Polly Toynbee (A sticking plaster budget for a country in decline, Journal, 30 October) reports Paul Johnson of the Institute for Fiscal Studies as asking rhetorically why most countries in Europe raise more money in taxes than the UK. The answer is because they have higher levels of public spending. As I explain in my book Debt or Democracy, in the same way banks increase the money supply as they lend, states increase the money supply when they spend. By the same token, repayment of bank loans and state taxes and charges remove money from circulation.

As Philip Hammond’s budget demonstrates, the level of proposed public spending is based on speculation about the likely future tax take, not some pre-existing tax piggy bank. It is only after each accounting period that the balance between tax and spending is revealed. Rather than squeezing money out of the pocket of a beleaguered (private) taxpayer, public spending is putting money in people’s pockets. Through taxation of both the public and private sectors, the state is asking for some or all of it back. The level of tax and spend is therefore a matter of political choice, not some immutable neoliberal economic logic.

Mary Mellor

Newcastle upon Tyne

• As your editorial states (30 October), austerity has “promoted a self-defeating idea that this country could retain its economic vigour by a form of economic bloodletting”. According to the IMF, the average fiscal multiplier for public spending is around 1.5. This means that every £100 spent by the government increases GDP by £150.

An example of how this works is shown by UK government spending in the years 1945-80. In 1945, the government debt was £225bn. Yet, despite a massive investment in the NHS, education and the welfare state, the debt had been reduced to £45bn by 1980. In other words, most public spending more than pays for itself.

Mark White

Wolverhampton

• It is welcome news that new PFI contracts will no longer be used for building infrastructure in the UK (Hammond abolishes PFI contracts for new infrastructure projects, 30 October). But this does not deal with the huge costs of existing schemes.

Furthermore, the UK has taken a lead in promoting PFI around the world, including to some of the most impoverished countries. The Foreign Office, Department for International Trade and Department for International Development have all marketed PFI-style contracts to other countries, despite them costing the government more than double traditional procurement. The government should end its promotion of PFI overseas and tell other countries the real story of the disaster these projects have been in the UK.

Sarah-Jayne Clifton

Director, Jubilee Debt Campaign

• The £2bn to be spent on mental health (Hammond budget to give £2bn extra for mental health services, 29 October) is very welcome and long overdue. But the suggested spend is unwise. The funding needs to be ringfenced to mental health services exclusively, or the managers at each NHS trust will simply use the money to pay for their overspending. The suggested priority of mental health in A&E departments is doubly unwise, since it could easily vanish into the black hole of A&E, and would encourage the mentally disordered to seek help at A&E, which will add to the difficulties of these departments.

A large proportion of the funding needs to go to child and adolescent services, which are everywhere (in England) collapsing. The rest should be used to rebuild our community and inpatient staffing, where nurses and social workers are unable to maintain a community service and prevent the strain on admission beds. The funding could also be used to return emergency inpatient care to the NHS, instead of sending patients to distant and expensive private sector beds.

Dr RL Symonds

Consultant psychiatrist

• Given that NHS providers started the 2017-18 financial year with a £4bn black hole, which deepened further over the year, the extra £20bn over five years allocated in the budget will mainly be required to pay off debts rather than fund increased demand. We need proper funding, particularly to care for elderly people, which could best be addressed by revaluing property rates.

Dr Richard Turner

Beverley, Yorkshire

• While government plans and strategies talk about getting more people walking and cycling, it is roads that have received the biggest budget boost. To combat childhood obesity and climate change, and improve air quality, physical and mental health, we need to make walking the easy choice and invest in creating high-quality, well-connected, accessible networks of paths and green spaces.

Recent research highlighted that new housing developments are trapping people in car dependency, yet the budget focused more on potholes than on pedestrians. To realise the environmental, social and health benefits of walking, we deserve a financial commitment on a scale proportionate to our investment in roads.

Gemma Cantelo

Head of policy and advocacy, The Ramblers

• Philip Hammond referred to “the Labour recession” of 2008 in at least one pre-budget interview. This calumny should be challenged every time it is uttered. Labour did not cause the global economic downturn – it was the bankers, who recklessly gambled with the world economy.

Cherry Weston

Wolverhampton

• In the post-election budget of 8 July 2015, George Osborne announced, for workers aged 25 and over, “a new national living wage. We will set it to reach £9 an hour by 2020.” Yet the 2018 budget will only raise it to £8.21 in April 2019. The £9 target has been quietly buried.Those aged 18-20 and 21-24 are paid significantly less than 25-year-olds, a situation almost without parallel in the west. And the gap is increasing.

Dr Dave Lyddon

Keele University

• In your “key points” article (A guide to the budget, from potholes to Brexit, 30 October) you give us a paragraph under the subheading “Regions”, with the figures for funding to Scotland, Wales and Northern Ireland. Really? After two decades of devolution? The word “nation” as opposed to “country” may be contested territory in Northern Ireland, but many readers in Wales and Scotland will be irritated and disappointed by the demeaning description “region”.

Phil George

Cardiff

• I wonder if Phil Hammond’s digital services tax is going to be as successful as George Osborne’s diverted profits tax?

Jerry Hodgkinson

London

• The government has announced we are to have a “Brexit 50p piece”. How much will it be worth?

Shaun Pye

Leeds

• There’s already a Brexit 50p coin: the pound.

Alasdair McKee

Lancaster

• Join the debate – email guardian.letters@theguardian.com

• Read more Guardian letters – click here to visit gu.com/letters

• Do you have a photo you’d like to share with Guardian readers? Click here to upload it and we’ll publish the best submissions in the letters spread of our print edition