Two Sets of Boundary Conditions in Cyclical Systems with Goodwill in Capitalization

Round 1

Reviewer 1 Report

This manuscript may be recommended for publication after its revision according to the following comments. 

1. Improve the linguistic part (grammar, misspelled words, punctuation, etc.) of the manuscript, for example, see lines 50-51, 54, etc. Also, see the punctuation appearing after equation numbers. 

2. Include more details for illustrating equations (2) and (3).

3.  The author needs to add more details about vanishing/non-vanishing  of the product sales rate in terms of capital/goodwill. Also explain the impact of  vanishing of the product sales rate on equations (2) and (4). 

4. It will be interesting to see the comparison of the preset results with the known ones on the topic. 

This manuscript may be recommended for publication after its revision according to the following comments. 

1. Improve the linguistic part (grammar, misspelled words, punctuation, etc.) of the manuscript, for example, see lines 50-51, 54, etc. Also, see the punctuation appearing after equation numbers. 

2. Include more details for illustrating equations (2) and (3).

3.  The author needs to add more details about vanishing/non-vanishing  of the product sales rate in terms of capital/goodwill. Also explain the impact of  vanishing of the product sales rate on equations (2) and (4). 

4. It will be interesting to see the comparison of the preset results with the known ones on the topic. 

Author Response

Thank you very much.

A linguistic revision of the text has been implemented.

The Equations are built in sentences. Correspondingly, there is a comma after any Equation if the sentence is about to continue. If the sentence is about to terminate, there is a period instead of a comma.

The text related to Equations (2) and (3) has been elaborated.

As the text related to Equations (2) and (3) has been elaborated, the concept “product sales rate” has been replaced by “value extraction rate”, or synonymously “the rate of distributed dividends”. Thís should make the text much more comprehensible.

Vanishing of the value extraction rate has no connection to Eq. (4). In Eq. (2), the value extraction rate may vanish only if the production rate of tangible value vanishes.

The author has made an attempt to find literature where periodic boundary conditions would be abandoned, and the consequences investigated. Naturally, many such references were found from the physical sciences, and a few ones are now referred to. Within the fields of economics and finance, a variety of boundary conditions is applied, but the periodic ones seemingly do not appear within the literature. Correspondingly, the only preliminary study found is the one referred to as reference [14], now renumbered as [20].

Reviewer 2 Report

In this paper, a mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if a physical system is periodic, an agent can abandon the corresponding boundary condition by divesting. Example cases are  shown in terms of boreal forestry systems

The results are interesting and the paper is well written. Here are some comments that might be useful for improving the quality of this paper.

[1] In order to improve the quality of paper, the English expression of the whole paper should be checked and improved. 

[2] More recent related works should be updated and added in the reference part. In addition, all references should be formatted in the MDPI style.

The English expression of the whole paper should be checked and improved. 

Author Response

Thank you very much.

A linguistic revision of the text has been implemented. Also some significant changes have been implemented in terminology.

The author has made an attempt to find literature where periodic boundary conditions would be abandoned, and the consequences investigated. Naturally, many such references were found from the physical sciences, and a few ones are now referred to. Within the fields of economics and finance, a variety of boundary conditions is applied, but the periodic ones seemingly do not appear within the literature. Correspondingly, the only preliminary study found is the one referred to as reference [14], now renumbered as [20].

Thank you for the remark regarding the formulation of the references.

Reviewer 3 Report

This work is generally well-presented and of interest to a  potentially wide readership.  There are a few small departures from normal usage.  'Let us' immediately evokes the response 'no!'  'Things' would benefit from the inclusion of 'nin'.  Some of the authors have initials followed by surname.  Some have the reverse order.  Assuming that there is no reason for the variation the author should  adopt a consistent  style.

See above.

Author Response

Thank you very much.

There appeared to be four instances where the expression “Let us” was used. For the author, two of them appeared appropriate. Two of the expressions were replaced by another phrasing.

Thank you for the note about the misspelling of “thinning”.

Thank you for the remark regarding the formulation of the references.

Reviewer 4 Report

All is as in the report!

Comments for author File: Comments.pdf

Author Response

Thank you very much.

A rather significant conceptual change has appeared in the Introduction, as well as in the beginning of the mathematical formulations. A closed integral of the rate of distributed dividends is equated with the closed integral of the tangible value production rate. This is necessary to satisfy the periodic boundary condition. This conceptual change does not affect the mathematical formulations.

Discussion regarding Eqs. (7) and (8) has been elaborated. In particular, it is now emphasized that the expected tangible value appearing in the denominators depends on the schedules of the value growth rate and the dividend distribution rate.

The author has made an attempt to find literature where periodic boundary conditions would be abandoned, and the consequences investigated. Naturally, many such references were found from the physical sciences, and a few ones are now referred to. Within the fields of economics and finance, a variety of boundary conditions is applied, but the periodic ones seemingly do not appear within the literature. Correspondingly, the only preliminary study found is the one referred to as reference [14], now renumbered as [20].