Erratum to “An Economic Instrument to Improve Society” [Theoretical Economics Letters, 9, 1804-1816]

Objectives: A general strive exists for achieving the wanted results with as limited resources as possible. There is a need for ever more cost-effective organisations, making this paper required to improve the policy efficiency and raise the technological standard in various communities. The Naturally Optimised Revenue Demand in Communities (NORDIC) model is introduced to improve the flow of physical and intangible utilities through entities of different kinds, such as producing companies and nations. The launched economic instrument also improves the ecological footprint of the organisations in question. Methods: The basis for the work is the existing Efficient Use of Resources for Optimal Production Economy (EUROPE) model, which is developed to become more powerful. Constructed shadow costs are added to the bookkeeping systems of organisations to give economic incentives to improve the economy, technology and environment. The design of the scientific work emphasises a logical-historical disposition. Results: The NORDIC model gives managers a management tool. The model is applicable to the public sector and commercial activities. The method provides a key indicator to assess and improve actors’ performance. A manual for the practical use of the NORDIC model is presented. The case study shows how to induce an economic incentive to reduce the costs and increase the efficiency for the health care, education and social services in the nation of Sweden. Conclusions: The model shows utility for various entities, such as public sectors, within nations. CitiHow to cite this paper: Stenis, J. (2021). Erratum to “An Economic Instrument to Improve Society” [Theoretical Economics Letters, 9, 1804-1816]. Theoretical Economics Letters, 11, 447-461. https://doi.org/10.4236/tel.2021.113029 Received: April 16, 2021 Accepted: May 31, 2021 Published: June 3, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/


Scientific Background
The background for this work is the common strive for achieving the wanted results with as limited resources as possible. This general motivation points at the importance of the subject. The need for ever more cost-effective organisations justifies taking up the study. This paper is required to improve communities. The Naturally Optimised Revenue Demand in Communities (NORDIC) model is introduced. The objective is to improve the flow of physical and intangible utilities through different entities, such as producing companies and nations. The Efficient Use of Resources for Optimal Production Economy (EUROPE) model [1] [2] [3] [4] [5] is developed to become even more powerful. Furthermore, the practical use of the EUROPE model [6] is improved. Shadow costs, or prices [7] constitute the basis.

Methodology
The design of the scientific work emphasises a logical-historical disposition. It follows the research process that contains, for example, the background, presentation of the problem and theory used, description of the data collection and processing, the analysis of the results and the conclusions and recommendations. Explanative investigations are featured to investigate the causal relationship between the variables in the new model. The investigation is also explorative since the study seeks new knowledge to present in the written form.
The main hypothesis in this paper is that the flow of physical and intangible utilities through entities of different kinds can be improved by applying the NORDIC model. The main goal is to facilitate the daily use of the NORDIC model by managers and practical operators. The nation of Sweden was chosen as the object of a case study for the following reasons: first, there are good, statistical data available on nations; and second, Sweden offers an extensive public sector for the case study. More broadly, I hope that this study will contribute to improving the economic, environmental and technological standards for organisations, which also improve the living conditions for related communities. The research gap that this study aims to fill is the need to develop new economic instruments to manage communities. The case study concerns the application of  [7]. These shadow costs are inserted into the budgets and accounting systems of the entity using the NORDIC tool. The changes that occur over time in the shadow costs provide a versatile tool that enables organisations to reduce the inefficiencies of the flows that these shadow costs are allocated to, one by one, in order of declining importance, or lowering the costs of the flows in question. In both cases, it is considered that the versatile NORDIC model can be applied to produce robust results, given the inherent logic of the mathematical theories underlying the model, and its good application in the presented case study.
Mainly, the problem has been analysed from a public perspective. The re- When modifying the present economic models, an analytical, economic-logic approach is mainly applied. A descriptive systems theory is used for the model's context. A non-personal approach is chosen that is more positivistic than, for example, humanistic.
An attempt is made to describe and establish as a part of the results and to predict and guide as a part of the discussion. The prediction is tested to induce discussed theories. Concrete actions to take are suggested to improve the problem situation in economic, environmental, and technological terms. Recommendations for the suggested and relevant actors are given, based on the statements about the findings, provided in the present study.
The sources of information for the study have included relevant literature and articles and database search, the Internet and personal E-mail contacts. This data is processed. Thus, trustworthy, secondary data is used, because primary data is new and unprocessed.
The quantitative research methodology is prevailing since the scientist is a detached observer, more than part of the study himself. The passing from theory to empiric encompasses an operationalisation by employment of the defined concepts for certain exemplified units. The processing of neutral data takes place in the detached case study.
Traditional economic modelling constitutes the validity of the methods developed in this study. The use of relevant literature and the relevant case study grant the reliability.
The instrument that is developed in this work is based on financial incentives.
It is hence an economic instrument (EI) which strengthens the dialogue between different actors.
The concepts presented here contribute to reducing the misuse of resources in society. The external environment will improve by time to enhance the citizens' quality of life.

Literature Review
The purpose for the literature review was to explore the previous findings, which may contribute to the model-development of this study. The literature review resulted in the author's discovery of some scientific theories and models, showing a certain resemblance with the previously introduced EUROPE model and the new NORDIC model, which is based on the EUROPE model. For example, the following approaches can be mentioned.
The review of the earlier findings, mainly within the fields of economy, models and optimisation theory, resulted in information about, for example, Sekerka and Stimel [8] having studied how and why firms move to engage in sustainable enterprise. Ooi [9] studied the transition and evolutionary models of urban en-  [12] found that a conventional commandand-control model focusing on pollution control drives environmental policy making in Hong Kong. Phyllis et al. [13] applied a model that uses fuzzy logic, called SAFE, to measure the sustainability of a country, based on a multitude of basic indicators. Gavazov et al. [14] coupled experimental and modelling approaches to assess the impact of climate change with a spatially explicit model.
Jepson [15] proposed the incremental integration of the expansionist and ecological views, using a decision model that incorporates project and context information to identify appropriate method and role.
More recently, Dror [16] has stated that the interest in the study and improvement of policymaking has been on the increase since around 2002, but no breakthroughs have occurred. A few, useful concepts have been developed, but no major advances in policymaking theory have taken place. No shift for the better in overall policymaking has occurred. In 2011, Vedung [17] suggested that one should concentrate on the generic tools of government action, public programs and says that the alternative tools of public action are the real "missing link" in the theory and practice of public management. These findings point at the approach presented in this paper being in line with the current movements of public management theory. Thus, the NORDIC model contributes to solving the problem of how to improve the overall policy efficiency for government action and public programs.
Regarding the use of shadow costs as a model component, Matsumura and Tomaru [18] introduced shadow costs of public funding as "the excess burden of taxation" and found that in a mixed duopoly, the level of product differentiation is too low for social welfare, in sharp contrast to the private oligopoly, where the level of product differentiation is too high. They showed that when the shadow cost is high, privatizing the public enterprise improves the welfare. However, according to Pentland [19]

Research Methods
The EUROPE model [1]- [6] formed the basis for the present work. The EUROPE model was adapted to community issues with emphasis on health care, education and social services to design the NORDIC model.

The Subjects
The basis for the work is the existing EUROPE model. This concept is further developed into an even more versatile expression denoted the NORDIC model.
The components of the EUROPE model are studied and reduced to improve the model's generality, and tested on the Swedish, public sector in a case study that employs real-world facts and figures.

Experimental Interventions
Personal computers were used as the main tool to acquire and process relevant data. Thus, no direct intervention with humans and/or animals took place during the conducted work. The author hence was highly detached when performing the present study, without being impersonal due to the many humans affected by the results of this study, if implemented.

Sampling Procedures, Sample Size and Ethical Considerations
Recent and reliable data were obtained from reliable and public Internet sources.
No agreements or payments were made. The sample size was the care, schools and welfare, Swedish: vård, skola, omsorg, in the nation of Sweden. No living individuals or animals were directly involved. The study required no particular physical safety precautions or special arrangements to prevent harming the objects of study.

Measurement Approaches
Observations of the important and relevant study-groups via online sources were made. Only reliable sources on the Internet were consulted. Usage of impersonal socio-economic data granted the cultural validity when processing the obtained information.

The Research Design
In practice, the research methods of this paper are designed as follows. First in the manuscript, a descriptive Introduction gives the background for this work and points at the importance of the subject. The need for taking up the study is clarified and why this paper is required. The new acronym NORDIC is explained and how it is related to the acronym EUROPE, whose scientific basis is given in the references by the author.

Theory Foundation
The NORDIC model is expressed by Equations (1) and (2).
The shadow cost: The entity to be optimized: where SC represents the positive shadow cost; ( ) represents the net worth of the entity to be optimised, or at least improved, if optimisation is not feasible; V represents the value of X; C represents the cost of X; Y represents the sum of the entities to be optimised, or improved; Z represents the value of the activities connected to X, and; W represents the weight factor (without unit, it is a decimal value) for the impact on society by X, per period for an administrative unit that is studied. Unit: currency, kilogram, litre or Joule.

Application of the NORDIC Model to Communities
The constructed, but useful, shadow cost SC is additionally inserted into the profit and loss account of the studied organisation in question to accomplish monitoring, management and evaluation of the development of X. The addition of SC gives strong economic incentives to improve the current situation, if SC is considered as a real phenomenon to be applied.

Logical Analysis of the Introduced Theory
If SC increases, this means that the organisation in question has improved, as regards optimising, or improving, X. When SC decreases over time, this calls for corrective actions to be taken by management to avoid inefficiencies with a negative impact on the economy. In practice, SC is continuously monitored to detect signs of a declining resource economy.

Manual for the Practical Application of the NORDIC Model
Constructed shadow costs are added to the values of economic significance, to improve the efficiency of the resource utilization in the targeted organisations.
This procedure increases the shadow costs, if X is useful and yields revenues.
The cost development is studied over time to make the phenomenon in question 1) Determine which losses to pinpoint, step by step, by estimating X.
2) Estimate Y, V and C using the studied organisation's book keepings.
3) Determine Z and/or the total breakdown cost from the actor's ledgers. 4) Determine the weight factor W for the organisation's impact on society. 5) Calculate SC and insert it into the accounting system of the current entity. 6) Determine SC for any additional item X of commercial or public interest. 7) Re-calculate SC to study it carefully to monitor, manage and evaluate X. 8) Take actions to increase the organisation's efficiency, if SC decreases.

The Swedish Health Care, Education and Social Service in 2018
By Equations (1) and (2), X represents the Swedish health care, education and social services. X given by the Swedish municipalities' purchases of services was 11.5 billion US dollars (SEK115 billion) [20].

Results and Discussion
The benefit of the NORDIC model is that the shadow cost provides management with an instant view of the performance of their business. The SC conveys important aspects of how the community performs. Thus, a better possibility for CEOs to manage well is the major value of knowledge added by the paper. The previously developed EUROPE model provided an economic instrument, which was more developed into the NORDIC model. The case study exhibits the practical usefulness for the NORDIC model, also on higher, administrative levels. A reasonable shadow cost of 25 billion US dollars is obtained, compared to the Swedish GDP of 555 billion US dollars in 2018 [24]. Thus, the NORDIC model can be used where a "black box" system is present. Ultimately, the gain from using the model is a better life for the citizens, due to the strengthened economy. The model shows utility for entities, such as nations. SC constitutes a versatile tool. The reliability is good because the outcome of the case study gives a realistic result.
The main strength of the model is its generality. The disadvantages are the less good precision when employing the shadow costs, and the difficulties to get access to input data to apply the theory in practice. Further research can develop mathematical algorithms adapted to the public sectors and add some relevant factors to the current model-design.
Examination of SC over time shows the changes in the organisational efficiency. SC is a key indicator. If SC decreases compared with the previous years,  If the SC decreases from one year to the next, the management understands that it must act. The NORDIC model alerts management that it must act but leaves the determination of the improvements to the employees and CEO of the current organisation. If the SC increases from one year to the next, the NORDIC model tells management that the business has improved, in general terms.
The NORDIC model does not enable to determine in detail which solutions should be implemented. It indicates that when the SC decreases, there is an issue with the system that requires action. The model does not indicate precisely which solution the CEO will choose. It provides managers with an overview. This is how economic instruments work in general. The development of the NORDIC model includes a stepwise manual that covers its practical application.
This manual that is presented in Section 3.6, provides the very step-by-step instructions for application of the launched model. In this paper, the NORDIC model is based on currency as the dominant unit for the model calculations, rather than physical entities.
In the case study, the fraction X is a certain public sector. The step-by-step  (1) and (2)  The case study presented here shows the viability of the NORDIC model, when applied to Sweden's public finances, to improve the performance of the Swedish health care, education and social services. The case study results in the calculation of a rather reasonable shadow cost SC of 25 billion US dollars, which managers can utilize to guide their own decisions. SC provides a comprehensive key indicator, which summarizes the performance of most organisations also in other sectors than the public, as in the present case study.
SC is a constructed entity that is added to the revenue of the organisations that use it. The addition of SC to the revenue results in an incentive for management to start increasing the fraction X, or to decrease the total costs C connected to fraction X, if X is a useful fraction.
The manual associated with the NORDIC tool is applicable to the schemes in industries. Therefore, practical application of the NORDIC model is useful for businesses in general. It may also be possible to apply the model to developing countries, subject to training.
Notably, the NORDIC model and its related manual promotes the circular economy, a regenerative system in which resource input and waste, emission, and energy leakage are minimized by slowing, closing, and narrowing energy and material loops [25]. The launched tool namely reduces spillages at the source, by providing economic incentives to achieve that goal.

General Conclusions
The main hypothesis in this paper is that the flows of physical and intangible utilities through entities of different kinds can be improved by applying the NORDIC model. The hypothesis is verified, because the logics of the theory designed support this conclusion, and because the introduced theorems are mathematically correct. The results from the case study support the main goal of facilitating the daily use of the NORDIC model by civil servants and operators. As more communities adopt the NORDIC model, the objectives of improving the economic, technological and environmental conditions in the organisations will be supported. The gap is filled in the existing research, regarding novel, economic instruments to manage communities and other organisations needing artifacts like the versatile NORDIC model, which was developed with the very aim to improve communities.
The results of the study, and the previous discussion, provide answers to the research questions posed, regarding how to use the NORDIC model to improve the efficiency of economic units, such as nations and communities, and how an economic instrument can be designed and modified for this purpose. The provided research contribution involves the development of a versatile, economic tool that enables managers to better understand how their organisations can become more efficient in economic, environmental and technical terms. In this study, this tool has been shown to be useful for public finances, particularly the health care, education and social services, and to help them improve the well-being of communities and municipalities.
The work contributes to the literature by providing novel solutions to promote the optimization of the economic efficiency and to assist public managers, and managers in industries, to improve their companies' performance. This improved management situation in the public and the private sector is the major value of knowledge added by this paper.
The real finding of the present study is that the NORDIC model represents a versatile theory to improve the situation in various entities, such as nations. The evidence for this statement consists of the realistic results of the performed case study with real-world data.
The novelty of the approach is the innovative usage of the shadow cost construct to create the economic incentives for improvement of the functionality of management systems. The introduction of a single key indicator to simultaneously monitor most aspects of interest for a management system is a highlight. The most interesting findings are the method to facilitate managers' policy decisions and their positive impact on the economic development that is a prerequisite for a sound technology that promotes environmental sustainability.
The method aids managers and practical operators to reduce losses in economic systems and improve the efficiency, based on the well-known concept of Theoretical Economics Letters shadow costs. The most important conclusions, based on my developed model and the case study, are as follows.
1) The research is useful for managers to reduce losses in their organisations.
2) Managers obtain an economic instrument to monitor, manage and evaluate.
3) The constructed economic incentives improve the utilization of resources. 4) Cost-effectiveness and equity increase due to the reduced risk of spillages. 5) Managers can apply economic instruments to prevent people's discontent.
The main limitation of the introduced methodology is its less specified impact on the targeted communities. The employed shadow costs namely work on a general level, which mainly gives overall results for the current entities of interest. Therefore, some additional algorithms should be developed, and integrated into the present NORDIC model, to enable a more specific impact on the sub-units that are intended to be improved by the model.
In the future, studies could be conducted to determine how the NORDIC model can be applied to larger units. There is potential to apply the model to the international context, particularly as regards higher policy analysis organizational levels within major areas of social concern, for example, the migration issue and how to improve the workforce.

Benefits of Using the Model
 The NORDIC model gives managers a versatile management tool.
 The model is applicable to the public sector and commercial activities.
 The method provides a key indicator to assess and improve performance.
 The method is based on the well-known concept of shadow costs.
 The method is comprehensible, robust and easy to grasp.

Recommendations
 Apply the NORDIC model to organisations to improve their performance.
 Apply the NORDIC model based on the manual presented in this study.

Conflicts of Interest
The author declares no conflicts of interest.

Availability of Data and Material
All data generated or analysed during this study are included in this article.

Research Involving Human Participants and/or Animals
No human participants or animals were directly involved in this study.