Angela Merkel’s government is coming under increasing pressure to spend some of its record budget surplus on tax cuts and investment in Germany’s ageing infrastructure.

Despite months of weakening economic growth, the German state had a surplus of €13.5bn (£11.6bn) of income over expenditure at the end of 2019, thanks to increased tax revenues and a low interest rate.

On Tuesday a banner headline in the Bild newspaper read “Chancellor, Hand Out the Money!” summing up the mounting cries by economists, commentators and lobbyists for the government to abandon its obsession with balancing the books – known colloquially as the Schwarze Null or black zero – and to use the money to invest in much-needed infrastructure projects across the country, as well as to reduce income tax levels.

The government on Tuesday signed a multibillion investment deal with the national rail network, Deutsche Bahn, to which the government will contribute €62bn, and the company €24bn.

But critics said much of the money, which was announced last year, would be insufficient to make up for years of neglect.

By comparison, the most recent projections of the costs of Britain’s High Speed 2 project are £88bn.

Across Germany, the strains of underinvestment in everything from school buildings to bridges, parks and town halls is growing increasingly visible. A lack of infrastructure in rural areas, including a failure to address digital technology, is contributing to economic decline and forcing people to move away.

In her almost 15 years in office, no Merkel government has ever reduced the tax bill. In 2007 the chancellor presided over a VAT rise of 3% to boost the ailing economy.

An editorial in Bild reminded Merkel how she had once promised to reform German tax laws and relieve the taxpayer but instead, in her 5,167 days in office had only ended up increasingly burdening them. The average tax rate – 19.7% when she came into office in 2005 – has risen to 23.2%.

On top of the €13bn at the finance minister Olaf Scholz’s disposal, he has a further €5.5bn that was set aside during the refugee crisis of 2015.

Announcing the surplus, Scholz said: “We had a bit of luck, but of course this is also down to our good economic management.”

He has categorically dismissed the idea of lowering the tax rate and has rejected plans to reduce the so-called solidarity tax, payable from all German incomes to finance the almost 30-year-old German reunification project.

Meanwhile, the issue of what to do with the surplus is causing open rifts within the government. The economics minister, Peter Altmaier, is reported to have concrete plans to reduce corporate tax and to get rid of the solidarity tax, or Soli as it is known.

The president of Germany’s taxpayers’ association, Reiner Holznagel, said it was time Germans saw something of the surplus. “This overhang of billions of euros obliges Scholz and Altmaier to bring forward the end of the Soli completely,” he said.

Marcel Fratzscher, head of the German Institute for Economic Research, likened tax cuts to distributing water with a watering can “that would be the worst thing the government could do with this excess”.

He added: “We should be clear that these immense surpluses despite shaky economic growth are very lucky and a chance that should not be lightly given away. The need for investment in infrastructure, education, digitalisation and climate protection is overwhelming. What the government needs to do is to come up with a clear and long-term plan which will make the German economy fit for the future.”

The Green party, as well as some members of Merkel’s own Christian Democrats, are pushing for surpluses to be invested in climate friendly technologies and climate shares, which would connect economic growth more directly to climate protection.