John Maynard Keynes suggested that in an economic downturn you needed to inspire confidence in the economy - consumers tend to stop spending through a lack of income but also fear*, businesses do the same, so it takes the government to step in and start spending to get the whole thing moving again - perhaps through investment on infrastructure like roads and schools which gets people working and spending.
*(If you are really interested then further reading on 'the paradox of thrift' and 'the circular flow of income' would prove useful)
Keynes suggested that this government expenditure could be funded by borrowing. This is fine if the government doesn't have too much debt but not so fine if you have the debt levels of Greece. Interestingly, the USA, despite its debt levels, has tried this kind of 'fiscal stimulus' over the last few years and it has been relatively successful; in the UK, however, the government has been against this policy, has aimed to cut government spending and some have argued this has made the downturn in the UK worse.
How does 'the multiplier' fit into this?
The multiplier suggests that if an economy gets an injection of new money, this money gets spent a number of times and so multiplies in value. Think about a new housing development - money gets paid to the developers, they pay suppliers and workers, those groups spend it in local shops or down the pub, etc, etc. Bits of that initial pot of money will get spent thousands of times over the next few years which will boost the economy and increase Gross Domestic Product.
However, does all the money get spent? No. Some of it leaks out.
Some it gets saved, some of it goes to the government in taxation, some of it gets spent on imports. So we need to know how much leaks out and how much gets spent.
Let's assume the following:
There is an injection of new money into the economy - this could be £1000 of government spending on a new road, or £1000 investment in a new factory or an extra £1000 of exports we sell to a foreign country.
Of that £1000, assume that 40% goes in tax to the government, 10% gets spent on imports and 5% gets saved. This means that 45% actually gets spent and 55% gets withdrawn.
In economic terms, the above information means that the marginal rate of taxation is 0.4 (40%), the marginal propensity to import is 0.1 (10%) and the marginal propensity to save is 0.05 (5%). 'Marginal' means what happens to each extra bit of money, i.e. the injection of £1000.
Therefore the marginal propensity to consume is 0.45 (45%) - this is the bit that gets spent each time.
So how do we calculate the multiplier?
Two ways but they are both the same.
1 divided by 1 minus the marginal propensity to consume = 1/(1-0.45) = 1/0.55= 1.82
OR 1 divided by the marginal propensity to withdraw (or leak) = 1/0.55 = 1.82
What does the multiplier mean?
This figure of 1.82 is the multiplier. It means that if there is an injection of new money into the economy of £1000, some if it will be spent (the marginal propensity to consume) and some of it will be withdrawn (the marginal propensity to withdraw or leak). Taking all this into account, £1000 will be worth 1.82 times more because of this multiplier effect, therefore, £1820.
Why should we care?
If you're the government and you want to boost the economy by £18 Billion it means that you don't need £18 Billion to do it. You need £10 Billion if the multiplier is 1.82.
This makes it very important to know what the multiplier is - and like many things in economics it can be difficult to measure and there are varying opinions. However, after a little bit of research there seems that there is an average estimate for the UK of around 1.3. There is debate about this and also a suggestion that it can vary with the state of the economy.
So was Keynes right about trying to boost the economy?
If you are a Keynesian then of course. However, there are a group of economists who believe it is more important to get public spending under control, to balance the government budget and to reduce debt. They believe that government gets in the way of individuals, crowds out the private sector and stifles enterprise. This is the attitude taken by the republicans in USA and by the conservatives in the UK.
Those on the Keynesian side would suggest that if the economy is in a downturn and you have low consumer confidence, low business confidence and high unemployment, the worst thing you can do is exacerbate this through cutting government spending.
It's an interesting one.