) is set in the homogeneous solution .