Take a macro model of an economy with two different goods being produced; call them Carrots and Grapes (there can be many different varieties of carrots, and many different varieties of grapes, if you like). Suppose the demand for grapes falls, because of a change in preferences. Will there be an equal and offsetting increase in the demand for carrots? Well, that depends. It depends on what the central bank is targeting.
Suppose the central bank targets 2% Carrot Price Inflation. And suppose the central bank gets it exactly right, and responds perfectly to the preference shock, so the Carrot Price Inflation rate stays at exactly 2%.
What happens to real GDP?
If land, labour, and capital equipment were perfectly mobile between the Carrot and Grape sectors, we might see no change in real GDP. Firms that had been producing Grapes would simply switch to producing Carrots instead, without needing any increase in the relative price of Carrots to Grapes. The central bank could allow the demand for carrots to increase to fully offset the fall in demand for grapes, without this causing any increase in Carrot Price Inflation.
If all prices and wages were perfectly flexible, we might see no change in real GDP. The rise in the relative price of carrots needed to induce resources to switch from grape production to carrot production could be accomplished by a fall in the nominal prices of everything else, the nominal price of carrots growing as before at the central bank's 2% target.
But that is unlikely. More likely resources will not all be perfectly and instantly mobile between the two sectors. If prices and/or wages are sticky, and the central bank keeps the Carrot Price Inflation rate constant at 2%, there will be a temporary fall in real GDP, until relative prices and wages eventually adjust fully, and production eventually adjusts fully to the new pattern of demand, so that the central bank can allow the demand for Carrots to increase to fully offset the fall in demand for Grapes, without causing the Carrot Price Inflation rate to increase above 2%.
Your answer would probably be different if you assumed the central bank targeted the nominal value of Carrot plus Grape production instead of the Carrot Price Inflation rate. Because if it targeted NGDP the central bank could allow the demand for carrots and the price of carrots to rise, if grape production fell.
Would it make any difference to your answer if the government were the one buying all the Grapes, and households bought only Carrots? I don't think it would make any difference.
G=Grapes=Government expenditure. C=Carrots=Consumption. The central bank targets 2% CPI inflation. (Just in case it wasn't obvious).
David Andolfatto has the best post on empirical evidence of the effects of the recent UK fiscal "austerity". David's point is very simple: the data on real GDP are consistent with the view that tighter fiscal policy prolonged the recession; but the data on inflation, employment and unemployment are not consistent with that view. (Not that we can really draw any conclusions from a sample of one, because we don't really know what would have happened otherwise, but that never stops us doing it anyway.) This post is a footnote to David's post, trying to add a little bit of theory.
[My blogging has been non-existent for the last fortnight because I was back on the farm in England. So I'm late to join in this debate.]
Worthwhile Canadian Initiative 
Can you extend this model to an open economy with competitive suppliers of both products? That would be the more useful discussion and slightly closer to reality.
Jci: I think it could be done. But unless you assumed zero transport costs, that foreign and domestic carrots (grapes) were perfect substitutes for each other, and small economy, I think the results would be just the same. Because otherwise you would still need the relative price of carrots to rise to get no change in real GDP.
I’m wondering if David might say that if the govt was borrowing money to buy all the carrots and every year increased its borrowing by 2% to pay the higher carrot prices until one year it decided it wanted to slow down the rate of increase of its total debt. Then the CB would find it unsustainable to maintain carrot inflation at 2% in the long run and would start missing its target.
Grapes not carrots 🙂
What does a graph of UK nominal GDP look like over the same timespan?
I think that monetary offset plus NGDP targeting (not that the UK did this) could achieve results that look like the UK result.
Imagine that the government does nothing but build roads, which are not built by the private sector. In the absence of roads, the private sector builds inefficient footpaths (plus its normal output of carrots and haircuts). Fiscal austerity results in the government building fewer roads, since that’s the only thing that it does in this model, and the monetary authority responds by keeping NGDP perfectly aligned with a prescribed path.
If the marginal road was a “bridge to nowhere,” then not building that road increases real GDP, since anything produced by the private sector would be of greater value.
If the marginal road was more effective than a footpath, however, then not building the road decreases real GDP, as the private sector must devote resources to less-productive substitutes. With a fixed aggregate demand, we would expect to see higher inflation, less labour market productivity, and higher employment, in ratios that depend on elasticities. This seems to be consistent with UK results.
In turn, this gives the nice and cozy suggestion that with monetary offset, the socially optimal level of government spending is slowly-varying.
MF: I don’t think David would say that. The government could keep the nominal prices of carrots (and grapes) growing at 2% per year just by increasing the money supply by 2% per year.
Majro: “If the marginal road was a “bridge to nowhere,” then not building that road increases real GDP, since anything produced by the private sector would be of greater value.”
Remember that government-produced goods are valued at cost in National Income Accounting, so if the road to nowhere cost $1 billion to build, it would be valued at $1 billion in calculating NGDP.
Nick,
Isn’t David’s recent post (http://andolfatto.blogspot.ca/2015/05/understanding-lowflation.html) saying that the CB couldn’t sustainably increase the money supply without fiscal support?
“If the central bank holds the money-to-debt ratio fixed, then inflation is determined by the growth rate of nominal government debt (minus the growth rate in the real demand for such debt). The two forces determining inflation in this case are (1) the fiscal authority, which chooses the growth rate of nominal debt and (2) the economic forces, domestic and foreign, influencing the rate of growth in the demand for government debt.”
(And in addition I understood him to mean that it is not sustainable to increase the money-to-debt ratio to hit the target).
For a second there I thought you were channelling Arnold Kling. Alas it was not to be.