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Inframarginal Models of Spatially Allocated Economic Structures and the Analysis of Production Processes

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Inframarginal Models of Spatially Allocated Economic Structures and the Analysis of Production Processes R-ECOMONY, 2018, 4(2), 72–78 doi: 10.15826/recon.2018.4.2.011 Original Paper doi: 10.15826/recon.2018.4.2.011 Inframarginal models of spatially allocated economic structures and the analysis of production processes Dmitry S. Petrenko Regional Development Center Ekaterinburg, Central Bank of the Russian Federation, Ekaterinburg, Russia; e-mail: [email protected] ABSTRACT KEYWORDS The article discusses designing of labor division networks. Designing of the inframarginal analysis, technology, economic structure of labor division constitutes the main part of infram- division of labor, network effects, aginal analysis. Inframaginal analysis normally uses predefined economic economic structures, regional structures, which means that in certain cases some economic structures economy may be neglected. Such inaccuracies may be not important in the analy- sis of small enterprises but in the analysis of spatially allocated economic structures, some important aspects may be left unnoticed, which will lead to wrong decisions regarding labor allocation. To make an enterprise compet- itive it is essential to understand what is the optimal economic organization and the form of labor division in the given region. If some economic struc- tures are not taken into account in the analysis, the general equilibrium FOR CITATION will be incorrect, which will negatively affect the decision-making. If we use Petrenko, D. S. (2018) inframarginal models to analyze the production process, it will allow us to Inframarginal models of spatially take a fresh perspective on the problem. All possible structures of the divi- allocated economic structures sion of labor are designed by using production factors and goods to reduce and the analysis of production the risk of errors in the process of decision-making, which will make the processes. R-economy, 4(2), 72–78. production process of the enterprise more efficient. doi: 10.15826/recon.2018.4.2.011 Инфрамаргические модели пространственно разнесенных экономических структур и анализ производственных процессов Д. С. Петренко Региональный центр развития «Екатеринбург», Центральный Банк Российской Федерации, Екатеринбург, Россия; e-mail: [email protected] РЕЗЮМЕ КЛЮЧЕВЫЕ СЛОВА В статье обсуждается проектирование сетей разделения труда. Проек- тирование экономической структуры разделения труда составляет ос- инфрамаргинальный анализ, новную часть инфрамагинального анализа. Инфрамагинальный анализ технологии, разделение обычно использует предопределенные экономические структуры, а это труда, сетевые эффекты, означает, что в некоторых случаях некоторыми экономическими струк- экономические структуры, турами можно пренебречь. Такие неточности могут быть не важны при региональная экономика анализе малых предприятий, но при анализе пространственно распре- деленных экономических структур некоторые важные аспекты могут остаться неучтенными, что приведет к неправильным решениям отно- сительно распределения рабочей силы. Чтобы сделать предприятие кон- курентоспособным, важно понять, что является оптимальной эконо- мической организацией и формой разделения труда в данном регионе. Если в анализе не учитываются некоторые экономические структуры, FOR CITATION общее равновесие будет неверным, что негативно скажется на процессе Петренко, Д. С. (2018) принятия решений. Если мы используем инфрамаргинальные модели Инфрамаргические модели для анализа производственного процесса, это позволяет нам взглянуть пространственно разнесенных на проблему с новой точки зрения. Все возможные структуры разде- экономических структур ления труда разработаны с использованием факторов производства и и анализ производственных товаров для снижения риска ошибок в процессе принятия решений, что процессов. R-economy, 4(2), 72–78. сделает производственный процесс предприятия более эффективным. doi: 10.15826/recon.2018.4.2.011 72 www.r-economy.ru Online ISSN 2412-0731 R-ECOMONY, 2018, 4(2), 72–78 doi: 10.15826/recon.2018.4.2.011 Introduction The transaction cost coefficient is 1− k, k is viewed There are two types of business decisions: as a transaction service and depends on the quan- decisions associated with the choice of activity tity of labor used in transactions. As a service, it and decisions of resource allocation. Decisions can be self-provided or purchased on the market: of the first type can be illustrated by the choice k = rc + rd. of majors students make when entering the uni- In this case, rc and rd as transaction services versity. These are inframarginal decisions. Then relate to the distance between a pair of trade students choose the courses they want to study partners and their location problems. All indi- and decide on the time they want to spend on viduals are evenly spaced and the distance be- each of the learning courses. These are decisions tween each pair of neighbors is a constant. The of the second type – marginal decisions of time distance between a pair of trade partners may allocation. In the context of the division of la- differ from the distance between a pair of neigh- bor, inframarginal decisions are more important bors. For example, they can be engaged in rural than marginal decisions. or urban relations. In most cases of inframarginal analysis, a The utility function is identical for all individ- set of economic activities which can be chosen uals and has a form of the Cobb-Douglas utility by individuals is set exogenously and infram- function [5, p. 337]: arginalists are concerned with the problem of αβ mathematical optimization of utility functions ux=[(c ++ rrx cdd )] [ y c ++ ( rry cdd )]× [4, p. 14]. The set of economic activities which × ++ γ can be used in the division of labor is usually [(zc r c rz dd )] . limited and well known. In real life, however, The set of activities known to an enterprise managers have enough practical experience to describes the technical opportunities of this en- determine the optimality of particular structures terprise. This set is called technology and is desig- of the division of labor in various cases. Complex nated by symbol T [7, p. 43]. and specific results of inframarginal articles are Therefore, technology can be written the fol- not practically useful for the decision-making lowing way: process, which leads to a situation when “infra- marginalists write papers mainly for inframar- −l ginalists” [6, pp. 177]. x The technology-oriented theory of produc- tion can be divided into function analysis and ac- T==y | l 1, xyz , , ≥ 0 . tivity analysis depending on the object of analysis z [1, p. 1055]. Inframarginal analysis is based on r activity analysis, proposed by Koopmans. Func- tion analysis was introduced by Fandel [7, p. 41] Labor restrictions are equal for all economic to find the types of possible economic structures agents and can be written as: in the process of inframarginal analysis. Activity llll++ += 1, was defined by Koopmans as “the combination of xyzr certain qualitatively defined commodities in fixed li ∈[0,1,] quantitative ratios as ‘inputs’ to produce as ‘out- i = xyzr, , , . puts’ certain other commodities in fixed quantita- tive ratios to the inputs” [9]. Using the theorem of optimum configuration ‘the optimum decision does not involve selling Method and model more than one good, does not involve selling and Let us now consider the asymmetric mod- buying the same good, and does not involve buy- el with trading activities and heterogeneous pa- ing and producing the same good’ [11], we can rameters introduced by Yang [13, pp. 111]. In the find vectors of activities for technology T. model of specialization, there are three types of The producer-consumer uses only one pro- goods x, y, and z. The number of goods which are duction factor l (labor) in the production pro- sold on the market have index s. The number of cesses. The economic agent can produce a good goods which are purchased on the market have only for their own consumption xc or produce index d. The self-provided goods have index c. an additional part of the good for sale in order 73 www.r-economy.ru Online ISSN 2412-0731 R-ECOMONY, 2018, 4(2), 72–78 doi: 10.15826/recon.2018.4.2.011 to purchase other types of goods that the eco- Results nomic agent does not produce on their own xs. The simplest case is autarky: an individual If the economic agent does not produce a good self-provides three goods. Therefore, the num- and purchases the good on the market, we put 0 ber of goods sold and purchased and the number (zero) in the activity vector. of transaction services are 0. The technology has All the possible activities vectors can be writ- only one activity vector ten the following way: −l −−ll x c xx cc T = y . c yycc, zc zzcc r 0 0 c −−−−−lllll−l The utility function can be written as: xx+++ xx xx 0 x x cs cs cs c c u=> xyzα βγ 0. 0 ,,,,yc y c yy cs++ yy cs, yycs+ c cc zc00 zzcc zc In this case only one activity vector is sufficient rrcc0 rrcc 0 to achieve a positive value of the utility function and −−−−−−llllll there is no network of labor division. The pattern of 00 xx xx labor division is shown as a graph [2] in Figure 1. cc cc yc ,00 , yycc ,, , yc zz+++ zz zz z z 0 [y] A [x] cs cs cs c c rc r c 0 rrcs+++ rr cs rr cs T′ = . −−−−−−llllll [z] xx+++ xx xx x 00 cs cs cs c Figure 1. Autarky 00 ,,,,,yc yycs+++ yy cs yy cs 00zz0 0 cc Activities rr 0000 cc−−ll − l −−− lll −−−−−− ll llll x 0 0x 00 xxcs++ xx cs 00xc xc c c 00 ,,,,,y yy++ yy y 0 , ycc ,00 ,,y , 0 c cs cs c zz+ zz++ zz 00z z 00z zz++ zz cs cs cs c c c cs cs 0 0 r rr+++ rr rr c cs cs cs rrc c r c rrr c cc −−−lll −l exist in cases of partial division of labor. In this xx+ 00 x cs c + case an individual sells one of the produced goods 00 ,,yycs , yc and purchases one of the goods for consumption.
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