THE second presidency of Sebastián Piñera, a billionaire businessman turned politician, will begin on March 11th in seemingly auspicious circumstances. Mr Piñera won a resounding victory in a run-off election in December, with 55% of the vote. Chile’s economy is growing at its fastest rate for two years and the price of copper, its main export, is rising. The 11-country Trans-Pacific Partnership, a trade deal from which Donald Trump opted out, is due to be signed in Santiago on March 8th. And a Chilean film has just won an Oscar.

Yet the sunny appearance may deceive. Mr Piñera, who was a successful but unpopular president of the centre-right in 2010-14, must deal with the conflicting pressures of restoring rapid economic growth by boosting private investment while trying to meet the demands of a society undergoing far-reaching change.

For two decades after the end of Augusto Pinochet’s dictatorship in 1990, Chile offered a successful model of an open, free-market economy and gradual social reform under centre-left governments. Chileans became less poor, and millions of people went to university for the first time. Mr Piñera continued this approach. The economy boomed on his watch. But faced with a powerful student movement angry over the cost of higher education, he struggled politically.

His successor (and predecessor), Michelle Bachelet, swung to the left, adopting the students’ demands. When one of her allies promised to take a retroexcavadora (the graphic Spanish word for a backhoe loader) to Pinochet’s “neoliberal model” under which many public services are privately provided, she did not contradict him. Ms Bachelet pushed through reforms of tax, education and labour, all aimed at making society less unequal. To achieve this, she abandoned the consensual approach of her predecessors. However laudable her intentions, many of her reforms were polarising, technically flawed and unpopular.

Business took fright. Investment has fallen for the past five years. The economy averaged growth of just 1.8% a year under Ms Bachelet, compared with 5.3% under Mr Piñera. Her people blame low copper prices; her critics blame her reforms. It was Mr Piñera’s economic record, and fear that Ms Bachelet’s candidate would tack even further left, that brought him victory.

His main aim is to restore economic growth to 3.5-4% a year, the most the economy can now manage, says Felipe Larraín, who will be finance minister (as he was in 2010-14). A key measure will be improving Ms Bachelet’s hugely complicated tax reform and gradually cutting the corporate income-tax rate from 27%, among the highest in Latin America.

“We want to build on what we have,” says Mr Larraín. “There will be no retroexcavadora.” The new president could not demolish Ms Bachelet’s legacy if he wanted to. Unlike her, he will lack a majority in congress and will have to woo the Christian Democrats, centrists who belonged to Ms Bachelet’s coalition.

She promised universal free higher education and banned top-up fees and profits in privately run but publicly financed schools. Mr Piñera is likely to tweak rather than scrap these changes. Free higher education would cost 3% of GDP. “We don’t have that money, we’re not Norway,” says Mr Larraín, who inherits a much weaker fiscal situation than he left. The new government will focus on making most technical education free and allowing limited top-up fees and selection in schools. It also promises to put more public money into health care and the privately managed pension system.

Chile needs better schooling and worker training to raise productivity, diversify the economy and reduce inequality. The question facing Mr Piñera is whether he can sell his policies politically. Chile’s success has made the country harder to govern. The student movement has waned, but not much. Unions were empowered by Ms Bachelet’s labour reform. Her electoral reform has made congress more proportional, but weakened the stable two-coalition system of post-1990 politics. A new far-left group, akin to Spain’s Podemos, won 20 of the 155 seats in the lower house of congress.

In his first government Mr Piñera often seemed to Chileans more the businessman—arrogant, impatient, unempathetic—who understood investors than the politician who cared about ordinary people. One source close to him insists he has mellowed. Some of his cabinet appointments look odd. He has placed Alfredo Moreno, a fellow tycoon, in charge of the social-development ministry, for example. But his team includes a core of experienced politicians. He will need them.