Monday, October 18, 2010

Economics eventually boils down to queuing theory

Most of what the macros are doing is looking for short cuts in analyzing queuing problems that show up as inventory mismatches. We individuals as economic agents basically solve queuing problems throughout the day. In July, 2008, tankers queued up for oil faster than OPEC could produce it, later shippers queued up for goods faster than retailers could sell it.

In QM theory we would look for a time and place where the set of finite, and large potential contracts OPEC dealt with had no solution. That is, no combination of market outcomes would result in a random walk, on that particular week, some region was going to be out of oil. So that pair of variables, transaction rate and transaction size, had to be remade at the OPEC level. The first part of the remake is a contraction of the network and equilibrium about the sub graph. The distribution network had to be simplified. With a reduced network rank, each sub-dividing node along the way would hold more inventory The overall shape of the network retains its shape, but it has to operate in the deflated state for some time, inventories build up along the nodes and the probability of someone being noticeably short goes below normal.

There is no exact solution, quantum noise builds up in deflated state and depletes in the inflated; but both states are balanced. If the economy attempted an equilibrium with an unbalanced network, the bubble would be noticeable and Stein's Law activated.

The queuing model tells us that the only aggregate stimulus is speed, lower the transaction time for everyone, which is why we always invent faster transportation. A depression is one in which we remake the cargo transportation network, streets, roads and rails. In these depressions we always seek to satisfy the demand for point to point constant velocity travel, it is the demand for new transportation, generally more speed, that changes suddenly, usually a result of information shock, but not always. A good horse epidemic in 1870 could paralyze an economy, but even in the horse epidemic one looks underneath and notices the horses queued up way to long in crowded port cities. And again, the horse queues loo long in our ports because oversea cable was activated.

It would seem to me that economists would be the first to recognize that reset and remake of transportation technology would cause the greatest economic dips. I would speculate that transportation is at the heart of language development, it came about as a method to speed things up.

Micro assumptions of QM
The theory assumes the firm or household manages inventories inside the firm first, worries about market prices second. For example, the auto driver buying gas. I suspect the first reaction he has to shortages is the line at the gas station, then he notices price. The driver fixes the queuing problem by buying at off peak hours, but that entails a change in inventory cycle for the gas tank. He ends up driving a bit longer per tank, lengthens his whole household inventory cycle and occupies a larger portion of the energy yield curve. As long as the line at the pump is not visibly large, the driver will make small linear changes to household inventory and accommodate a range of prices.

Both the gains of scale economies and the costs of disruptive change occur because all drivers have nearly the same definition of an observably long line at the pump, we are all biologically tuned to the same level of discomfort, there is a biologically constant probability of error we like to live with.

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