Thursday, October 7, 2010

My mathematical model of the economy

I mention it often, it is based on the idea of precision.
The more bits of precision the production system has, the more accurate it can deposit final lot_size * transaction_rate at the short end, the consumer end. The economy can count smaller variations in demand for a more diverse array of products. Bits of precision indicates the rank of the distribution network, the length of its production chain.

This is the essence of the entropy model. Really just a finite queuing model.

My model has a hydraulic macro equivalent, the production spectrum. The model has a standard form for inventory growth along the production network, the generalized yield curve. In hydraulic macro this can be treated like a frequency spectrum, measuring the 'impulse' response or the sectorial or aggregate production response.

The difference between the regressed hydraulic model and the precision model is quantization. We would expect mass changes at higher level of production, both positive and negative; hence this model would view the paradox of thrift as mostly changes happening with economies of scale. Economies of scale imply quantization, intermediate steps in production are moved inside the firm, hence fewer market interfaces between stages of production, hence less accurate and a higher quant at the finest level of final demand.

Errors in the system occur where the level of inventory variation with respect to inventory averages exceeds a constant double bound, the constant SNR value.

My model is based upon a biological assumption, the economic brain operates with the same basic measuring capability across all environments, the uncertainty constant. The existence of this constant makes us comfortable in production chains, it makes specialization work, it makes us habitual. When things are too certain, we began a search for yield; when things too uncertain we began to contract in consumption.
The units of the uncertainty constant are: The number of items we can track before we are comfortable that one will be tracked badly. We would see this constant in measures of the optimum team size. We should have a neurological measure of entropy maximization by reduced pattern neuronal firing, that is a direct measure of entropy encoding by inhibitor neurons.

1 comment:

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