Cuts in government expenditure will not reduce the deficit. If anything, they may increase it as consumer and the corporate confidence gets further undermined. How can this be? Surely, cutting government expenditure and increasing taxation must get the government’s finances into better shape. Unfortunately, they won’t  - and here is why.

Buried in Table I in the ONS’s quarterly publications on the UK economy are some crucially important figures. The table contains values for four key variables. There is the government deficit, a net figure for the corporate sector, showing whether its expenditure on investment is greater than its retained profit, and a net figure for consumer borrowing and lending. The fourth figure is the UK’s current account foreign payments balance.

What the table does not show is that all these four figures always have to sum to zero. This is because all of them involve either borrowing or lending and total borrowing as an accounting identity has to equal total lending. The table below shows the same numbers as the latest Office for National Statistics quarterly accounts but with the net figures added. The numbers for 2011 and 2012 do not quite sum to zero because the ONS has not yet completed its final reconciliations for these years, but they will do when this process is completed.

Now, if the figures have to add up to zero, the crucial question is how this outcome is achieved. Which of these variables are the drivers and which are the residuals? The critical problem now faced by the UK is that it looks as though the residual is the government deficit. Here’s why. All the other figures are close to being fixed. The foreign payments deficit is running at about £60bn a year and if anything appears to be on an upward trend. Consumers, who were net borrowers in 2008 have now pulled their horns in and are net lenders, a condition which seems unlikely to change. Because the outlook for the economy looks so poor, business investment is low and does not seem likely to rise much – if at all – in the near future.

This is then the problem. If we have a foreign payments deficit of £60bn, net lending by consumers of, say, £20bn and a corporate surplus of perhaps £40bn, none of which look likely to change significantly, the government deficit has to be £120bn. This indeed is where the underlying figure for the government deficit, net of a few essentially one off subventions, seems to have settled down.

Because the total size of the government deficit is very largely the residual and not the driver in all the borrowing and lending which takes place, cutting expenditure or raising taxes will not materially reduce the government deficit. Instead, it will change the level of output in the economy. Lower net government expenditure will not stop the figures summing to zero. They will still do so, but with equilibrium re-established at a lower level of GDP output. The process will be that cuts in government spending will increase unemployment and lower the tax take. They will also depress consumer expenditure and business investment. The foreign balance may improve a bit but probably not much. The economy will shrink but the government deficit will stay the same – or may even increase.

This is why the current Coalition policies are not working. It is also why attempts to impose austerity on the weaker Eurozone economies are causing output there to plummet. In addition, though, it presents a really major problem for the next Labour government. UK government debt is already just under 90% of GDP. It is increasing by an average of about £2.3bn a week. If it continues accumulating at the rate of £120bn – just under 8% of our national income - per annum while the economy stagnates, then by 2015 total government debt will be well over 100% of GDP (and still rising strongly). If debt is accumulating far faster than the economy’s capacity to repay it, the situation is clearly unsustainable.

What could the next Labour government do? At present, it is inclined to take a more reflationary stance than that of the Coalition and, if cuts in government expenditure cause the economy to shrink, it seems logical that reversing these cuts should increase GDP. Unfortunately, however, a strategy along these lines is equally unlikely to be successful. Reflating the economy is likely to worsen the foreign payments position while doubts about whether such a policy is viable will almost certainly cause consumers and businesses to retrench rather than increase their net spending. Again, the figures have to sum to zero but this time they are likely to do so with the government deficit being perceived to be spiralling out of control.

Is there, then, nothing that can be done to get out of the UK’s current bind? There is a policy which would work but it goes against all the established conventional wisdom. The way out is to tackle the foreign trade deficit. To do this, however, we have to overcome the root problem with the UK’s competitive position which is that we depend on manufactured exports to pay our way in the world and we charge far too much for producing them. This is because the exchange rate is much too high.

For most manufacturing operations, about 20% costs are raw materials and about 10% is depreciation on machinery and equipment. All the other 70% comprises locally determined costs, and the rate at which we charge these out to the rest of the world is entirely an exchange rate matter. Some simple maths shows that if – for example – we reduced the exchange rate by 50%, our manufactured export prices to everyone abroad would fall by half of 70% - in other words by 35%. To make our exports sufficiently competitive to enable us to pay our way in the world, we would not have to devalue by as much as 50% - but we would have to bring sterling down by about a third – to just over £1.00 = $1.00 or around €0.80.

A devaluation of this size would get the foreign payments position back into balance over a year or two. A reflationary policy would then work, increasing consumer confidence and business investment. The government deficit would go down and – even better for a Labour government – cuts in expenditure to make this happen would not be necessary, although the economy would very probably work better if government expenditure was slowly reduced to around 40% of GDP. This would be relatively easy to achieve against a background of GDP increasing at 3% to 4% per annum and unemployment falling to perhaps 3% over a period of a few years. If small government deficits were then needed, to keep the economy on track, they could easily be afforded. If the economy is growing much faster than the rate at which debt is accumulating, borrowing ceases to be a major problem.

The real problem of course is that selling a major devaluation to the electorate as a positive policy is a massively difficult project. If this is not done, however, the alternative may well be that sterling eventually collapses in a totally unplanned way as confidence evaporates. The run up to the 2015 election is going to highlight some very tough economic policy choices.

John Mills is a donor to openDemocracy.