The Error of Government Spending by Way of the Magic & Mythical Multiplier

One of the most persistent economic fallacies that permeates economics and politics is the notion that by government spending money, there will be more prosperity.

It is said that if one man spends a £1 the other man who gets this £1 may save £0.10 and spend £0.90. We now have £1.90 of spending. This chain of events can go on forever and a day until the final penny is spent. £1 can become like magic: £10.

When this is said to you by journalists, media people, economists, politicians and other monetary quacks, you should ask them, if the multiplier works, why do we not eliminate world poverty today by just spending lots of money and letting the multiplier do its work?

The theory, simply put, is that if someone spends, say, £1m on building a new restaurant, the money will go to the contractors , so consumption will rise , aggregate demand in the whole economy will rise. The contractors will spend money on their suppliers and so-on-and-so-forth.  If the economy is not performing well, it is held that the government can step in and spend money where the private sector is not spending. This will lift back up aggregate demand and hey presto! we will go back to a satisfactorily performing economy.

Most economists will argue that the multiplier is greater than 1 x, therefore it is the role of government to boost aggregate demand. This can be done as a fiscal stimulus as proposed by all governments around the world at present.

There is a whole great series of maths behind this notion that is used to justify a fiscal stimulus even by way of deficit spending . See the notes section [i].

The enclosed document is a typical statement of affairs by the respected Chief Economist at Moody’s It is the testimony he gave before the US House Committee on Small Business on July 24, 2008. Via

I strongly support efforts for a second fiscal stimulus plan designed to help the economy by early 2009. Like the first stimulus plan, it should be temporary and not raise the long-term budget deficit. The plan should also be targeted to help lower- and middle-income households and smaller businesses that will use the help quickly and aggressively to stimulate the economy.


Mark Zandi argues in support of the second big USA fiscal stimulus plan of that year and says:

Extending food stamps is the most effective way to prime the economy’s pump. A $1 increase in food stamp payments boosts GDP by $1.73. People who receive these benefits are very hard-pressed and will spend any financial aid they receive within a few weeks. Because these programs are already operating, increased benefits can be quickly delivered to recipients.


On the face of it, increased infrastructure spending appears to be a particularly efficacious way to stimulate the economy. The boost to GDP from each $1 spent on building bridges and schools is estimated to be a large $1.59, and who could argue with the need for such infrastructure? The overriding limitation of such spending as a part of a stimulus plan, however, is that it generally takes a substantial amount of time for funds to flow to builders and contractors and into the broader economy.1 Many infrastructure projects can take years from planning to completion. Even if the funds are used to finance only those projects that are well along in their planning, it is difficult to know just when the projects will get under way and when the money will be spent. Another complication arising from infrastructure spending is the politics of apportioning these funds across the country in a logical and efficient way. Despite these caveats, if projects that could be started quickly can be identified, they could prove to be an efficacious stimulus.

He even supplies a table of the multiplier rates.

Fiscal Bang for the Buck

One-year $ change in real GDP per $ reduction in federal tax revenue or increase in spending

Tax Cuts

Nonrefundable Lump-Sum Tax Rebate 1.02

Refundable Lump-Sum Tax Rebate 1.26

Temporary Tax Cuts

Payroll Tax Holiday 1.29

Across the Board Tax Cut 1.03

Accelerated Depreciation 0.27

Permanent Tax Cuts

Extend Alternative Minimum Tax Patch 0.48

Make Bush Income Tax Cuts Permanent 0.29

Make Dividend and Capital Gains Tax Cuts Permanent 0.37

Cut Corporate Tax Rate 0.30

Spending Increases

Extend Unemployment Insurance Benefits 1.64

Temporarily Increase Food Stamps 1.73

Issue General Aid to State Governments 1.36

Increase Infrastructure Spending 1.59

Source: Moody’s

So faced with this weight of applied maths expounded by the majority of economists, why are we just not spending and spending as they suggest?

If I have £100 and I spend it on goods and services, my demand to hold cash or my money demand goes down by £100 and I receive goods and services in exchange. The person(s) who sold me the goods and services receives the £100 in exchange for those goods and services and his demand for a cash balance, or money demand has gone up. Where is the multiplier in this? It does not exist.

Money has passed from one participant in the economy to another participant in the economy in exchange for goods and services.

What we must be clear to watch here is this physical exchange that money facilitates.

Following Mark Zandi and the table above where he asserts, for example, that spending on food stamps will raise expenditure for every dollar spent by an extra $0.73 cents. Here he asserts the impossible: that when $1 of taxation is levied (and this means one $1 less of exchange for goods and services has taken place in the private sector), then this dollar, now given to a welfare recipient, will command $1.73 of expenditure on goods and services!

You can hopefully see that all that has happened is that, in the private sector, the money demanded has fallen by a dollar by way of the taxing of this wealth and the goods and services that would have been bought are now being bought by the welfare recipient.  Even if, in the private sector, this $1 was not going to be spent, but saved, it is only being saved to be spent on a good or a service in the future. Nothing new is ever going to happen other than one dollar exercising a command over goods and services in the private sector or, if taken by taxation, then in the public sector. 

If the private sector is deprived of its savings, then no investment will take place leading to an impoverishment of society.

As I have said before, here, the only way to create wealth is by saving a portion of our production, investing in more productive ways of doing things and focusing or reorganising those factors of production in better ways and combinations to produce more goods and services that people want at better prices than before.

There is so much error concerning Alice in Wonderland concepts such as the spending multiplier, that few people can see the wood from the trees.  I despair!

[i] Notes (Taken from Wikipedia for easy reference here )

Ct = c0 + cYt-1

so present consumption is a function of past income (with c as the marginal propensity to consume). Investment, in turn, is assumed to be composed of three parts:

It = I0 + I(r) + b (Ct – Ct-1)

The first part is autonomous investment, the second is investment induced by interest rates and the final part is investment induced by changes in consumption demand (the “acceleration” principle). It is assumed that 0 < b . As we are concentrating on the income-expenditure side, let us assume Ir = 0 (or alternatively, constant interest), so that:

It = I0 + b (Ct – Ct-1)

Now, assuming away government and foreign sector, aggregate demand at time t is:

Ytd = Ct + It = c0 + I0 + cYt-1 + b (Ct – Ct-1)

assuming goods market equilibrium (so Yt = Ytd), then in equilibrium:

Yt = c0 + I0 + cYt-1 + b (Ct – Ct-1)

But we know the values of Ct and Ct-1 are merely Ct = c0 + cYt-1 and Ct-1 = c0 + cYt-2 respectively, then substituting these in:

Yt = c0 + I0 + cYt-1 + b (c0 + cYt-1 – c0 – cYt-2)

or, rearranging and rewriting as a second order linear difference equation:

Yt – (1 + b )cYt-1 + b cYt-2 = (c0 + I0)

The solution to this system then becomes elementary. The equilibrium level of Y (call it Yp, the particular solution) is easily solved by letting Yt = Yt-1 = Yt-2 = Yp, or:

(1 – c – b c + b c)Yp = (c0 + I0)


Yp = (c0 + I0)/(1-c)

The complementary function, Yc is also easy to determine. Namely, we know that it will have the form Yc = A1r1t + A2r2t where A1 and A2 are arbitrary constants to be defined and where r1 and r2 are the two eigenvalues (characteristic roots) of the following characteristic equation:

r2 – (1+b )cr + b c = 0

Thus, the entire solution is written as Y = Yc + Yp

  1. It should be noted that Table 1 estimates the change in GDP one year after the spending occurs and says nothing about how long it may take to cut a check to a builder for a new school. []
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