Our preferred estimate of the relationship between PM2.5 exposure and the all-cause mortality rate in Indian urban areas, denoted “log-log,” expresses the natural log of mortality as a function of the natural log of the PM2.5 concentration. This estimate produces the supralinear shape of the C-R at higher concentrations (see orange line on left panel of Figure 1). The relative risk between exposure at the mean (49.7µgm−3) and 10 units below the mean is 1.024 (95% CI: 1.006 to 1.042, p<0.01). With log-log, a one-unit reduction in PM2.5 at an already low concentration location has a much larger reduction in mortality compared with a similar reduction at a high-concentration location—e.g., the reduction in the relative risk is 4.3 times greater for a reduction from 20 to 19 µgm−3 than for a reduction from 100 to 99 µgm−3 (see orange line in right panel of Figure 1).

Our alternative estimate for comparison, denoted “log-linear,” expresses the natural log of mortality as a function of the PM2.5 concentration. The log-linear form is common in the epidemiological literature of health effects from air pollution. The relative risk between exposure at the mean and 10 units below the mean is 1.014 (95% CI: 1.0004 to 1.028, p<0.05). With the log-linear C-R, every unit reduction in the PM2.5 exposure has a similar change in the relative risk (see gray line in right panel of Figure 1). Log-log is our preferred estimate over log-linear (and several other specifications) as it improves the goodness of fit of the model to the data according to the AIC and BIC measures (see S.2 in Supplemental Information for discussion of model selection and goodness of fit). As a comparison to our estimated C-R relationships, we also calculate the results using GEMM. The GEMM function is steeper than our estimates (i.e., more lives are saved for each unit of PM2.5 reduced), but has less curvature than our log-log estimate (i.e., the difference in shape between low- and high-exposure locations is not as large) (see black dotted line on left panel of Figure 1).

Figure 2 illustrates the key tradeoff between lives saved and inequality in air pollution exposure that we explore across the three scenarios and for the three functional forms of the C-R relationship. The three scenarios all utilize the same budget of person-PM2.5 unit reductions, but employ them very differently. The size of the budget is set by assuming a 10-unit reduction across all districts. This is the *Equal* scenario. Instead of reducing all districts by 10 units, the *Standard* scenario reduces pollution in the dirtiest locations first, and exhausts its budget by ensuring no district is exposed to more than 53 µgm−3. The *Optimized* scenario picks those locations where a one-unit reduction in PM2.5 will have the largest effect on the mortality rate, and continues until the budget is exhausted—we limit reductions in any district to no less than 5 µgm−3, roughly equivalent to a very clean location in the United States.

The *y*-axis of Figure 2 shows the percent reduction in the Gini coefficient compared with the status quo pollution exposures—where positive values represent greater equality in exposures across districts, and negative values a widening of inequality. For each functional form, the *Standard* scenario provides the greatest gains in pollution exposure equality, but the fewest lives saved; the *Equal* scenario delivers more lives saved than the *Standard* scenario and a small reduction in inequality; and the *Optimized* scenario increases inequality of exposure but saves the greatest number of lives. Our focus is on the steepness of the lives saved/inequality tradeoff between the scenarios.

For our alternative log-linear, the tradeoff is very steep, suggesting that a relatively small number of additional lives are saved (13,600 lives) in the *Optimized* scenario compared with the *Standard* scenario, but at a huge cost in inequality of exposure (65% reduction in inequality to 9% increase in inequality).

For our preferred log-log, the tradeoff is much flatter, which means that although exposure inequality declines sharply as we move from the *Optimized* scenario to *Equal*, and then to the *Standard* scenario, the number of lives saved declines by over 80%. The *Standard* scenario, which reduces inequality by 65%, saves 28,000 fewer lives than reducing pollution by 10 units in all locations (*Equal* scenario), which reduces inequality by only 14%. Compared with the *Equal* scenario, the *Optimized* scenario saves an additional 79,400 lives, but comes with an increase in the inequality of exposure (19% increase compared with the initial situation).

For GEMM, the tradeoff is similar to log-log but shifted to the right—more lives are saved in all scenarios compared with log-log.

Figure 3 examines the number of lives saved in each scenario (by the height of the bars) and also shows the initial concentration of the districts where the lives are being saved (by the colors). Across the three scenarios, it is not just that the number of lives saved varies, but the lives are saved from very different locations. The S*tandard* scenario protects those who are initially exposed to the highest concentrations, whereas the *Optimized* scenario generally saves lives for those with relatively low initial concentrations. If the relationship is log-linear, the gains in lives saved are relatively small in the *Optimized* and *Equal* scenarios over the *Standard* scenario, but the composition of those lives is very different.

With log-log, large gains are achieved under the *Optimized* scenario over the *Standard* scenario, in total lives saved (18,300 versus 125,700). However, the *Standard* scenario saves 14,000 lives for those exposed to over 75 µgm−3, whereas the *Optimized* scenario saves zero lives from these groups. The vast majority of the lives saved in the *Optimized* scenario (91%), are those of people living in below average PM2.5 concentration locations. Again, GEMM illustrates a similar tradeoff in terms of lives saved and inequality of exposure to log-log, with larger overall magnitudes of lives saved, but lesser ratios of lives saved between the *Optimized* and *Standard* scenarios.

In aggregate, the outcomes from our three scenarios show vast differences. Examining how the scenarios direct their budget of person-PM2.5 units to different Indian districts, leading to these differences, is instructive for understanding how the scenarios are implemented. Figure 4 plots four outcomes (panels A, B, C and D) for each Indian district, across the three scenarios, using our preferred log-log estimate. The districts are organized across the *x*-axis according to the initial PM2.5 concentration (each bubble represents a district, and the bubble size is proportional to the population). In panel A, we see the concentration reduction for each district. In the *Equal* scenario (blue), all districts are reduced by 10 units. The *Standard* scenario (red) takes the 27 districts with the highest concentrations and reduces them each down to 53 µgm−3. With this standard, 82% of the person-PM2.5 units are spent on reducing the eight districts with initial concentrations above 80 µgm−3. The *Optimized* scenario utilizes its budget very differently, mostly reducing exposure for the cleanest districts. This scenario reduces pollution for 50 districts, 48 of which are in below average concentration locations. The pollution in each of these districts is reduced to a pristine level of 5 µgm−3.

In panel B, we see how the concentration reductions change the relative risk of mortality. This panel appears similar to A, but here we see the effect of the supralinear shape of the C-R function. The *Equal* scenario reduces the risk of mortality substantially more for the initially low-concentration districts than the initially high-concentration districts, even though their concentration change is the same. This flattening is also seen in the other scenarios, most obviously for the *Standard* scenario such that despite very large reductions in concentrations, there are less substantial reductions in risks for the initially high-concentration districts.

Panel C is subtly different from panel B, in looking at the reduction in the mortality rate, rather than the change in the relative risk. All else equal, a given unit of reduction in pollution in a location with a high initial mortality rate will reduce the absolute mortality rate more than that same reduction in a location with a low initial mortality rate. The *Optimized* scenario directs its pollution reductions to those locations with relatively low initial concentrations—to take advantage of the steepest portion of the C-R function—and to those locations with the highest initial mortality rates. Panel C highlights the enormous improvements in conditions the *Optimized* scenario makes to the selected districts that are included.

Finally, the number of lives saved for each scenario and each district is shown in panel D. In the *Equal* scenario, despite reducing all locations by 10 µgm−3, 87% of the lives saved are to the half of the population living in the initially cleanest locations. The clearest distinction between the scenarios is illustrated by the large red bubble in the upper right of panel D, representing Delhi. The *Standard* scenario saves 7,400 lives in Delhi (40% of the total across all districts for the scenario, expending 42% of the exposure-reduction budget), and reduces the concentration from 106 to 53 µgm−3. The *Equal* scenario saves 1,070 lives in Delhi, representing 2.3% of the lives saved in the scenario but 8% of the person-PM2.5 units in the budget. The *Optimized* scenario spends no resources on improving pollution from Delhi. In comparison, the *Optimized* scenario spends 9.4% of its budget of person-PM2.5 units in the district of Bangalore (one-fourth as much of the budget as the *Standard* scenario spent on Delhi), reducing the concentration from 26.9 to 5 µgm−3 and saving 8,200 lives.