A regionalized climate-economy Integrated Assessment model with region-specific physical capital depreciation rates endogenously increasing under effect of global warming is proposed. An analytical steady-state solution is obtained; the transitional dynamics is studied numerically. It is shown that the dynamics of modeled climate-economy system consisting of two macro-regions is characterized from certain point in time by a dramatic amplification of differentiation of economic growth rates and by subsequent collapse of economy in the macro-region that is more vulnerable to climate change.