E.4.  Inefficient spend deferred

Instead of assuming that unproductive spend is spent immediately (as above), it is possible to assume that the 'inefficient' spend is "stored up" to form part of future expenditure. The stock therefore contains both efficient and inefficient spend and the value of spend in the stock increases with delays. Assume that the inefficient spend accumulates at a rate proportional to the total spend in the EPP with the factor R. Figure E-2 shows an illustration of the model and the differential equation describing the value of total spend in the EPP, P(t).

Figure E-2: (a) Diagram of simple conceptual model of the equipment plan with inefficient spend deferred; (b) Equations that govern the model. Descriptions of the main variables can be found in the text; constant c is defined by starting conditions.

The general solution given in Figure E-2b shows that if spending is constrained, inefficient spend also accumulates exponentially.  If expenditure has to cover both efficient and inefficient spend then, as found before, the amount of 'efficient' spend in the EPP shrinks at an exponential rate as more of the spend has to be committed to generating 'inefficient' output.