The Economics of Enlightenment: Time Value of Knowledge and the Net Present Value (NPV) of Knowledge Machines, A Proposed Approach Adapted from Finance

Ravi Kashyap

doi:10.1515/bejeap-2019-0044

Article

The Economics of Enlightenment: Time Value of Knowledge and the Net Present Value (NPV) of Knowledge Machines, A Proposed Approach Adapted from Finance

Ravi Kashyap

Published/Copyright: March 3, 2020

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From the journal The B.E. Journal of Economic Analysis & Policy Volume 20 Issue 2

Abstract

We formulate one methodology to put a value or price on knowledge using well accepted techniques from finance. We provide justifications for these finance principles based on the limitations of the physical world we live in. We start with the intuition for our method to value knowledge and then formalize this idea with a series of axioms and models. To the best of our knowledge this is the first recorded attempt to put a numerical value on knowledge. The implications of this valuation exercise, which places a high premium on any piece of knowledge, are to ensure that participants in any knowledge system are better trained to notice the knowledge available from any source. Just because someone does not see a connection does not mean that there is no connection. We need to try harder and be more open to acknowledging the smallest piece of new knowledge that might have been brought to light by anyone from anywhere about anything.

Keywords: knowledge valuation; time value; money; finance; Net Present Value; economics; enlightenment

MSC 2010: 91B06 decision theory; 91B25 asset pricing models; 68T30 knowledge representation

JEL Classification: D81 criteria for decision-making under risk and uncertainty; G12 asset pricing; D8 information, knowledge, and uncertainty; D46 value theory

Appendix

A Appendix: List of All Definitions and Assumptions within the Paper

Assumption.

As a first step, we recognize that one possible categorization of different fields can be done by the set of questions a particular field attempts to answer. Since we are the creators of different disciplines, but we may or may not be the creators of the world (based on our present state of knowledge and understanding) in which these fields need to operate, the answers to the questions posed by any domain can come from anywhere or from phenomenon studied under a combination of many other disciplines.

Question. What is the value of knowledge in any field?

Assumption.

Questions & Answers, Q&A, are important, but Definitions and Assumptions, D&A, are even more important since changing D&A could require us to consider different Q&A.

Assumption.

Despite the several advances in the social sciences, we have yet to discover an objective measuring stick for comparison, a so called, True Comparison Theory, which can be an aid for arriving at objective decisions. Hence, despite all the uncertainty in the social sciences, the one thing we can be almost certain about is the subjectivity in all decision making.

Definition.

Type A person, who has All the known knowledge in the universe. So if any new knowledge becomes available, he is desperate to have it, since without this new knowledge he is incomplete.

Definition.

Type Z person, who has no knowledge about anything in the universe. So he cares nothing about any knowledge, wants nothing and his valuation for all pieces of knowledge would be Zero.

Assumption.

The homogeneous expectations assumption in finance is perhaps a very futuristic one where we are picking the best habits and characteristics from our fellow beings (maybe not just humans?); and the environment we live in and the external stimulus we receive tends to become more similar (or we start to perceive it as more alike?), and at some point in the future, we might tend to have more in common with each other, fulfilling this great assumption, which seems more of a prophecy.

Assumption.

Using a related concept from economics regarding equilibriums (Dixon 1990; Varian 1992; Footnote 10), when we continue to evolve and evolve towards similarity, both the typeA and typeZ kind of person can be equilibriums, since they are (they become?) the same kind of person with respect to their views on identifying the value of elements around them.

Definition.

Knowledge is a connection between different elements of this universe. The elements could be many (more than two), two or in some cases, a link from one element to the same element and all other combinations. This requires us to clarify what is an element. We suggest that the element discussed here is anything that belongs to this universe and any characteristic of that element, as observable in this universe (Footnote 12).

Definition.

Knowledge machines are elements themselves that look to create, or discover, or record, connections between the various elements. They are people, research journals, books, music, robots and everything else that fulfills the property of being part of the efforts to add to the collective pool of knowledge. We can also term them knowledge seekers.

Axiom. Knowledge never decreases in value. If it decreases in value, it was never knowledge to begin with. This gives the following discount function, h ( k , n ) , for knowledge.

(15)h(k,n)=(1+k)n≥1⇒k≥0

Assumption.

Past knowledge is important the older it is. That is knowledge from long ago is more valuable than knowledge yesterday.

Assumption.

Future knowledge is important the closer it is to us. That is knowledge that is far away from today is less valuable than knowledge about tomorrow.

Assumption.

Certain knowledge could be useful at certain points in time, and then decays around a certain point of high importance.

B Appendix: Dictionary of Notation and Terminology

PV (present value) is the value of money at time = 0 or at the present moment.
FV (future value) is the value of money at time = n or in the future.
n is the number of periods (not necessarily an integer).
i,k are the rates (of money or knowledge, known as interest rate or knowledge rate) at which the corresponding amount (of money or knowledge respectively) compounds each period.
k ¯ is also a knowledge rate.
FV _t, is the value of cash flows at time t.
g is the growth rate of money or knowledge over each time period.
f ( ⋯ ) , is the discount function, which for money is less than one, that is f(i,n)=1/(1+i)n≤1 or f(i,g,n)=(1+g)n/(1+i)n≤1 when the growth rate g is included.
h ( k , n ) or h¯(k¯,n) are the discount (or weight) functions for knowledge which are equal to or greater than one, that is, h(k,n)=(1+k)n≥1⇒k≥0.
PAVK, PRVK and FUVK denote the past (PA), present (PR) and future (FU) Value of any element of Knowledge.
≜ is sometimes used in mathematics (and physics) for a definition. The notation t≜m (often) means “t is defined to be m” or “t is equal by definition to m” (often under certain conditions).

C Appendix: Proof of Theorem 1

Proof.

We first try to establish the present value of a particular piece of knowledge that will become known in the future.

Relationship between PRVK and FUVK

We divide the time between the future and the present into many intervals. The possibility of some knowledge becoming known in the future will depend on the knowledge we have today and how we will add to it in the intervals between now and later as we approach the future time when the new knowledge will become known. The new knowledge rests on the many connections it has with the knowledge we know today and the knowledge that we will accumulate from now till the future point in time. Even if the new knowledge does not depend on any of the existing knowledge and its connections from now to the future, we would still need all this knowledge from now to the future to be able to establish that this new knowledge is independent of the other knowledge elements. We can then consider that this new knowledge will have to be linked (or still requires connections) to many pieces of knowledge in the intervals between now till later or we need to be aware of all this knowledge to establish that there is no relationship between the new future knowledge and the knowledge in between. This can be viewed as the change in the connections the new knowledge will have or the growth in the new knowledge based on the connections it will have, as given by the weight functions (Assumptions 6, 7 and 8):

PRVK ≜ FUVKh(k,n).

We then consider the limit as the number of intervals goes to infinity, that is as n→∞. The present value is then given by,

PRVK ≜limn→∞ FUVKh(k,n)

Using the property of the weight function,

h(k,n)=(1+k)n≥1⇒k≥0

Also, noting that since the knowledge across all those time intervals, between the future and now, needs to be connected as discussed in Assumption 7, the growth rate of knowledge is strictly greater than zero or, k>0. By Axiom 1 every piece of knowledge has value and hence the value of the piece of knowledge that becomes known in the future when it becomes known is greater than zero, FUVK>0. We then have,

P R V K ≜ lim n → ∞ F U V K ( 1 + k ) n

P R V K ≜ ∞ .

Next, we consider the future value of any piece of knowledge that we have today,

Relationship between FUVK and PRVK

Using a similar method of dividing the time between the present and future into many intervals, we consider the connections the piece of knowledge we have today is likely to establish with other elements of knowledge as time passes. As before, there will be direct connections between the knowledge today and the knowledge we will accumulate based on it; and to know that the knowledge today does not depend on other knowledge will still require knowing about the other knowledge elements. This can be viewed as the growth in this knowledge or change in this knowledge based on the connections it will have as given by the weight functions (Assumptions 6, 7 and 8)

FUVK ≜ PRVKh¯(k¯,n).

We then consider the limit as the number of intervals goes to infinity, that is as n→∞. The future value is then given by,

FUVK ≜limn→∞ PRVKh¯(k¯,n).

Using the property of the weight function,

h ¯ ( k ¯ , n ) = ( 1 + k ¯ ) n ≥ 1 ⇒ k ¯ ≥ 0

Also, noting that since the knowledge across all those time intervals, between now and the future, needs to be connected as discussed in Assumption 7, the growth rate of knowledge is strictly greater than zero or, k>0. By Axiom 1 every piece of knowledge has value and hence the value of the piece of knowledge that we have today is greater than zero, PRVK>0. We then have,

F U V K ≜ lim n → ∞ P R V K ( 1 + k ) n

F U V K ≜ ∞ .

The relationships between the present value and past value; the past value and present value; the past value and future value; and future value and past value can be established using similar arguments as above. To summarize, the below relationships can be shown to give the results in the statement of Theorem 1.

Relationship between PRVK and PAVK

Relationship between PAVK and PRVK

Relationship between PAVK and FUVK

Relationship between FUVK and PAVK

□

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Published Online: 2020-03-03

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Articles in the same Issue

https://doi.org/10.1515/bejeap-2019-0044

Keywords for this article

knowledge valuation; time value; money; finance; Net Present Value; economics; enlightenment