Tuesday, November 10, 2009

When the economy deals with a resource constraint

Aggregate Output mostly follows the constrained resource flow.

Output, as a function of the constrained resource is highly concave downward. That means the economy gets the highest payoff by applying technology to the constrained resource, money flows to the bottlenecks.

If we use a multi-stage flow model then econometrics would become statistical queuing problem. A linear multi-stage queue would be a collapsed version of a spanning tree, in the more generalized case. The economy, as a spanning tree under a severely constrained input, will have a backbone determined mainly by the efficient delivery of the constrained resource. Technology allows us to build appropriate sub branches around the backbone.

So, if we held to a structural theory (rather than hydraulic) down to the transaction level, then each transaction is a partial rebalance of the total spanning tree, an additional branch on one side, the destruction of a branch on another side. Asymmetry modifies the branch decay/growth process, branch decay occurs faster. Constant uncertainty says that the tree is further restricted in growth to have a strong self similarity, as fractalists point out.

The last point is the more difficult. If we take the banker's yield curve, interpreted as the simple linear multi-stage stochastic flow, then the curve will be a weighted composite of inventory flows of all goods, including banker's goods. So if you take the banker's curve, grap it in the middle with your finger nails, and sort of spread it out into its spanning tree form, the sub branches that result look like the main backbone, but to a lesser degree as the tree unfolds. Each sub branch will be coherent with the finite boundaries of the backbone because it follows the aggregate division of available certainty across and the optimum shaped term structure.

The premise of constant uncertainty and our level of collective action are highly related biologically and economically; a bridge that sorts of connects economics and biology. There is a level of observed similar activity among our neighbors that triggers in us level of certainty that action is useful. When we see regular numbers of workers with lunch pails we are excessively certain that it is a work day, the certainty synapse fires as Kling might say.

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