[doc sps="1.7" acron="eys" jtitle="Economía y Sociedad" stitle="Economía y Sociedad" issn="2215-3403" pissn="1409-1070" eissn="2215-3403" pubname="Universidad Nacional, Costa Rica" license="http://creativecommons.org/licenses/by-nc-sa/4.0" volid="23" issueno="53" dateiso="20180600" season="Jan/June" order="01" fpage="1" lpage="18" pagcount="18" doctopic="oa" language="es"]Doi: [doi]10.15359/eys.23-53.1[/doi]
[toctitle]Artículo[/toctitle]


[doctitle language="en"]Financial resource contribution to production growth and return on producer's capital[/doctitle]
[doctitle language="es"]Contribución de los recursos financieros al crecimiento de la producción y retorno al capital de los productores[/doctitle]
[doctitle language="pt"]Contribuição dos recursos financeiros para o crescimento da produção e retorno ao capital dos produtores[/doctitle]

[author role="nd"][fname]Daniel[/fname] [surname]Villalobos-Céspedes[/surname][xref ref-type="aff" rid="aff1"]1[/xref][/author]

[normaff id="aff1" ncountry="Costa Rica" norgname="Universidad de Costa Rica" icountry="CR"][label]1[/label] [role]Economista, politólogo, Catedrático[/role] en [orgname]Universidad de Costa Rica[/orgname] (UCR) y Universidad Nacional (UNA), Costa Rica. Correo electrónico: [email]daniel.villalobos.cespedes@una.ac.cr[/email][/normaff]

[hist]Fecha de recepción: [received dateiso="20170813"]13-08-2017[/received].
Fechas de reenvíos: 22-08-2017, 25-08-2017, 20-10-2017, [revised dateiso="20171120"]20-11-2017[/revised].
Aceptado el [accepted dateiso="20171130"]30-11-2017[/accepted].
Publicado el 01-01-2018.[/hist]


[xmlabstr language="en"][sectitle]Abstract[/sectitle]
[p]Financial resource contribution to production growth is a taboo issue in economic theory, especially if its source is the financial capital, which is part of the dynamic of any vigorous economy. Financial capital is a pivotal instrument of production growth due to the fact that its participation contributes to the process of transforming and transferring values from inputs to outputs. By doing so, financial capital encourages producers to generate not only outputs but also profit. Producers must transmute financial capital into financial resources in order to obtain output and profit. Therefore, the rate of interest becomes the way in which financial capital and producers get into the production process. This is to what this theoretical research is concerning. [/p][/xmlabstr]
[kwdgrp language="en"][sectitle]Keywords:[/sectitle] [kwd]cost of production[/kwd]; [kwd]loan[/kwd]; [kwd]deft[/kwd]; [kwd]resource[/kwd]; [kwd]profit[/kwd]; [kwd]interest[/kwd][/kwdgrp].

[xmlabstr language="es"][sectitle]Resumen[/sectitle]
[p]La contribución de los recursos financieros al crecimiento de la producción es un tema tabú en la teoría económica, en especial si se trata del capital financiero, el cual es parte activa de la dinámica de una economía vigorosa. El capital financiero es un instrumento central del crecimiento económico en cuanto su participación contribuye en los procesos de transformación y transferencia de valor de los medios de producción al producto. Ese capital puede permitir a los empresarios generar productos y, por su medio, obtener ganancias. Para lograrlo, los productores transmutan el capital financiero en recursos financieros. La tasa de interés es un mecanismo que facilita al capital financiero y, a los productores, la incursión en procesos globales de producción.[/p][/xmlabstr]
[kwdgrp language="es"][sectitle]Palabras claves:[/sectitle] [kwd]costo de producción[/kwd]; [kwd]crédito[/kwd]; [kwd]deuda[/kwd]; [kwd]recurso[/kwd]; [kwd]ganancia[/kwd]; [kwd]tasa de interés.[/kwd][/kwdgrp]

[xmlabstr language="pt"][sectitle]Resumo[/sectitle]
[p]A contribuição dos recursos financeiros para o crescimento da produção é um tema tabu na teoria econômica, especialmente em se tratando do capital financeiro, que é parte ativa da dinâmica de uma economia vigorosa. O capital financeiro é um instrumento central do crescimento econômico, na medida em que sua participação contribui para os processos de transformação e transferência de valor dos meios de produção para o produto. Esse capital pode permitir que os empresários gerem produtos e, através deste, obtenham lucros. Para conseguir isso, os produtores transmudam o capital financeiro em recursos financeiros. A taxa de juros é um mecanismo que facilita o capital financeiro e, para os produtores, a incursão em processos globais de produção.[/p][/xmlabstr]
[kwdgrp language="pt"][sectitle]Palavras-chave:[/sectitle] [kwd]custo de produção[/kwd]; [kwd]crédito[/kwd]; [kwd]dívida[/kwd]; [kwd]recurso[/kwd]; [kwd]lucro[/kwd]; [kwd]taxa de juros.[/kwd][/kwdgrp]


[xmlbody][sec sec-type="intro"][sectitle]Introduction[/sectitle]


[p]Production growth depends on various factors, many of which are challenging to explain. Economic theory uses facts that could be measured by different techniques, although this is not easy to conclude. What happens with financial capital and financial resources is where we must dig deeper into the concepts and facts. But to do so, we must make rational connections between concepts and between concepts and their fundaments. This is the purpose of this theoretical research, analyzing concepts and their relations as they seem to occur in a real economy. We examine financial resource contribution to production growth and financial capital participation on profit.[/p]
[p]This research is an advance on "Production Cost, Prices and Income of Firms" (Villalobos, [xref  ref-type="bibr" rid="r5"]2015[/xref]). In the process of transforming inputs into outputs (Jehle & Reny, [xref  ref-type="bibr" rid="r2"]2011[/xref], p. 126), input attributes are transferred into outputs. Money, as a coin or banknote, can be used to acquire resources, but itself alone is not a resource. Money as a concept can refer to anything, even those that can be a resource. As a means of transaction, money can facilitate the acquisition of goods and services of almost any kind. Some goods and services acquired by money are resources. Thus, money has the ability of acquire values as inputs, and by that it becomes capital.[/p]
[p]What is called capital is anything (e.g. money) that can be used to generate any sort of benefit (e.g. economic profit [graphic href="?a1v23n53"][/graphic]). By financial capital we understand certain amounts of assets, such as money, that could be reproduced by its profitable use no matter where it comes from (banks, stock market). This is possible if financial capital (credit, bonds, and shares) becomes a financial resource, because there is no way for financial capital to reproduce by itself. It is as a financial resource that financial capital (money or any other goods or services) given as loan [graphic href="?a1v23n53"][/graphic] could make the global production process possible. Loans would not only facilitate the production process and production growth but also profit, and by this act, it would receive interest.[/p]
[p]Interest is a ratio of profit, and because of this, financial resources would reflect the financial capital contribution to production growth. If an economy is a conjunction of resources, then money given-taken as a loan could be transmute into resources. A resource is anything useful for something else, especially to produce goods and services. However, it is not enough to produce it for sale; resources must be profitable. So, [graphic href="?a1v23n53"][/graphic] becomes a financial resource, and as such, it seeks to participate in profit distribution. The rate of its participation is called the rate of interest [graphic href="?a1v23n53"][/graphic], and so [graphic href="?a1v23n53"][/graphic] and [graphic href="?a1v23n53"][/graphic] define debt [graphic href="?a1v23n53"][/graphic].[/p]
[p]In a real economy, firms must deal with loans to acquire resources. In the production process, any resource assumes the form of production cost, so a loan becomes part of the cost as it is used to obtain resources. Credit is the way by which financial capital participates in the production process and also profit. The rate of interest is the means by which financial capital gets a fraction of profit as interest. Loans become financial resources in the hands of producers and through this, they contribute to production growth and generating profit.[/p]


[subsec][sectitle]Financial Resource on Production Cost[/sectitle]


[p]We call debt [graphic href="?a1v23n53"][/graphic] and it is formulated as [graphic href="?a1v23n53"][/graphic]; [graphic href="?a1v23n53"][/graphic] and [graphic href="?a1v23n53"][/graphic] represents the total value of the cost of production including fixed resource [graphic href="?a1v23n53"][/graphic], intermediate resource [graphic href="?a1v23n53"][/graphic] and labor [graphic href="?a1v23n53"][/graphic], and the rate of interest [graphic href="?a1v23n53"][/graphic]. So, [/p]
[p][graphic href="?a1v23n53"][/graphic] then, [graphic href="?a1v23n53"][/graphic] and [graphic href="?a1v23n53"][/graphic][/p]
[p]For producers, [graphic href="?a1v23n53"][/graphic] is the amount of money that corresponds to a part or total value of resources on production cost. Thus, [graphic href="?a1v23n53"][/graphic] represents the magnitude of financial resources in the real value of production cost. So, [graphic href="?a1v23n53"][/graphic] is not a cost but rather the quantity of interest (money) owed to financial resources for their contribution to production growth.[/p]
[p]We will not complicate the computation of [graphic href="?a1v23n53"][/graphic] by using compound interest due to the economy periodically paying a quota composite of [graphic href="?a1v23n53"][/graphic] plus a portion of [graphic href="?a1v23n53"][/graphic]. This quota may or may not imply proportional pays of [graphic href="?a1v23n53"][/graphic] and [graphic href="?a1v23n53"][/graphic]. Experience shows that financial capital charges a large proportion of [graphic href="?a1v23n53"][/graphic] instead of [graphic href="?a1v23n53"][/graphic] almost always from the beginning of [graphic href="?a1v23n53"][/graphic]. This is to say that financial capital charges interest on producers and also on loans to consumers, even before they generate profit as value. It is a fact that producers periodically require [graphic href="?a1v23n53"][/graphic] to finance the production process, so it is not easy to calculate how much producers pay on past-present debt. What we can suppose is that every so often (e.g. per month or year), the economy pays fractions of the value of production [graphic href="?a1v23n53"][/graphic] to the financial sector.[/p]
[p]To simplify our discussion in this research, we suppose that [graphic href="?a1v23n53"][/graphic] correspond to the effective real value annually paid by the economy to the financial sector. So, [graphic href="?a1v23n53"][/graphic] could vary from time to time depending on changes on [graphic href="?a1v23n53"][/graphic] and the debt-term. Thus, to introduce [graphic href="?a1v23n53"][/graphic] to the production process as part of the value of production cost, we proceed as follows: [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Equation (3) denotes the ratio of loan and thus the magnitude of loan in relation to the whole cost of production. Hence, [graphic href="?a1v23n53"][/graphic] denotes the composition of the cost of production as a loan plus the producer's own capital (depreciation, profit). This means that [graphic href="?a1v23n53"][/graphic] expresses the ability of the economy to sustain its production process. For this reason, it is necessary to analyze changes on [graphic href="?a1v23n53"][/graphic]; thus, differentiating equation (3) obtains[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Let [graphic href="?a1v23n53"][/graphic] be the rate of change on the loan amount and [graphic href="?a1v23n53"][/graphic] the rate of change on the cost of production, and by equation (3), we obtain[/p]
[p][graphic href="?a1v23n53"][/graphic] [/p]
[p]So, [graphic href="?a1v23n53"][/graphic][/p]
[p]Let us call [graphic href="?a1v23n53"][/graphic] the rate of change in the ratio of loan. Therefore,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]As result, [graphic href="?a1v23n53"][/graphic] will depend upon [graphic href="?a1v23n53"][/graphic] and on [graphic href="?a1v23n53"][/graphic] in opposite directions. So, the greater (lower) [graphic href="?a1v23n53"][/graphic] is than [graphic href="?a1v23n53"][/graphic] ceteris paribus ([xref  ref-type="fig" rid="f3"]Figure 3[/xref]), the greater (lower) the participation of financial resource on profit. If [graphic href="?a1v23n53"][/graphic], [graphic href="?a1v23n53"][/graphic] will be the opposite of [graphic href="?a1v23n53"][/graphic], which is an indicator of the amount of profit that producers retain ([xref  ref-type="fig" rid="f1"]Figure 1[/xref]) or the contrary ([xref  ref-type="fig" rid="f2"]Figure 2[/xref]). In such a way, [graphic href="?a1v23n53"][/graphic], ceteris paribus, indicates the rate of participation of entrepreneurs on profit. For financial capital, we can say that its income is [graphic href="?a1v23n53"][/graphic], while for producers it is just [graphic href="?a1v23n53"][/graphic]. [/p]
[p]But, we must keep in mind that participation on profit and contribution on profit have different connotations. For financial capital, its participation on profit is measured in terms of the rate of interest; meanwhile, for producers, it is computed in terms of the rate of profit. Contribution is measured here in relation to the value of production growth, which is possible only by producers. So, financial capital participates in profit because producers transform [graphic href="?a1v23n53"][/graphic] into a financial resource (into [graphic href="?a1v23n53"][/graphic]), and as such it contributes to production growth. Of course, financial capital indirectly participates in production growth due to producers transforming loans into capital resources. But, if we discuss capital resources, we also talk of capital resource contribution.[/p]

[figgrp id="f1"][graphic href="?a1v23n53"][/graphic]
[label]Figure 1 [/label].[caption][graphic href="?a1v23n53"][/graphic]. Source: prepared by the author.[/caption][/figgrp]

[figgrp id="f2"][graphic href="?a1v23n53"][/graphic]
[label]Figure 2. [/label] [caption] [graphic href="?a1v23n53"][/graphic]. Source: prepared by the author.[/caption][/figgrp]
[figgrp id="f3"][graphic href="?a1v23n53"][/graphic]
[label]Figure 3. [/label] [caption][graphic href="?a1v23n53"][/graphic]. Source: prepared by the author.[/caption][/figgrp]

[p]By operating on equation (1) and substituting the result in equation (3), we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and by reorganizing it in function of [graphic href="?a1v23n53"][/graphic], we obtain[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]If [graphic href="?a1v23n53"][/graphic] is the total value of the cost of production including fixed resource [graphic href="?a1v23n53"][/graphic], intermediate [graphic href="?a1v23n53"][/graphic] and labor [graphic href="?a1v23n53"][/graphic], the result is[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]This equation illustrates the composition of the real value of the cost of production, in which [graphic href="?a1v23n53"][/graphic] is included if it exists. This is very important for the economy due to its ability to obtain loans effectively, and producer's own capital will rely on which kind of resources they invested. So,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By this equation, the resources that will require financing by financial capital are determined. [/p]
[p]Defining the real value of production [graphic href="?a1v23n53"][/graphic] as[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and the average cost of production [graphic href="?a1v23n53"][/graphic] is[/p]
[p][graphic href="?a1v23n53"][/graphic] [/p]
[p]So, by equation (5), [graphic href="?a1v23n53"][/graphic][/p]
[p]and operating on the above equation, [graphic href="?a1v23n53"][/graphic] is obtained which is equivalent to equation (5): [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]In equation (10), it is perceived that [graphic href="?a1v23n53"][/graphic] are given as part of [graphic href="?a1v23n53"][/graphic] denoted by [graphic href="?a1v23n53"][/graphic]. Additionally, [graphic href="?a1v23n53"][/graphic] plays a role on [graphic href="?a1v23n53"][/graphic] through [graphic href="?a1v23n53"][/graphic], which will impact [graphic href="?a1v23n53"][/graphic]. By differentiating that equation, the result will be the change on [graphic href="?a1v23n53"][/graphic], taking into account all its components; that is to say,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Let [graphic href="?a1v23n53"][/graphic] be the rate of change in the rate of interest and [graphic href="?a1v23n53"][/graphic] be the rate of change in debt, which will be influenced by changes in [graphic href="?a1v23n53"][/graphic] and the debt-term. By replacing it and equation (10) in the previous equation, the result is[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Let [graphic href="?a1v23n53"][/graphic] be the rate of cost. By reorganizing this result, we can rewrite that equation as[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Equation (11) expresses [graphic href="?a1v23n53"][/graphic] influenced by [graphic href="?a1v23n53"][/graphic], which considers [graphic href="?a1v23n53"][/graphic] as part of [graphic href="?a1v23n53"][/graphic] and the amount of interest [graphic href="?a1v23n53"][/graphic] that the economy must pay, [graphic href="?a1v23n53"][/graphic] and the rate of change of the rate of interest [graphic href="?a1v23n53"][/graphic].[/p]
[p]Through equation (4), we can rewrite equation (11) as follows:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p] then, [graphic href="?a1v23n53"][/graphic][/p]
[p]So, after simplifying,[/p]
[p][graphic href="?a1v23n53"][/graphic]and thus, [graphic href="?a1v23n53"][/graphic][/p]
[p]Equation (13) denotes that [graphic href="?a1v23n53"][/graphic] depends on [graphic href="?a1v23n53"][/graphic] and on the change of the rate of interest. If [graphic href="?a1v23n53"][/graphic], then [graphic href="?a1v23n53"][/graphic], but [graphic href="?a1v23n53"][/graphic] would occur, ceteris paribus, due to changes in the rate of profit in the economy and in the rate of financial capital participation on profit, which defines the path of debt. [xref  ref-type="fig" rid="f4"]Figures 4[/xref] and [xref ref-type="fig" rid="f5"]5[/xref] illustrate two possibilities. [/p]

[figgrp id="f4"][graphic href="?a1v23n53"][/graphic]

[label]Figure 4.[/label] [caption]Path of debt due to [graphic href="?a1v23n53"][/graphic] and change in [graphic href="?a1v23n53"][/graphic] at different rates of profit ceteris paribus. Source: prepared by the author.[/caption][/figgrp]

[figgrp id="f5"][graphic href="?a1v23n53"][/graphic]
[label]Figure 5.[/label] [caption]Path of debt due to [graphic href="?a1v23n53"][/graphic] and change in [graphic href="?a1v23n53"][/graphic] at different rates of profit and diminishing financial capital participation on profit ceteris paribus. Source: prepared by the author.[/caption][/figgrp]


[/subsec][subsec][sectitle]Reasons of change in interest[/sectitle]


[p]By equation (10), we obtain [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]The quantity of interest [graphic href="?a1v23n53"][/graphic] paid (e.g. per annum) by the economy (firms, industries) is[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]From equation (14), it is clear that [graphic href="?a1v23n53"][/graphic], when it exists, is a result of the global process of production, where resources are combined to get a value of production. It also means that [graphic href="?a1v23n53"][/graphic] is a value that comes from [graphic href="?a1v23n53"][/graphic] every time [graphic href="?a1v23n53"][/graphic] is part of [graphic href="?a1v23n53"][/graphic]. By the derivate of equation (14), we obtain [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Where [graphic href="?a1v23n53"][/graphic] and after simplifying, the following is obtained:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]If [graphic href="?a1v23n53"][/graphic] is the rate of change in the rate of interest and [graphic href="?a1v23n53"][/graphic], then,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]And[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]After simplifying,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]In addition, due to [graphic href="?a1v23n53"][/graphic], then,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Now, let [graphic href="?a1v23n53"][/graphic] be the rate of change of [graphic href="?a1v23n53"][/graphic], and substituting it in the above equation and by reorganizing it, we attain[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]After reorganizing, the result is[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]This last equation expresses that the rate of change on [graphic href="?a1v23n53"][/graphic] will depend directly upon the rate of production growth [graphic href="?a1v23n53"][/graphic], the rate of change of production costs, the rate of change of loans, and the rate of change in interest rate. It refers to how the economy gets [graphic href="?a1v23n53"][/graphic] from profit to pay it to financial capital. By replacing [graphic href="?a1v23n53"][/graphic] and equation (4), we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Equation (15) points out that the rate of change on [graphic href="?a1v23n53"][/graphic] is determined by the rate of change in loans and on the rate of change in interest rate. But this equation occults the fact that [graphic href="?a1v23n53"][/graphic] could influence the direction and magnitude of [graphic href="?a1v23n53"][/graphic]. So, expectation of financial capital on [graphic href="?a1v23n53"][/graphic] could establish a fundamental role in defining [graphic href="?a1v23n53"][/graphic]. If by equation (4) [graphic href="?a1v23n53"][/graphic], then equation (15) will denote that producers will retain [graphic href="?a1v23n53"][/graphic].[/p]


[/subsec][subsec][sectitle]Interest and profit on resource contribution[/sectitle]


[p]Profit is the prime inducement for investors to go into global production and financial activities in an economy. Profit [graphic href="?a1v23n53"][/graphic] is measured by production value minus production cost value. So,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]But gross profit is a result of every economic activity contribution to production growth by using productive resources. To get gross net producer's profit, we deduce from [graphic href="?a1v23n53"][/graphic] the interest [graphic href="?a1v23n53"][/graphic] they will pay for financial resources. By equation (16) and [graphic href="?a1v23n53"][/graphic], we obtain [/p]
[p][graphic href="?a1v23n53"][/graphic] [/p]
[p]And[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, equation (17) denotes [graphic href="?a1v23n53"][/graphic]as featured in equation (14): the financial resource contribution to production growth. This fact is hidden by resource contribution to production growth expressed by [graphic href="?a1v23n53"][/graphic]. But, as we said before, this financial resource contribution to production growth reflects the financial capital participation on profit. [/p]
[p]We can get the same result by a simpler proceeding, defining that[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and by equation (14), [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]then, after some manipulations,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Where [graphic href="?a1v23n53"][/graphic] was deduced by equations (2) and (14). If [graphic href="?a1v23n53"][/graphic] is the rate of profit calculated as[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By equations (7) and (10), we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and by substituting equation (9), we have[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]The rate of profit and the rate of interest could not exist if capital as money did not get to transform into productive resource (Robinson, [xref ref-type="bibr" rid="r4"]1953-1954[/xref]). Capital is not as simple as any stock of things, like money, but rather those things that become production resources and by this on production cost. So, [graphic href="?a1v23n53"][/graphic] is not a stock of resources but instead resource values used to be capitalized, and not just as simple capital. It is the nature of equation (20) to measure, relatively, profit resource contribution. But the motivation of equation (19) is to deduce how much profit corresponds to financial resources. Both rates result from the same process, but they have to be split up when profit is distributed between financial capital and producers.[/p]
[p]By deducing equation (18) from equation (20), we get producer's net profit [graphic href="?a1v23n53"][/graphic] in the economy:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By operating on equation (3) and replacing its result in equation (22), the result is[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, each portion of production cost value will get the same [graphic href="?a1v23n53"][/graphic], and for this reason [graphic href="?a1v23n53"][/graphic] is just a fraction of [graphic href="?a1v23n53"][/graphic]. So, let[graphic href="?a1v23n53"][/graphic]be the coefficient as follows:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Substituting equation (25) in equation (23), we obtain[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]which is equivalent to equation (17).[/p]
[p]Furthermore, by also substituting equation (20) in equation (25), the following is obtained:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By deriving equation (27), we find the change of [graphic href="?a1v23n53"][/graphic] due to changes in production cost and profit:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By simplifying,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Then,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]If [graphic href="?a1v23n53"][/graphic] is the rate of change on profit, then, [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Finally, let [graphic href="?a1v23n53"][/graphic] the rate of change on the coefficient [graphic href="?a1v23n53"][/graphic], so,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]And[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]The result is that the rate of interest will change due to changes in the rates of changes [graphic href="?a1v23n53"][/graphic]. It is shown in equation (28) that, ceteris paribus, [graphic href="?a1v23n53"][/graphic] will introduce changes on [graphic href="?a1v23n53"][/graphic]. It could motivate the financial sector to vary [graphic href="?a1v23n53"][/graphic] as a way of changing its participation on [graphic href="?a1v23n53"][/graphic]. In addition, it could happen as a result of changes in production growth. We already know that[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, replacing it in equation (28), we obtain[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]And now we can define the rate of change on the rate of interest by using equation (25) to get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]As [graphic href="?a1v23n53"][/graphic]is the rate of change on the rate of interest, then,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, [graphic href="?a1v23n53"][/graphic] is also determined by production growth due to the financial capital expectation and the rate of cost. In the short-term, it is probably [graphic href="?a1v23n53"][/graphic], which will be reflected in equation (30). [/p]


[/subsec][subsec][sectitle]Return on producer's capital[/sectitle]


[p]Additionally, if producers are paying [graphic href="?a1v23n53"][/graphic] to financial resource [graphic href="?a1v23n53"][/graphic], it is clear that [graphic href="?a1v23n53"][/graphic] represents the opportunity cost [graphic href="?a1v23n53"][/graphic] for using its own capital as capital resource.2 This is to say that producers will attain a net rate of profit [graphic href="?a1v23n53"][/graphic]. By deducing equation (18) or (19) from equation (21), we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By multiplying both sides of equation (31) by [graphic href="?a1v23n53"][/graphic], we get the producer's net profit [graphic href="?a1v23n53"][/graphic] as follows:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Then, by equation (8),[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By replacing [graphic href="?a1v23n53"][/graphic], we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Now we found in equation (32) that the interest [graphic href="?a1v23n53"][/graphic] owed to financial resource and the interest as opportunity cost [graphic href="?a1v23n53"][/graphic] appear as [graphic href="?a1v23n53"][/graphic], so,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]To prove the result given by equation (33), we deduce equation (32) from equation (18) as follows:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By simplifying,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and then,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Consequently,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and after rearranging that result,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Due to [graphic href="?a1v23n53"][/graphic], we get equation (33) again.[/p]
 
[p]Thus, the minimum return expected by producer's own capital is what they could receive from financial capital at [graphic href="?a1v23n53"][/graphic].3  Minimum return can be estimated by operating on equation (33) as follows: [/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]So, by equation (3), [graphic href="?a1v23n53"][/graphic], and replacing it in the previous equation we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Now let [graphic href="?a1v23n53"][/graphic] be the producer's own capital, so,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]and ì is the minimum rate of return expected for producers and is equal to the rate of interest. By operationalizing, we find the minimum return expectation for producers as follows:[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]By deriving equation (34), we obtain the changes in return due to changes on [graphic href="?a1v23n53"][/graphic]. So, [/p]
[p][graphic href="?a1v23n53"][/graphic] [/p]
[p]Let [graphic href="?a1v23n53"][/graphic] the rate of change on producer's own capital, and at the rate of change on the rate of interest [graphic href="?a1v23n53"][/graphic], we have[/p]
[p][graphic href="?a1v23n53"][/graphic] So, [graphic href="?a1v23n53"][/graphic][/p]
[p]And by equation (34), we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Then, let [graphic href="?a1v23n53"][/graphic] be the rate of change on the rate of return expected by producers, and thus,[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]In equation (35), we show that the rate of change on the rate of return depends on the rate of change on the rate of producer's own capital and the rate of change on the rate of interest. This equation is the counterpart of equation [graphic href="?a1v23n53"][/graphic]. [/p]
[p]Let us see some extreme calculations as an academic matter; first, if [graphic href="?a1v23n53"][/graphic], then of course [graphic href="?a1v23n53"][/graphic]. Second, if [graphic href="?a1v23n53"][/graphic], then [graphic href="?a1v23n53"][/graphic]. Third, if [graphic href="?a1v23n53"][/graphic], then [graphic href="?a1v23n53"][/graphic]. Between these two last points, some combinations appear to show [graphic href="?a1v23n53"][/graphic] defining [graphic href="?a1v23n53"][/graphic]. These arrangements will not necessarily illustrate straight or curved lines but rather a cyclical situation, depending on economic dynamic. If [graphic href="?a1v23n53"][/graphic] rises at a different [graphic href="?a1v23n53"][/graphic], the expectation of the rate of return could be lower than [graphic href="?a1v23n53"][/graphic] and producers could be motivated to invest their own capital. This means that producers could have a lower opportunity cost investing their own capital over a loan. In a case like this, producers would retain a great amount of profit by using their own capital rather than loans. [/p]
[p]By equalizing equations (35) and (15), by replacing [graphic href="?a1v23n53"][/graphic]in equation (35), we can illustrate different situations in an economy.[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]And after operating on equation (15) and substituting the result in the previous equation, we get[/p]
[p][graphic href="?a1v23n53"][/graphic][/p]
[p]Thus, the expectation of producers on its own capital will depend on changes to financial capital expectations on [graphic href="?a1v23n53"][/graphic]. [/p]
[p]Supposing [graphic href="?a1v23n53"][/graphic], ceteris paribus, during certain periods does mean that [graphic href="?a1v23n53"][/graphic] remains constant in that period. This also signifies in equation (25) that [graphic href="?a1v23n53"][/graphic] stay constant, which at the same time means that by equation (30), no changes occur in the economy. But [graphic href="?a1v23n53"][/graphic] could change at the constant [graphic href="?a1v23n53"][/graphic] and thus by equation (35), [graphic href="?a1v23n53"][/graphic]. So, it is possible, ceteris paribus, for producers to use loans to finance maintaining or replacing [graphic href="?a1v23n53"][/graphic], for instance, at the regular [graphic href="?a1v23n53"][/graphic]. If, ceteris paribus, it happens [graphic href="?a1v23n53"][/graphic], then [graphic href="?a1v23n53"][/graphic]. If the economy is stable, financial capital could change their propensity [graphic href="?a1v23n53"][/graphic] on constant [graphic href="?a1v23n53"][/graphic] and so [graphic href="?a1v23n53"][/graphic] will change, as suggested by equations (25) and (30).[/p]


[/subsec][/sec][sec sec-type="conclusions"][sectitle]Conclusions[/sectitle]


[p]Financial capital is an amount of money that indirectly participates in production growth. As financial capital becomes a financial resource, it contributes to production growth and in the generation of profit. It is as a financial resource that financial capital participates in production cost. Interest rate is a ratio of the rate of profit and the means by which financial resource participates in profit. Financial resource contributes to production growth and thus in the generation of profit. Periodically, producers pay financial capital an amount of money as interest which is a part of profit. Interest is just a name that a portion of profit assumes when it must be paid to financial capital. Together, financial capital and interest becomes the producer's debt.[/p]
[p]So, changes in production cost must reflect changes in loans by means of the rate of change on a loan. This rate is an indicator of the participation of financial resources and producers in production growth and profit. These facts are revealed by the value of production and the rate of debt growth. In the long run, the rate of change on interest will depend on the rate of production growth and also on the technical feasibility, technological feasibility, and financial capital propensity on profit. For these reasons, the rate of profit could change, but it is less probable than the rate of interest. It would be due to the fact that the rate of profit is also influenced by market prices and rivalry intensity. So, the rate of interest as a ratio of the rate of profit could not vary by changes in the rate of profit. This explains why the rate of return of producer's own capital could change from time to time.[/p]
[p]We propose to have found different theoretical results with respect to those we know about harmonizing concepts and its fundamentals. Futures investigations must contribute to improving this analysis on production growth and financial capital participation. So, this study would be a useful contribution to enrich on the economic theory debate. [/p]

[p]Notas[/p]
[p]2 Keynes (1936, p.40) assumed a different criterion for defining user and supplementary cost, and normal profit in the long-period, introducing the interest cost and the third term he called risk-cost. [/p]
[p]3 It is not an equalizing rate as Fischer (1930, p. 55) defined as rate of return over cost which it is but also an average rate of interest. However, we can state that  measures the minimum return of profit expected by producers on their own capital. That is to say: [graphic href="?a1v23n53"][/graphic] then [graphic href="?a1v23n53"][/graphic]. If [graphic href="?a1v23n53"][/graphic] appropriate enough to their [graphic href="?a1v23n53"][/graphic] prospect, producers will probably wish to use loans. So, by comparing [graphic href="?a1v23n53"][/graphic], producers could decide on using credit and own capital or only their own capital.[/p][/sec][/xmlbody]


[refs][sectitle]References[/sectitle]


[ref id="r1" reftype="book"][authors role="nd"][pauthor][surname]Fisher[/surname], [fname]I.[/fname][/pauthor][/authors] ([date dateiso="19300000" specyear="1930"]1930[/date]). [source]The Theory of Interest[/source]. Retrieved from [url]http://files.libertyfund.org/files/1416/Fisher_0219.pdf[/url][/ref]
[ref id="r2" reftype="book"][authors role="nd"][pauthor][surname]Jehle[/surname], [fname]A.[/fname][/pauthor], & [pauthor][surname]Reny[/surname], [fname]J.[/fname][/pauthor][/authors] ([date dateiso="20110000" specyear="2011"]2011[/date]). [source]Advanced Microeconomics Theory.[/source] Retrieved from [url]https://www.amazon.com/Advanced-Microeconomic-Theory-Geoffrey-Jehle/dp/0273731912[/url][/ref]
[ref id="r3" reftype="book"][authors role="nd"][pauthor][surname]Keynes[/surname], [fname]J.[/fname][/pauthor][/authors] ([date dateiso="19360000" specyear="1936"]1936[/date]). [source]The General Theory of Employment, Interest, and Money[/source]. Retrieved from [url]https://cas2.umkc.edu/economics/people/facultypages/kregel/courses/econ645/winter2011/generaltheory.pdf[/url][/ref]
[ref id="r4" reftype="book"][authors role="nd"][pauthor][surname]Robinson[/surname], [fname]J.[/fname][/pauthor][/authors] ([date dateiso="19530000" specyear="1953-1954"]1953-1954[/date]). [source]The Production Function and the Theory of Capital. Review of Economics Studies[/source], [volid]21[/volid]([issueno]2[/issueno]), [pages]81-106[/pages]. Retrieved from [url]https://pdfs.semanticscholar.org/c70f/61352de7ee1641f0bc456639108c85029013.pdf[/url][/ref]
[ref id="r5" reftype="journal"][authors role="nd"][pauthor][surname]Villalobos[/surname], [fname]D.[/fname][/pauthor][/authors] ([date dateiso="20150000" specyear="2015"]2015[/date]). [arttitle]Production Cost, Prices and Income of Firms[/arttitle]. [source]Economía y Sociedad[/source], [volid]20[/volid]([issueno]48[/issueno]), [pages]1-17[/pages]. doi: [pubid idtype="doi"]http://dx.doi.org/10.15359/eys.20-48.1[/pubid][/ref][/refs][/doc]


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Economía y Sociedad, Vol. 22, Nº 52 Julio-diciembre 2017, pp. 1-22
EISSN: 2215-3403 URL http://www.revistas.una.ac.cr/economia


1
El manuscrito pre-publicación es una versión aceptada del artículo previo al proceso final de edición, diagramación y revisión, por lo que puede diferir de la versión final publicada.

Daniel Villalobos Céspedes

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Creado a partir de la obra en http://www.revistas.una.ac.cr/index.php/economia