In which I take question number 3 from Bryan Caplan

which he asks of the Recalculationists:

"By what percentage do real GDP and employment fall if nominal GDP unexpectedly declines by 5%?"

I go back to Bryan's original example, mud pies. The mud pie industry deflates because mud pie utility suddenly drops. I use bits of precision as my recalculation metaphor.

Pie utility has dropped, so the industry wants to simplify its supply chain, increasing lot sizes at each stage and gaining economies of scale. The pie distribution network drops from a four stage network to a three stage. Measurement accuracy drops from 1/16 to 1/8, but the transaction rates reduce from 4log4 to 3log3, and employment drops in proportion to transactions. Before and after adjustment, at each stage of production, the lot size is set to present an inventory variation equal to the constant uncertainty.

Now, if we make no other assumptions, especially assumptions about rates of deflation and asymmetry in trades, but assume the same a completeness* of the banking sector, then the central bank would notice increased imprecision in its measurement of NGDP proportional to the net loss in utility of mud pies. The economy is restored to precision when the mud pie industry is absorbed into a four stage food conglomerate. The one time restructuring fee is the precision loss weighted by the mud pie share of the economy. (Mud Pie industrial equipment will be devalued as it is less precise in matching input rates to output rates in the firm).

Note 1) QM theory would have various distribution networks popping between deflation and inflation states with differing probability, based on constraints. Banking and all other sector would change the relative probability of being deflated vs inflated based on the net loss.

Note 2) If there is not a large drop in mud pie utility, then the industry stays in its corridor, and over the business cycle will display nominal precision.

* Complete (my definition) : The dimensionality of the domain equals dimensionality of range. The bankers track the economy with acceptable uncertainty.