On Economic Stimulus

From a front page article in the Press on Thursday:

By new capital spending I assume they mean capital investment in infrastructure and so forth. It’s not terribly important – either way, this paragraph appears to say that despite increased spending, debt is increasing. Well, duh – if you spend money, you can’t use it to pay down debt.

It’s reasonable to argue, but by no means given, that money invested in infrastructure could serve to increase productivity and thus decrease long term debt through increased revenues. So, it’s arguable that spending $1b now on infrastructure could support economic activity exceeding that over the long term. However, economic stimulus based on tax cuts pose a deeply puzzling problem: How does a tax cut of $X lead to increased economic activity of more than $X?

For this to work, consumer spending needs to result in a positive sum game with very high growth – that is, it needs to be the case that $X spent >> $X worth of increased productivity through investment. Furthermore, some will be disappear as it is used to pay down debt, and some will be spent on foreign sourced goods. Of that remaining, only a small quantity will make its way back to NZ public coffers. It seems completely bizarre to expect that economic activity, and thus tax revenues, could increase by even a small fraction of X.

Here’s the best argument I can dream up:
Of the money given to the public, some large fraction (S) will be spent on NZ goods, some fraction (I) of which will be re-invested in NZ companies, leading to increases in productivity (V) over the long term whose value exceeds the adjusted value of the money injected in the first place.

That is, $X invested leads to $(X x S x I x V) of long term value. If $(X x S x I x V) exceeds $X, then, over the long term, the stimulus could be considered useful. If not, its a poor expenditure of money. To be realistic, $(X x S x I x V) would also shrink by some factor reflecting inflation, potential interest and lost flexibility by virtue of the government not having $X to spend as other needs and opportunities arise. But, it seems that it’d be hard enough for $(X x S x I x V) to exceed $X in the first place, so let’s leave that out.

Let’s take a simple example. 1,000,000 New Zealanders are each given $1000, reflecting a total investment of $1b. 70% of that is spent on NZ goods (S = 0.7), and of that money received by NZ companies, 20% is re-invested (I = 0.2). Let’s further assume that money invested returns 400% of its value to the public coffers over the long term. This gives us $560,000,000 of value for $1b spent. Not a good investment. Furthermore, my understanding is that the numbers I’ve used in this example are quite optimistic.

What marginal effects could contribute to make this work? Where is the extra money coming from? Either my understanding of this is completely naive (which it may well be), or this form of economic stimulus is just a shell game.