The reserve system using Shannon Theory

Assume the firm that has a five year machine and replaces it every five year, plus or minus 3/4 of a year. The arrival of the next machine can vary by 15%. The firm balances income and expenses to buy the machine but must hold 15% of the cost in liquid reserves, available on a moments notice when the next machine arrives. If money were perfectly accurate, then the firm loses no opportunity cost, the yield curve is flat.

But money itself varies. The price of money is set every 1/4 of a year and the price of five year machines is set every five years, to accuracy. The yield curve is generally drawn for liquidity, not five year machines. It is the bankers curve.

The price variation in the price of a five year machine is the five year interest rate. How do we compute that interest rate? We have to assume pricing is measered ten  years, or 40 pricing events.

The variation on 1/4 year money is -(1/4)log(1/4)
The variation on five year money is -(1/10)log(1/10)
The negative log value is the interest rate,y the cucrve is drawn as -log(1/4) -log(1/7) etc. and the X axis is the relative arrive rate.


These are set in a congested system that is balanced so the inventory of both five year prices and one year prices have the same variation, the two values above must be within an integer of each other.

Machines also have the same relationship, in a value added network, the Shannon system maximize the mutual entropy between money and machines. Whether money, or machine; whether one year of five year, the probability that an inventory runs out is the same. Run the same curve pn a valie added net makong pne year machines. The -log value is then the relative price of any machine measured in units of machine.

Machines do not completely populate the curve, they are illiquid.  But, at equilibrium, the machine curve, written to the nearest polynomial is a factor of the money curve.

The short hand way to handle this is with accuracy, machines have about an 8% accuracy relative to the accuracy of money, which is closer to 3%. The difference in accuracy is the length of the value added, congested networks that deliver them.  Money is fast, machines are slow. But the slow network should fit into the fast network at equilibrium when mutual entropy is maximized.