The differential equation giving the general rule of change of the pure surplus-income ratio is:
Its solution is (using tall “S” as the integral sign)
Sdf = S (vdw + wdv)
f = vw
This differential equation is general, and it generally governs the change in the pure surplus-income ratio. The calculation of f in a particular case would be particular and would involve particular current velocities of I’, I”, and the fraction v. This is to say that there will be a family (or an infinity) of solutions to the general differential equation depending on the particular parameters or particular technical coefficient and rates of incomes in any particular situation.
Price and quantity flow indices in the basic, ordinary, and pure surplus circulations will enter the analysis as point values or incidental boundary values in a particular first-order solution of the second-order general, explanatory differential equation. And it is within these particular flow solutions that one may identify and quantify the particular current macrodynamic flow of returning principal, i.e. pure surplus income flow, i.e. return to entrepreneurs as a group.
And note: the solution gives the current rates of interdependent flows. It is not a retrospective evaluation of past investments. Relative to a norm based upon technical relations, these actual flows may be conformal or aberrant, i.e. equilibrated, or excessive or deficient. The economic process has laws to which human psychology must adapt. But the economic process does not possess the rigidity of planetary motion. Humans are its efficient cause, though not its formal cause. Norms can be violated. The process is rife with ignorance
Functional Macroeconomic Dynamics is the immanent intelligibility of the current, purely dynamic, economic process. Functional Macroeconomic Dynamics identifies a central tendency and norms. It explains how the process’ internal functional flows interrelate. It is an understanding of the process. It includes both classical laws and probabilities of realization. But, as probabilistic and involving diverging series of conditions leading up to events, it does not seek to predict precisely the course of the economy as one would, enjoying the rigidities of physics, predict planetary motion. Rather it seeks to continually adjust its activities and flows of consuming and investing to current aberrations and opportunities. The legitimate end of science is to verify understanding, not to predict the intrinsically unpredictable.
For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science. Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, xxxvii]