In a paper published Monday in Proceedings of the National Academy of Sciences, scientists demonstrate the full ramifications of a widely accepted theory about climate change: that it will almost certainly have a disproportionate impact on the poor. Acknowledging this fact in models, they find, can drastically change estimates of how climate change will affect the economy, and leads to a deeply troubling conclusion — climate change won’t just hit the poor hardest, but it will exacerbate existing inequality within societies.

The disproportionate effect of climate change on the poor isn’t a new idea. But in general, while the economic models used to inform climate policies have accounted for income inequalities between different countries or regions of the world, they’ve failed to acknowledge that these inequalities exist within countries as well.

“The lacking description of subregional/national inequality is one of the most glaring lacunae in these models,” said lead author Francis Dennig, an assistant professor of economics at Yale-NUS College in Singapore, in an email to The Post.

Dennig and his colleagues decided to see what would happen if they tweaked a leading climate-economy model, known as RICE (the Regional Integrated model of Climate and the Economy), to account for inequalities within different regions of the world — essentially acknowledging that different countries contain people of both higher and lower incomes. They found that when they assumed a scenario in which lower-income sectors of society were hit hardest by the effects of climate change, a key factor in our understanding of the economic effects of climate change changed drastically in comparison to models that didn’t take these inequalities into account.

Why carbon may be even more costly than we thought. This key factor is the optimal price that governments should place on emitting a ton of carbon as an incentive for individuals and industries to cut down on their greenhouse gas emissions. It’s an estimation closely tied to a value known as the “social cost of carbon” — the estimated economic cost of every additional ton of carbon dioxide emitted into the atmosphere, based on how much damage that ton could help bring about in terms of climate-related effects.

It turns out that the estimation of these values is heavily dependent on the way climate change impacts people of differing income levels. If people with lower incomes are disproportionately affected by climate change, as many scientists and economists believe they will be, then these damages could cause them to become less well-off than previous generations — essentially slowing, halting or — in extreme cases — even reversing their economic growth.

If this becomes true, and whole segments of the population are forced to endure more than their proportional share of climate change damages, then greater climate mitigation efforts — in the form of higher estimates of the social cost of carbon, which translate into higher carbon prices — will be considered optimal.

The danger with models that don’t take these inequalities into consideration is that they tend to average the economic conditions of people within regions or countries, and doing so can have the effect of masking the worst economic climate-caused damages in those countries. Thus, the models will assume that less intensive mitigation strategies are warranted.

So in the modified model used in the new study, when the income inequalities were factored in, suddenly the worst climate damages became apparent, and the model compensated for them by producing higher values for the carbon prices necessary to mitigate or prevent these future effects. What this means, in effect, is that climate change was suddenly viewed as even costlier because it was revealed to be keeping poor people poor to a greater extent than estimated in existing models.

“Most of the efforts on quantifying damage [from climate change] are still just trying to improve on estimates of damage to the economy as a whole, without looking at its incidence across the income distribution,” Dennig said in his email. “We need to start directing our efforts at quantifying the distribution.”

Furthermore, he added, the results suggest that existing models have been underestimating the need for aggressive climate policies by not taking into account the idea that income inequalities exist within regions, and that the poor will be disproportionately affected by climate change.

Discounting “discount rates.” The results help inform an ongoing debate about the way the social cost of carbon should be calculated. In existing models, the biggest variable that affects these cost estimates is a factor known as the discount rate. This is a rate, similar in concept to the idea of an interest rate, that’s applied to carbon cost estimates, and is meant to represent how much people value future generations — or, looked at from another angle, how important we think it is to avoid releasing a ton of carbon into the air, given that its effects aren’t immediate.

This is a tricky concept even for expert economists, and given that the whole idea of a discount rate revolves around murky ethical and social considerations, there’s no universally agreed upon answer. Therefore, different models apply different discount rates — for example, a rate of 3 percent versus a rate of 5 percent. Higher rates suggest that we value the future effects of climate change less, so they result in a lower estimated cost of carbon, which translates into weaker carbon pricing policies.

Economists who favor higher discount rates (and, thus, a lower social cost of carbon) often justify their position by the idea that the global economy as a whole is growing and future generations will be better off than current ones — thus, climate damages will have less of an impact on them, economically speaking. But the modified model suggests that this won’t necessarily be the case for lower-income segments of society, whose welfare may decline as a result of the impacts of climate change.

In their modified model, the researchers kept a discount value that some economists have argued is high. But notably, when they assumed a disproportionate effect of climate change on the poor, the model produced an optimal carbon price similar to what would be generated in an existing model that adopted a lower discount rate — in other words, the carbon price skyrockets.

The finding packs a punch, suggesting that climate inequalities could be just as important in informing policy as the discount rate.

“We all know that discounting is incredibly important for how to think about climate policy,” Dennig said. “But here we point out that there is another aspect about the climate that is equally important, namely, how the impacts of climate change are likely to be distributed.”

The new paper fundamentally challenges the idea that all people in the future will be more affluent than previous generations. The tweaked model suggests that unequal effects of climate change can slow the economic growth of people with lower incomes, and in some cases even halt growth altogether.

“If climate impacts are borne mostly by the poor, then the future poor will, in fact, be very poor indeed,” Dennig said in his email. “Even while the average income is growing inexorably, climate change would be exacerbating inequality and hindering poverty reduction.”

There’s no national carbon-pricing scheme in the U.S., although the government has produced several estimates for the social cost of carbon using existing models (which do not take such inequalities into account). Currently, the most widely acknowledged estimate is $37 per ton, which many economists feel is an underestimate already. The results from this paper further suggest that these estimates should be revised upward, taking income inequalities and potential disproportionate impacts of climate change into account.

In the meantime, Dennig suggested that further work should focus on gaining a better understanding of just how unequal the future effects of climate change will be. The scenarios assumed in his modified model, which assumed the poor would suffer a higher proportion of damages, were theoretical, even if many climate experts would agree that there’s a high probability this will be the case in many places.

Such work will be important to national governments looking for the best ways to slash their carbon output in the future — particularly if an international emissions reduction agreement is reached at the UN climate conference ongoing in Paris.

Producing the most accurate estimates for the social cost of carbon will, in turn, inform more effective and faster-acting emissions reduction schemes in the future. And that could make all the difference to subsequent generations, whose future — if this paper has anything to say about it — could be in greater jeopardy than we thought.