In setting out SFEcon’s physical circuit the market vector O_J was specified as the integrated difference between output Y_J and asset replenishment rates R_IJ. This portrait is inaccurate in one important aspect: goods on the market do not remain whole until they are taken into use; they will deteriorate; and will do so irrespective of their intrinsic durability.

It is obvious enough that perishable goods will perish at the same rate in the field, in the fruit stand, or in the pantry. Clothing will go out of fashion whether it is worn or not. Though less obvious, it is equally true that even the hardest hardware deteriorates on the market in the sense of becoming technically obsolete, having the environment in which it functions change radically, or being lost in the logistical system by which it arrives at the market:

We can be sure that there is at present perfectly serviceable heavy machinery that is offline only because it has been technically surpassed by computer-controlled equipment.

A gladius from the fourth century BC can still inflict the wounds it was designed to cause; a harquebus from the time of Henry VIII can still penetrate plate armor at close range; but these weapons are useless in modern battles because the tactics of their time have been supplanted in ours.

An example of logistical obsolescence might derive from a hardware or furniture chain contracting or going out of business. Merchandise already delivered to their retail outlets would constitute a bulge on the market that would not be dissipated by regular means. Hardware might be sold as scrap rather than re-stocked in other outlets. High quality furniture might be used-up by a cheap motel chain. It is not unusual for functional but logistically out-of-place stocks to be abandoned in shuttered stores or factories.

These realities are given visual expression in a modified physical circuit by attaching a rate (shown in faint red) to the market stocks O_J to gradually bleed away stocks as they accumulate:

One property of SFEcon’s matrix structure is its facility for making these awkward calculations by indirection. Recalling that our matrix has output Y_JK appearing as a negative in Row I=0 of the rates matrix R_0JK, E_0JK then becomes a higher-ordered delay on output, i.e.: the flow of the entire quantity of a good J that has been produced but not yet expended.

With E_IJK so defined, wastage from the market vector in our physical signal path is simply a matter of inference upon the original structure. For an isolated economy (one having no import/export profile) the unproductive deterioration of unsold goods J is simply a negative sum on the corresponding column of E_IJ: minus E_0J is the totality of J that is flowing toward extinction; E_IJ is the flow of J exhausting itself in the productive operations of the sectors I; and the residual of their sum must be the flow of J that is being wasted. Noting that these flows vary from their underlying levels by a factor of V_J, we can infer the level of commodity J on the market in economy K as follows: