=Paper=
{{Paper
|id=Vol-2667/paper19
|storemode=property
|title=Analysis of monopolistic competition in consumer goods markets with credit sales
|pdfUrl=https://ceur-ws.org/Vol-2667/paper19.pdf
|volume=Vol-2667
|authors=Michael Geraskin,Olga Kuznetsova
}}
==Analysis of monopolistic competition in consumer goods markets with credit sales ==
https://ceur-ws.org/Vol-2667/paper19.pdf
Analysis of Monopolistic Competition in
Consumer Goods Markets with Credit Sales
Michael Geraskin Olga Kuznetsova
Department of mathematical Department of mathematical
methods in Ecnomics methods in Ecnomics
Samara National Research University Samara National Research University
Samara, Russia Samara, Russia
innvation@mail.ru olga_5@list.ru
Abstract—The article considers the problem of the calculated further during the simulation, and they are
monopolistic competition in markets, which are interconnected presented in this figure to illustrate the possible scale of the
within a vertically integrated system of retailers, banks and system.
insurers. The system is organized to increase in the sale
volumes of consumer goods by means of the credit tools, and it
includes three levels. The retailers’ level corresponds to the
sale of goods, the banks’ level is related to the lending
transactions and the insurers’ level credit corresponds to the
insurance. There are a great number of competing firms
(hereinafter, agents) at each level of the system. The formulas
for calculating the maximum possible number of agents at each Fig. 1. Diagram of agents in the household appliances sale system.
level are derived. The simulation of the competition is carried
out on the basis of the household appliances market. We introduce the following definitions. The agent’s
environment includes the agents of the system excepting this
Keywords—integrated economic systems, retailer, bank, agent [20, 10]. If the agent’s utility (profit) function depends
insurance, demand kurves, interconnected markets on his own action and on the environment’s actions, then the
system is strongly connected [21]. In particular, in the
I. INTRODUCTION “retailer-bank-insurer” system, the agents’ costs are
Integrated economic systems [1, 2 ] are formed, when the interdependent (i.e., inseparable), therefore, the system
buyer's need for one product is due to the fact of the another stability is ensured by mutual payments (commissions,
product need. The “retailer-bank-insurer” system is a typical discounts, etc.). Agents’ revenues can be interdependent,
example of such integration [3]. In this case, the integrated when the system has a mechanism for distributing the
system is organized within the framework of the retailer’s aggregate utility [4,13]. In this case, the utilities of the agents
credit turnover. On the one hand, the demand for the are transferable [5, 6,]. The vertically integrated system that
expensive goods encourages the buyers to borrow loans in contains one agent at each level was considered in [14].
the banks. Then, the banks encourage the buyers to insure
theirs solvency. On the other hand, the possibility of As a consequence of the agents heterogeneity in the
obtaining the credit resources expands the demand for the terms of economic activity, the problem of coordinating the
expensive goods. Thus, the desire to increase in the demand agents’ interests in the integration process arises. If the
leads to an emergence of the integrated system [16]. Such agent’s good initiates the demand for goods of other agents,
integrated system arises in the process of selling the he is characterized by predominant economic activity and he
household appliances. is named as a meta-agent. In addition, the meta-agent has
information about the true utility functions of other agents or
At the state level, we consider the interaction between the theirs utility values.
following markets: the household appliance retail market, the
banking market and the insurance market. In the Russian The meta-agent can choose the distribution mechanism of
Federation, the economic system consists of 451 banks, 232 the aggregated integration effect in the system [7, 8]. In the
insurance companies [17] and more than 20 retail chains of “retailer-bank-insurer” system, the meta-agent is a retailer.
household appliances sellers [18]. For example, the Eldorado The Pareto-efficient [11] algorithm for the distribution of the
network consists of 328 branches [19], the M-Video network transferable utility for such strongly connected system [9]
consists of more than 358 branches. The relationship was developed in [15]. Our study considers the “retailer-
between the retailers, the banks and the insurers is bank-insurer” system, in which three levels correspond to the
demonstrated in Fig. 1. sale of goods (i.e., retailers), the transaction lending (i.e.,
banks) and the loan insurance (i.e., insurance companies),
In Fig. 1, we introduce the following designations: N is respectively. The initiator of integration in such system is the
the actual number of the retailers in the market, M is the retailer, because he has the greatest amount of resources for
actual number of the banks in the market, P is the actual distribution. Because the bank’s sales volume depends on the
number of the insurance companies in the market, Nmax is the retailer’s sales volume, the banking system is the second
maximum number of the agents in the retail market, Mmax is level of the interaction. Additionally, the insurer’s sales
the maximum number of the agents in the banking services volume depends on the bank’s sales volume, therefore, this is
market, Pmax is the maximum number of the agents in the the third level of the interaction. There are great numbers of
insurance market, Ri is the i-th agent in the retail market, Bi is competing firms at each level of the system. In this case, a
the i-th agent in the banking market, Ii is the i-th agent in the situation of the monopolistic competition arises at each level.
insurance market, indicates the agent’s affiliation to a The competition is monopolistic, because the firms’ products
particular market. The maximum numbers of the agents are differ in quality characteristics, that makes them different.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)
Data Science
Consequently, the agent’s sales volume depends on his own equal to the market capacity. The utilities (profits) of the
price and on the prices of the competitors. agents are calculated by using the following formulas:
Fig. 2 shows the interaction scheme in an integrated k (Q k ) a k Q k
Cv k Q k Cf k k {R , B , I}
bk 1
(1) i
system with many agents at each level. i i i i i i i
where πki(Qki) is the agent’s profit function; aki, bki are
The strong integration relationship occurs when the i-th coefficients of the price function of the i-th agent in the k-th
agent of the upper level interacts with the j-th agent of the market; K is the set of agents; k are the elements of the set
lower level. If the i-th agent of the upper level interacts with K, and k{R˅B˅I}; k R is the retail market, k B is the
several agents of the lower level or vice versa, the integration banking services market, k I is the insurance services
relationship is weak, because in this case the agent may market; Qk is the sales volume of the i-th agent in the k-th
choose the agents’ set at other levels for the interaction. market; Cvki is the direct cost per unit of goods of the i-th
If N is equal to 1, then the retail market is characterized agent in the k-th market, Cfki is the constant cost of the i-th
as a monopoly of the retailer. If M is equal to 1, then the agent in the k-th market.
banking services market is characterized as the bank’s We introduce the following assumptions.
monopoly. If P is equal to 1, then the insurance market is
characterized as a monopoly of the insurance company. If N, 1) The market capacity is defined as the total maximum
M, P are greater than 1, then these markets are defined as the sales volume of firms in the market.
monopolistic competition, and the occupied markets shares 2) The agents act in monopolistic competition markets,
are determined by the price ratio of the competitors. then the inverse demand functions are described by the
power functions
bk
p k a k Q k i , a k 0, bk 0, bk 1, k K
i i i i i i
where pki is the price of the i-th agent’s goods in the k-th
market.
We consider the following problem: to search for the
maximum number of agents Nmax, Mmax, Pmax that can
operate in the retail market, the banking market and the
insurance market, respectively, provided that non-negative
profit is achieved, i.e., the following inequalities hold
N
R ( Q R ) 0 Q Ri Q R (2)
Fig. 2. Scheme of agents interaction in system. i i
i 1
M
monopolistic competition, direction of vertical
B ( Q B ) 0 Q Bi Q B (3)
integration, Ri is the i-th retailer, Bi is the i-th bank, Ii is the i i
i 1
i-th insurer P
The following notation is used in Figure 2: LF (lending I (Q I ) 0i i Q Ii
QI (4)
fee) is a premium that the retailer pays to the bank, if the i 1
bank’s loans quantity corresponds to the retailer’s need; OF where πRi, πBi, πIi are the profits of companies in the retail
(operating fee) is the rent that the bank pays to the retailer market, the banking market and the insurance market,
for the right to participate in the integration; EF (exposure respectively; QRi, QBi, QIi are the sales volume of the i-th
fee) is the premium that the insurance company pays to the agent in these markets, respectively; QRΣ, QBΣ, QIΣ are the
bank, if the bank allows the insurer to sell his product (i.e., capacity in these markets, respectively.
to participate in the integration) by introducing the
compulsory credit insurance conditions. III. RESULTS
In each market, the agent is the i-th firm, therefore, we
Thus, our contribution consists of the following items.
use the designation ki where i (1,…,N) for k R, i
First, we investigate the interconnected markets with great
numbers of agents. Second, we calculate the quantitative (1,…,M), for k B, i (1, … , P) and for k I.
estimates of these markets, i.e. the maximum numbers of Accordingly, the firm achieves a non-negative profit in
agents. the following range
II. METHODS AND MATERIALS Q k Qk Q k
i i i
The market is described as a set of existing and potential
consumers, producers, intermediaries, which enter into where Q k , Q k , are the minimum and the maximum sales at
i i
relationships for the purpose of purchase, sale and which the i-th firm in the k-th market obtains the non-
consumption of goods and services. The market capacity negative profit. The boundaries of this interval are the sales
refers to the value of goods that consumers can purchase at volume in the firm’s break-even point (i.e., the profit is
the current price. The market capacity is a function of the zero).
product price. The market size is the value of goods that all
firms can offer at the current price. The total sales volume is k (Q i ) 0 , k (Q i ) 0 .
i i
determined by the prices set in the market; it is less than or
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 81
Data Science
The profit function has two points, which correspond to The aggregate demand curve of the retailer market is
this requirement, therefore, based on the conditions for the described by the following demand function
maximum number of firms in the market, we define pR(QR)=52812Q-0,067.
According to formula (1), the retailer’s profit function
Q k min{ Q k , Q k }
0
(5) has the form:
i i i
0
where Q ki is the minimum sales volume at which the i-th πRi (QRi)=49000QRi0,91-12500QRi-200000000.
firm in the k-th market obtains the non-negative profit. The capacity of the retail market is determined by rule
A substitution of (5) in (2), (3), (4) yields (6), and it is equal to 40054097 units.
From Fig. 4, it is obvious that the retailer’s profit is zero
Qk Qk
0
i
(6) at two points. The retailer’s profit function enables us to
and restrictions (2) - (4) taking into account (1) have the determine the retailer’s break-even point, and, accordingly,
following form: the sales volume interval in which the firm makes the non-
negative profit. A numerical solution of equation (9) for the
bk 1
ak Qk i Cv k Q k Cf k 0 (7) retail market demonstrates that Q i is 28 thousand units.
i i i i
We rewrite (6) as follows Based on the assumption of the firm identity in the retail
market, according to (10), the maximum number of firms in
Q
0
k
Q k p max 0
. (8) the retail market Nmax is equal to 76112.
0
In this case, the price p max is calculated as a maximum
of all firms’ prices in this market:
max
0
𝑝max = 𝑝 (𝑄 0 )
𝑘 ∈ 𝐾 𝑘𝑖 𝑘𝑖
The formula for calculating the minimum sales volume at
a break-even point of the firm is obtained from the following
equation
Fig. 4. Retailer’s profit curves.
bk 1
k (Q k ) a k Q k i
Cv k Q k Cf k 0 , (9) On the basis of the banking market data in 2017-2019
i i i i i i
and this equation has only numerical solution. [17] the aggregate demand curve of the banking market is
derived. Fig. 5 presents the statistics of three banks and the
If all firms in the k-th market have the different type aggregate demand curve.
parameters Cvki, Cfki, then the solution to problem (2) - (4) is
calculated by cumulative summation of the values Q0ki and
calculating the number of firms, then restrictions (2) - (4)
satisfy:
Qk
N max (10)
0
Qk
i
Qk (11) Fig. 5. Banks’ demand curves.
M max 0
Qk
i
The aggregate demand curve of the banking market is
Qk described by the demand function of the following form:
P max (12)
0
Qk
i pB(Q)= 4168QBi-0.36
Thus, we make formulas (10)-(12) for calculating the The capacity of the banking market is determined by rule
maximum numbers of the firms in interconnected markets. (6), and it is equal to 4147830 million contracts.
IV. NUMERICAL EXPERIMENT According to formula (1), the bank’s profit function has
the form:
The aggregate demand curve of the retailer market (Fig.
3) is derived on the basis of the statistical information about πBi(Q)=4168QBi0.63-0.053QBi-1000000
the firms’ activities in the market in 2017-2019 [18, 19]. The From Fig. 6 it is obvious that the profit of the bank at
parameters of the demand function are calculated similarly to two points is zero. The bank’s profit function allows us to
the procedure [16]. determine the bank’s break-even point, and, accordingly, the
sales volume interval of the non-negative profit. A
numerical solution of equation (9) for the banking market
shows that Q j is equal to 5.4 thousand loans.
Based on the assumption of the firms identity in the
bank’s market, from (11) it is possible to determine the
maximum number of the firms under the non-negative profit
condition. The maximum number of firms Mmax is equal to
Fig. 3. Retailers’ demand curves.
768115876.
The aggregate demand curve of the insurance market is
derived based on the insurance statistical data in 2017-2019
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 82
Data Science
[17]. Fig. 7 presents the statistics of three insurance for calculating the quantitative estimates of these markets,
companies and the aggregate demand curve. i.e. the maximum numbers of agents.
In practice, this technique provides a guideline for firms,
when they choose the market entry strategy. If in the market,
the number of firms reaches the maximum, then the entry of
a new firm into the market is disadvantageous, because it
may not achieve the non-negative profit.
In addition, we calculated the following specific results
for the analyzed markets. The retailer has the non-negative
profit when selling a product in the range from 28800 to
Fig. 6. Bank’s profit curve.
3650000 units. The bank achieves the non-negative profit in
the range from 5400 to 33411100 million loans. The insurer
obtains the non-negative profit in the range from 63655 to
930000 units. The maximum number of firms in the retail
market, in the banking services market and in the insurance
market are 1390 units, 76811587 units and 2736 units,
respectively.
REFERENCES
[1] S. Paltsev, E. Monier, J. Scott, A. Sokolov and J. Reilly, “Integrated
Fig. 7. Demand curves of insurers. economic and climate projections for impact assessment,” Climatic
Change, pp. 21-33, 2015.
In the insurance market, the aggregate demand curve is [2] O. Ellabban and A. Alassi, “Integrated Economic Adoption Model
described by the following demand function for residential grid-connected photovoltaic systems: An Australian
case study,” Energy Reports, vol. 5, pp. 310-326, 2019.
pI(Q)=0.6079Q-0.163 [3] P. Bolton and M. Dewatripont, “Contract Theory,” Cambridge: MIT
The capacity of the insurance market is determined by Press, 2005.
rule (6), and it is equal to 4524764 contracts. [4] K.M. Ortmann, “Fair allocation of capital growth,” Operational
Research, vol. 6, no. 2, pp. 181-196, 2016.
According to formula (1), the insurer’s profit function [5] J.W. Hatfield, S.D. Kominers, A. Nichifor, “Stability and
has the form: competitive equilibrium in trading networks,” Journal of Political
πIi(Q)=0.5107QIi0.834-0.05QIi -2000 Economy, vol. 121, no. 5, pp. 966-1005, 2013.
From fig. 8 it is obvious that the profit of the insurance [6] M. Ostrovsky, “Information Aggregation in Dynamic Markets With
company at two points is zero. Strategic Traders,” Econometrica, vol. 80, no. 6, pp. 2595-2647,
2012
[7] Z. Xu, Z. Peng, L. Yang and X. Chen, “An improved shapley value
method for a green supply chain income distribution mechanism,”
International journal of environmental research and public health,
vol. 15, no. 9, 2018.
[8] N. Hayashi and M. Nagahara, “Distributed Proximal Minimization
Algorithm for Constrained Convex Optimization over Strongly
Connected Networks,” IEICE Transactions on Fundamentals of
Electronics, Communications and Computer Sciences, p. 351-358,
2019.
[9] D. Wang, Z. Wang and W. Wang, “Distributed optimization for
Fig. 8. Insurer’s profit curve. multiagent systems over general strongly connected digraph,” 36th
Chinese Control Conference (CCC), 2017.
The profit function of the insurance company enables us [10] R. Shao and L. Zhou, ”Voting and the optimal provision of the
to determine the sales volume, which satisfies the zero profit public good,” Journal of Public Economics, vol. 134, pp. 3-41, 2016.
condition. A numerical solution of equation (9) for the [11] T. Wakayama and T. Yamato, “Comparison of the voluntary
contribution and Pareto-efficient mechanisms under voluntary
insurance market shows that Q s is 174142262 units. Based participation,” 2019, 143 p.
on the assumption of the firms identity in the insurance [12] Continuity and incentive compatibility in cardinal voting
market, according to (12), we determine the maximum mechanisms [Online]. URL: https: //papyrus.bib.umontreal.ca.
number of firms that can be in the market, in the case of all [13] H. Moulin, “Designing a single mechanism,” Theoretical
firms obtain non-negative profits. The maximum number of Economics, vol. 12, no. 2, pp. 587-619, 2017.
companies in the insurance market Pmax is 2736. [14] A. Ventura, K. Kafiero and M. Montibeller, “Pareto efficiency,
Coase's theorem and external effects: a critical look,” Economic
CONCLUSION Problems, vol. 50, no. 3, pp. 872-895, 2016.
[15] M.I. Geraskin, “Optimal mechanism for the distribution of the effect
We investigate the interconnected markets with great in an integrated strongly coupled system of anonymous agents with a
numbers of agents, such as the retail market, the banking transferable utility,” Problemy upravleniya, vol. 2, pp. 27-41, 2017.
market and the insurance market. Based on the statistical [16] M.I. Geraskin and V.V. Manakhov, “Optimization of interactions in
analysis of these markets, we prove that the aggregate a multi-agent, tightly linked "retailer-bank-insurer" system,”
demand is described by a power function. As a result, we Problemy upravleniya, vol. 4, pp. 9-18, 2015.
write in a similar form the profit functions of agents in these [17] Rating of banks and insurance companies [Online]. URL:
markets. The agent’s profit function has a maximum point https://www.banki.ru/insurance/companies/?page=29.
and two points with zero profit. Accordingly, the ranges of [18] Analytics on the market of household appliances and electronics for
non-negative profits are determined. An analysis of the 2017 - from smartphones to refrigerators [Online]. URL:
break-even point of the firm enable us to develop a technique
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 83
Data Science
https://www.shopolog.ru/metodichka/kompanii-i-rynki/analiz-rynka- [21] V.N. Burkov, I.I. Gorgidzeand D.A. Novikov, “Models and
bytovoy-tehniki-i-elektroniki-za-2017-god/. mechanisms for the distribution of costs and revenues in a market
[19] MAGAMAGNAT is portal about trade in Russia [Online]. URL: economy,” Moscow: ICS RAS, 1997.
http://megamagnat.ru/ts/86.html. [22] N.D. Morunov and D.L. Golovashkin, “Features of constructing
[20] D.A. Novikov, V.N. Burkov, M.V. Gubko and N.A. Korgin, block algorithms of the FDTD method when organizing
“Theory of management of organizational systems and other computations on a GPU using the MATLAB language,” Computer
sciences of organization management,” Problemy upravleniya, no. 4, Optics, vol. 43, no. 4, pp. 671-676, 2019. DOI: 10.18287/2412-6179-
pp. 2-10, 2012. 2019-43-4-671-676.
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 84