# Calculating Social Welfare from an Energy Subsidy

In Allcott and Greenstone's paper, "Is there an energy efficiency gap?", one finds the following figure

I quote now from p. 13:

"When there are investment inefficiencies, the original marginal consumer at quantity q gains amount af from being induced to buy the energy efficient good. In fact, there are allocative gains from inducing each of the consumers between q and and q′′ to purchase the energy efficient good, as each of these consumers has benefits that are larger than incremental cost c. The total private welfare gains are illustrated by the triangle abf...These benefits are then compared against the costs of the policy. A subsidy involves a transfer of public funds to consumers of amount hbjk , as illustrated by the shaded rectangle."

My question is rather straightforward: why are the benefits of the subsidy given only by the triangle abf, and not by all of the area between the two lines D and D' above the incremental cost line c? Is it not in fact true that every consumer upto the point j on the line D sees a gain equal to vertical distance between his present position and D'?

• Just to be clear, you are asking, "Why just $abf$ and not $abf + abj$?" – user18 Mar 24 '20 at 3:48
• No, I mean abf plus the quadrilateral with one side af and then extending upwards to the left. – Anthony Mar 26 '20 at 9:25