There are a number of reasons to believe that the costs of climate change will not be borne equally across income groups. First, regional variation is expected in future warming as well as in the climate sensitivity of agricultural production. Irrigated areas, for instance, may be wealthier and, at the same time, less vulnerable to rising temperatures. Secondly, households differ in their ownership of agricultural assets, notably land, as well as in their human capital and allocation of labor. The returns on land and labor (of different types) will probably respond differently to climate change. Thirdly, households will be exposed in varying degrees to changes in food prices that are likely to occur with global warming. Urban households tend to be net buyers of food to a much greater extent than rural households (as are non-farm households within rural areas), leaving them relatively worse o when prices rise.
A recent research paper from the World Bank analyzes how changes in the prices of land, labor, and food induced by modest temperature increases over the next three decades will affect household-level welfare in India. The authors predict a substantial fall in agricultural productivity, even allowing for farmer adaptation. Overall, the welfare costs of climate change fall disproportionately on the poor. This is true in urban as well as in rural areas, but, in the latter sector only after accounting for the effects of rising world cereal prices. The results suggest that poverty in India will be roughly 3–4 percentage points higher after thirty years of rising temperatures than it would have been had this warming not occurred.
The report also says that:
The substantial fall in agricultural productivity (17 percent overall) that we predict as a result of warming will translate into a much more modest consumption decline for the majority of households. This is because these households derive the bulk of their income from wage employment and (rural) wages are estimated to fall by only a third as much as agricultural productivity.
But here I loose the reasoning: If agriculture productivity is supposed to fall, realistically prices would go up. And if wages are also supposed to fall those poor that derive most of their income from wage labour must suffer hard from falling wages and increased food prices. Perhaps I am missing some part of the argument?