Sunday, April 18, 2010

Leverage cycle and QM Theory

QM Theory utilizes to simplifications that allow us to get at a theory of leverage. Production systems are multi-stage entropy encoders (or Huffman encoders) that seek to equalize inventory variances at each stage of production from wholesale to retail.

There are two states for the production network, the deflated state an N stage system, the inflated state an N+1 stage system. Each stage at the inflated state has smaller inventory and more precise sales rates. Hence, each stage of production holds a smaller proportion of the total yield curve for that good, measured in units of good quanta. The shape of the yield curve is constant at equilibrium, as measured in units of the good.

If N is 5, sales precision is 2**5. (a five bit calculator) . In stage two, precision is 6**2, or 64 (a six bit calculator) . In both cases the yield curve shape is constant, the stages hold a smaller proportion of the yield curve in the inflated state. If the production system is milk; the basic quanta is the quart of milk in the deflated state, and the pint of milk in the inflated state.

However, when the yield curve is measured in terms of money rather than good. That is, dairy production moves from measurement of yield in terms of units of milk to units of dollars problems arise because of the utility of money. Money adapts much faster than milk production.

Adjustment of milk production is a Ramsey search, each stage seeking to change the transaction rate and transaction volume, in order to optimize its share of the yield curve. This can take years, but money adapts to the current state of production within months. Hence, money will equilibriate about an unequilbriated diary system.

Example:

Small stores may see low inventory volatility in selling milk by the gallon. Hence, they try to inflate began selling it by the pint in various flavors, seeking to increase the transaction rate, and decrease the transaction volumes. The household normally modifies milk by the pints, adding condiments to the consumers liking. The retail stores want to commercialize that function, moving it from the household to a intermediate firm. This in effect is an attempt to make dairy delivery more precise, adding a stage of production. The yield curve of dairy production should adapt such that from the household to the wholesale production, the share of the yield curve becomes less, the whole system operates at the higher inventory variance. The intent is to increase the delivery rate (bit rate in Shannon terms) by reducing the quant measured from the quart to the pint.

This appears to be successful, and money increases the value of inventory in the small store, before the entire milk system has equilibriated. The shift in the bankers yield curve relative to the dairy yield curve causes wholesale inventories to drop in value. Hence the money illusion. Money signals are faster than dairy signals so the Ramsey search process is distorted, it tends to overshoot the adjustment process in real goods.

Real goods are heavy, money is lightweight. Solution? Perform maximum entropy analysis of the entire production chain of a real good, in units of the good, before one talks to the banker. This is what Walmart does.

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