The explanation is the following: in the initial situation the factor price equalization theorem
holds, and, as previously proved, capital grows everywhere at the same pace.
Regarding the factor price equalization theorem
, John Hicks considered two sets of equations for two countries, namely, ar + bw = ar'+ bw', and cr + dw = cr' +dw'.
International trade is introduced and general equilibrium yields the factor price equalization theorem
The factor price equalization theorem
in its most stringent form precdicts that if goods sell for the same price regardless of where they are produced, then workers who produce them will earn equal wages.
Given that all of the Heckscher-Ohlin-Samuelson-Jones pre-requisites are satisfied in this problem, that is, that both countries use the same linear homogeneous functions for abatement and sequestration as well as for production, that the level of pollution is global, and that pollution damage is identically multiplicative, the factor price equalization theorem
must in fact hold.
The "thousand percent" differential is fundamentally exogenous to the trading system, not determined by the factor price equalization theorems