If we look at a term structure, a yield curve, we are looking at a distribution of inventory growth at various frequencies. There is also the distribution of inventory growth at various lot sizes. These distributions are exactly the production structure of some good.
If we look at the production chain as a channel encoder, then we observe the direct sum of all transactions along the network, a series of symbols arriving in time sequence. When those symbols are properly coded by the supply chain, lot sizes and rates reach equilibrium, then the symbols arriving appear as a constant rate arrive of information units, each having a value dLdT, a fixed quanta of uncertainty equal to the product of uncertain arrival and uncertain lot size. That uncertainty is the SNR of a gaussian noise channel, the production line converts a skewed, lognormal channel into the gaussian white arrive of information units. Each inventory along the production chain converges to the constant variation of a normal distribution.
Highly skewed production chains have long term constraints, so more price variation is needed for long term investment and the problem has to be broken up into more liong term stages; each stage processing a chunk of the lot size reduction.
There is a valid reason for the finite uncertainty. it keeps a small correlation among distinct supply chains. The egg producer competes with the commuter and retail grocery shopper on the roadway. It is that unmeasurable interference that makes the adjustment process work. We deliberately leave unsolved problems to the hidden hand, as a temptation to find better solutions.
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