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Municipal workers protest outside parliament during a rally against the public sector reforms and layoffs Greece has promised its international lenders, in Athens on July 8, 2013.JOHN KOLESIDIS/Reuters

I've been at McGill University for 24 years and have had the good fortune of teaching macroeconomics to thousands of Canada's brightest young students. As smart as they are, they find some ideas especially difficult to understand. One thing that is really hard to get is the idea that the economic reasoning we use for individuals does not apply in the same way for the economy as a whole.

When thinking about decision-making by individual firms or consumers, we can almost always assume that the general economic environment is unaffected by their decisions. For example, a single consumer's decision to buy a TV does not affect the price of TVs, and nor does her decision to work affect the going wage. Similarly, a single firm's decision to purchase steel or borrow money rarely affects the price of steel or the market interest rate. Most firms and consumers are very small relative to the markets in which they operate, and this fact greatly simplifies microeconomic analysis.

Unfortunately, this simple micro logic does not apply in macroeconomics, even though many people think otherwise. And nowhere is this mistake more common, and potentially more damaging, than in the ongoing debate over "fiscal austerity" – the view that highly indebted governments can slash spending as a way of both reducing their debts and stimulating their sluggish economies.

"Austerians" typically argue that the government's fiscal situation is comparable to an individual's. If you or I have too much debt – meaning that it is so large relative to our income that we have difficulty making the interest payments – we should simply spend less, save more and gradually dig ourselves out of debt. As difficult as it is to do in practice, this logic is exactly correct for any individual. But the austerians then argue that highly indebted governments, for the same reasons and by the same logic, can and should act the same way. And here is where they get into trouble.

What's the austerians' problem? When an individual spends less (and saves more) of his income, there is no effect on his current income or the likelihood of losing his job. The individual makes this decision while taking his income and employment prospects as given, and rightly so. But this same logic does not apply for the government or for the economy as a whole. The larger the group under consideration, the more we have to recognize that one person's spending is another person's income – what economists call the "circular flow of income and expenditure."

In many European countries today, governments with high debt-to-GDP ratios have decided to slash their spending as a means of reducing budget deficits and eventually running budget surpluses. The cuts typically amount to several percentage points of GDP – large enough to have major effects on overall employment and national income. As governments reduce their spending, the immediate effect is to create layoffs of public servants and of private-sector workers whose firms used to sell their products to the government. So the cuts in government spending lead directly to cuts in GDP, at least until those workers find new jobs.

Unfortunately, the story does not end there. As those people get laid off and their income falls, it doesn't take long before their spending also falls. But their reduced spending means less income for still other people, who then reduce their spending, thus reducing other incomes, and so on. Through this dynamic process, a cut in government spending typically leads to an even larger fall in GDP – this is the famous "multiplier" that economics students need to master, and that today's policy makers apparently feel justified in ignoring.

The unpleasant truth of these macro relationships is that government attempts to balance budgets by cutting spending make the economy shrink in the short run, and by reducing GDP they may actually raise rather than lower the debt-to-GDP ratio. This explains why, after several years of European austerity and recessions that just keep on going, the debt-to-GDP ratio in most European countries hasn't declined, and in many cases has increased.

The austerians nonetheless insist that spending cuts can boost rather than reduce GDP, but this is mostly wishful thinking. Cuts in public spending, under some conditions, could lead to a large reduction in interest rates or to an enormous boost in private-sector confidence, in which case private spending could rise so much as to offset the reduction in government spending. This result is possible, but highly unlikely in practice, and so far has not happened in any of the countries currently experimenting with austerity.

Sadly, many European governments today appear to be run by people who either have forgotten or never understood the complexity of macroeconomic relationships. They have accepted the simple but misleading logic of the austerians, and millions of their countrymen are now paying the economic price.

Christopher Ragan is an associate professor of economics at McGill University. During 2009 and 2010 he was the Clifford Clark Visiting Economist at Finance Canada where he was a senior advisor to the Minister and Deputy Minister of Finance.