The events which have brought two countries to the brink were precipitated by apparently small policy shifts that proved emblematic of the ruling elite’s inability to answer or even understand their people’s basic needs while enriching themselves. Chile’s biggest political crisis since the return of democracy almost 30 years ago was triggered by a 3% rise in metro fares, the protests which have engulfed and paralysed Lebanon by a proposed tax on WhatsApp calls. But the underlying causes run far deeper, and have been building for much longer. There is deep anger at political and economic systems that have ignored most of the population.

These countries are, of course, very different. Lebanon has been staggering along for years, due to both political dysfunction and endemic corruption. The central bank governor warns that its economy – long shored up by remittances from overseas – is now days away from collapse. Recently it emerged that, before he became prime minister, Saad Hariri gave $16m to a South African model: a sum encapsulating the gulf between the lives of those at the top and the rest.

Meanwhile, Chile was seen as an economic success story, and its billionaire president Sebastían Piñera had portrayed the country as an “oasis” in a region of strife. But it is desperately unequal, a legacy of Pinochet’s dictatorship and of the neoliberal settlement it bequeathed the nation – with precarious access to basic services, and the poorest fifth of the population living on less than $140 a month. So while both governments dropped the offending proposals, the movements had already outrun their initial causes. Lebanon’s prime minister announced his resignation on Tuesday , though some suspect he is seeking political leverage. The Chilean president has fired hardline ministers, but protesters in Chilean cities lit fires and clashed with police following the announcements.

Hardline rhetoric and violence has further inflamed the public. Mr Piñera insisted that “We are at war with a powerful and uncompromising enemy that respects nothing and no one.” At least 20 have died, hundreds have been shot and beaten, and more than 7,000 arrested. In Lebanon, Hezbollah’s leader, Hassan Nasrallah – who holds no formal position, yet calls so many shots – warned of foreign “conspiracies” inflaming the movement. When hundreds of men ransacked the main protest site on Tuesday, demonstrators blamed Hezbollah and another faction, Amal. Lebanon is used to interim governments and political chaos, but the stakes are higher as the economic strains become ever less tenable. Chile faces the real prospect of social breakdown, or a return to authoritarianism.

Protest movements around the world are evolving at disorienting speed, partly thanks to technological developments and partly as they look to similar campaigns abroad. Meanwhile governments lumber along, unable to seize the initiative or even to respond at pace – not least because it is hardly in the interests of the powerful to offer the kind of fundamental concessions which will only weaken that power. But when things have reached this stage, there is no easy exit. Leaders may reach for sticks or sticking plasters, but there cannot be short-term solutions to long-term structural problems.