My daughter and I had a discussion about isocline functions today at lunch. An unusual topic for lunch but a topic of increasing interest in neuroscience, chaos theory and other areas which seek to model dynamic shifts in functions. Look for example at the current oil price markets and the foreign exchanges based upon them. They have sharply changed from steady rising prices to a sudden plunge in prices that has recovered slightly but still might fall further. The same sort of behavioural modeling might well be applicable in the realm of accelerating growth and the impact upon output as opposed to prices. For the time being most prices are not rising because the slack in the economy is still too large. But at some point there will be a sharp shift and the vector forces that now affect output and to a much lesser extent prices, will shift to largely affect prices and much less so output.

Policy makers at the Fed and other central banks will want to know when that point is likely to happen and indeed would prefer to be able to accurately anticipate that point. To come up with the appropriate algorithm one needs to take into account both aggregate demand and aggregate supply and how they interact when the supply function is signaling falling prices but the demand function growing demand.

The presence of a cartel complicates the calculation. In this case the complication is large since the officials responsible for output decisions in the cartel who represent the largest supplier in the cartel are stating that they will not not cut output no matter how far prices will fall all the way down to $20 a barrel.

In the past I suggested in my papers on the natural rate of inflation versus the natural rate of unemployment that after the economy had suffered an anti inflation shock induced by policy or by events like the crash of 2008 it takes a long period of time for that impact to dissipate. The natural rate of inflation you will recall was that rate of inflation below which there is accelerating unemployment the exact opposite of the natural rate of unemployment.It will be interesting to see if this oil price collapse follows a similar trajectory.