Can countries lower taxes and raise revenues?
The Laffer curve exists in principle, but the sweet spot is hard to find

RARELY has a dinner-table scribbling created such a legacy. In 1974 Arthur Laffer, an economist, sketched a simple diagram on the back of a napkin to illustrate a truism of tax policy. Set income-tax rates to zero and governments will not collect any revenue. Set them to 100%, and they will also collect nothing because people will have little incentive to work. Somewhere in between lies a sweet spot where government revenues are maximised. From this simple proof, it follows that when tax rates are very high, it might be possible both to lower tax rates and raise revenues. Tax cuts might thus pay for themselves, and more.

Russia’s summer Ukraine offensive looks like its deadliest yet
Our analysis of what it has cost both sides

Why was the flooding in Texas so deadly?
A mixture of geography, catastrophic rainfall and a lack of preparedness

Ten charts to explain Trump’s big, beautiful bill
The overhaul of taxation and spending spells trouble for America
Iran has come back online—for now
The regime has a long history of cutting access to the internet
Mapping Iran’s nuclear programme
American and Israeli strikes have done clear damage, but uncertainties remain about what has survived
How often do ceasefires in the Middle East work?
Donald Trump says he expects the Iran-Israel truce to last forever. Our analysis of more than 2,000 truces suggests that’s optimistic