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ECONOMIC AND MATHEMATIC EVALUATION OF PRICE FLUCTUATIONS INFLUENCE ON ECONOMIC INTERESTS OF MARKET RELATIONS AGENTS
Ptashchenko L. O.
Doctor of Economic Sciences, Professor
Poltava National Technical Yuri Kondratyuk University, Ukraine
ARTICLE INFO
ABSTRACT
Received 20 October 2015 Accepted 27 October 2015 Published 30 October 2015
KEYWORDS
Governmental price
regulation,
Prices formation,
Price fluctuations,
Economic interests of market
relations agents,
Pricing policy
Economic and mathematical model of price fluctuations influence on economic interests of basic market relations agents (represented by state, enterprises and households) is built. Factors of influence on price fluctuations and agent's welfare decrease are determined. On a basis of calculation of Kendall's concordance coefficient, conclusions about links absence between economic interests of market relations agents (in conditions of prices formation and governmental price regulation) are formed.
© 2015 The Author.
Introduction. According to conditions of competition and crises, manufacturer's price has great importance for economic system. The importance of pricing management is growing, as it has significant impact on enterprise's activity efficiency and its market place.
The price is a tool of harmonization of different agent's interests. According to this, the investigation of market pricing mechanism has great theoretical and practical importance.
Review of research on the issue. Scientists of different countries investigated theoretical aspects of prices formation. Own views on this issue were expressed by John Berman, P. Doyle, F. Kotler, M. Porter, T. Nehl, V. Pinishko and others [1-3]. Theoretical aspects of pricing tools investigated in scientific papers of Adam Smith, David Ricardo, A. Marshall, K. Buzhymska, I. Bakushevych, A. Kolesnikov and hothers [4-6]. At same time, the question of ensuring of all interests of manufacturer's contractors in aspects of adequate pricing is still urgent. At the same, time governmental competitive policy has great importance in aspect of price regulation on socially important commodity markets.
Primary material description. The most important component of antimonopoly policy in most countries is the policy regarding the sectors of social use, which contain natural monopoly segments (electricity, telecommunications, railway transportation). As effective form of these sectors regulation, can be creation of conditions for formation of prices, which satisfy both producers and consumers.
The problem of pricing optimization, in aspect of satisfaction of interests of producers, consumers and state has great urgency for science.
Furtherly will try to build economic and mathematical model of evaluation of pricing factors impact in cond of itions of commodity markets. We must define the set of attributes that are important for the formation of the social economics in society. That supposes determination of degree of prices fluctuation vulnerability of such subjects of national
economy as state, businesses and households. Ranking of prices volatility impact on welfare decrease of national economy subjects is based on 10-point scale based on expert estimates (Table 1).
Table 1
Ranking of significance of prices volatility impact on economic state of national economy subjects
№ Impact factors of prices volatility on socially important commodity markets Ranking of prices volatility impact on welfare decrease of national economy subjects. points
State Enterprises Households
1 The unstable political climate in the country and inept management of national economy 4 3 3
2 The high level of the shadow economy and uncontrolled activity of oligopolies 5 2 3
3 Hyper inflationary processes in the national economy 2 4 4
4 The massive agiotage and increase of demand for the products 1 2 7
5 Price discrimination by the monopolies 1 6 3
6 Total points 13 17 20
Consistency of expert assessments is checked by determination of consent coefficient (E), which is a coefficient of multiple correlation formula:
H R
E =
i=i i=i
m2
Where m - the number of experts;
R - correlation coefficient of i and l experts assessments.
According to author's conception, economic interests, which appear in process of pricing regulation, are considered as a system of three agents - state, enterprises and households. Coordinates present their significance of values.
The analysis of assessments
a) All ranks must be Rj integers or multiples of 1/2;
b) ¿J ^; (■ = iv,m).
j=i 2
There can be used Spearman's rank correlation coefficient and Kendall's coefficient of concordance. Spearman's rank correlation coefficient is more reliable.
According to results of calculations. we may ascertain the fact that market relations agents are uncoordinated in aspects of pricing regulation on commodity markets.
Thus. economic interests. which are considered as a system of three agents - state. enterprises and households - are contradictory to each other (this statement displayed on a Fig. 1).
According to the problem formulation. we have condition. which results the following systems:
1) HH - HH (household);
2) HH - E (enterprise). E-E;
3) E - S (state);
4) HH. E - S.
5
2
■ State
□ Entrepreneurs
□ Households
Fig. 1. Systems of economic interest of market relations agents
Paired relations are checked every time by the test of Spearman. "Counterparties E" can be limited by the number of i = 1,2, ..., N. Costs of "counterparty E" cfy) are dependent on produced productyi (whereyi B[0,<x>)). The price of services is defined as X. The objective function of i «counterparty E» is represented by difference of its income Ei(yi) (where Ei(yi) = ky) and costs ci(yi):
This class of functions is useable for displaying of expenses dynamics of «counterparty E». There are following features of these functions:
- availability of fixed costs of pricing policy implementation;
- the price growth is accompanied by a value decrease of unit costs before the fracture point achievement, after which their increase begins.
Four mechanisms are proposed for discussion, which are mentioned above. Comparison of economic motivation is prepared by using of following parameters:
- F (y) - utility function «counterparty C»;
- Y (y) - the result of actions of «counterparties E»;
- Fi (yi) - profit of the i-th «counterparty E»;
- W (y) - the sum of target functions of system participants. 1) Utility function «counterparty C»
(1)
In a process of further model building the following class functions will be used:
(2)
(3)
Differentiate formula (3) ony,0 and equate the result to zero:
(4)
According to the last expression, the following can be obtained:
(5)
It is obvious, that the maximum of «counterparty E» utility function can be achieved only in one case (5):
According to the said, the total amount of utility functions of all participants in the system is defined by formula below:
Spearman's rank correlation coefficient calculations confirm the lack of interrelation between the interests of market relations contractors (Table 2).
Table 2
The impact of price fluctuations on the economic interests of market relations agents
Pressure on price fluctuations on socially important commodity markets Ranking of price fluctuations impact on welfare reduction of national economy entities, points Comparison of ranks The sum of lines Squares amounts
№ State Entre prene urs Househ olds Rx Ry Rz di Y d
1 State political instability and inept national economy management 4 3 3 4 3 2 9 81
2 High level of shadow economy and uncontrollable activities of oligopolies 5 2 3 5 1,5 2 8,5 72,25
3 Hyperinflationary processes in the national economy 2 4 4 3 4 4 11 121
4 The massive hype and increase of demand for the products 1 2 7 1,5 1,5 5 8 64
5 Price discrimination on the part of monopolies 1 6 3 1,5 5 2 8,5 72,25
6 Total points 13 17 20 15 15 15 45 410,5
7 for Kendall's coefficient
The calculation of amount Spearman's coefficient for Yd2 = Lu xyi Yd2. = ¿-I il kd Yd2-(Yd)2/«=
26,5 22,5 26,5 5,5
8 Coefficients Spearman -0,325 -0,125 -0,325 Kendall 0,061111
9 Assessment of significance Using Student's Criterion Pearson's Criterion
10 Investigated criterion value -0,768 -0,282 -0,768 %kp 0,733333
11 Critical values 0,7649 0,7649 0,7649 II 9,487729
=1 _ 6-M.
Ryz = 1 - 3
y n - n
According to formula, results of calculations are following:
6-y d2
Ryz = 1--^ = -0,125
y n - n
Evaluation of Spearman's rank correlation coefficient %2 Investigated value is equal to:
tP= RtP"2 =-0,282.
P - r2 '
According to the received results of calculations, an extremely weak inverse interrelation between enterprises and households is determined. That fact is proved by Spearman's coefficient, which values are statistically insignificant. Analogically, calculations for other systems are the same (for HH - EE, EE - EE).
The calculation of «Counterparty S» utility function is similar to (7):
In this case the economic motivation mechanism involves the following points:
(8)
Total sum of utility functions of all participants has the following form:
Thus, the total sum of utility functions of all system participants has the following
form:
S-EE ' ^
In this case, provision of pricing services is logical at the price equal to X, excluding some normative y. This normative reflects the proportion of «counterparty E» income transmitted to «counterparty S» as a return of profit (of VAT). Normative y belongs to interval of [0,1). The interval is open on the top side, so in case when y=1 we has situation,
when «counterparty E» has benefit of being inactive. In other case, it is that activity of «counterparty E» will be unprofitable, what contradict to content of economic motivation mechanism.
Taking into these conditions, the benefit of i-th «counterparty E» Hi(yi) will be equal to (l-y)yyi. The objective function has the following for these conditions be (including (1) and (2)):
(10)
Normative y can be represented in a form of internal tax rate on income. In order to determine the actions of «counterparties E», there must be done operations similar to (4), (5):
(11)
(12)
Analogically to (6), its possible to determine the variant of probable maximum of «counterparty E» utility function:
(13)
The action, which chosen by «counterparty E», doesn't depend on value of b. According to his statement we can exclude this term from further calculations. Calculation of «counterparty S» utility function is analogical to (7):
= yX(aN +
(14)
In this case, result of actions of all «counterparties E» is presented in the following form:
A benefit of the i-th «counterparty E» is represented by formula below:
A (yd = CI - ~ ri (.}'i -a)2 -b =
Total utility functions of all participants has the following form:
(15)
(16)
= ÄaN + 1
bN
(17)
It is obviously, that expressions (14)-(17) are dependent on normative «y», which managed by «counterparty C». It is possible to determine optimal ratio of normative «y» for «counterparty S». In order to do that we need to define the value of normative «y», which will maximize the expression (14). At the same time, this value mast positive (16).
6 -X d2
R. = 1--^^
n - n
2
6-V d;
K = 1--^ = -0,325
y n - n
Calculation of Spearman's rank correlation coefficient resulted the following value:
I n - 2
t= Rj-- =-0,768
p \1 - R2
According to received results, there is a weak inverse interrelation between enterprises and the state, and the COP is not statistically significant.
In this case, the price is the sum of cost for services provision and profit return ratio p, expressed as a percentage share of the cost. The rate of «counterparty E» profit return p is profitability. In case of profit return ratio p equal to 0, the situation refers to the first observed mechanism of economic interests.
Analogically to the first option, the implementation of planned y{J objectives is optimal scenario for «counterparty E».
According to the conditions of this mechanism, reformulate form of (3) is the following:
(18)
After differentiation (18), we simplified results and rejected unnecessary decisions. As result we received the following statements:
a +
3(l-p)Ti
3(1-p)ri'
(19)
(20)
(21)
According to calculations, for this economic motivation mechanism we has the following:
-M* )-™z ik
+p)n
+.
= A.aN + -l 1 2
a -JsCi+p}
EZiJï-hNa+p).
(22)
(23)
(24)
AaN + -Î2 + -?-) I
3 \ 1+pJ^
3(1+p)
EiU \--bN
(25)
:1 _ 6-z d2
Ryz = 1 _ 3
y n _ n
Results of provided calculations: Rxz = 1 _
6-z df 1 —
= _0,375
n _ n
Evaluation of Spearman's rank correlation coefficient. According to calculation, we have received following results: I n _ 2
i = Rj-r = _0,768
p V1 _ R
HH-E- S
Objective function of «contractor S» has the following view:
(26)
After differentiation (18), we simplified results and rejected unnecessary decisions. As result we received the following statements:
(£'(yi) = VA-3ri(yi-ay = 0
+ , fäÄ
yt- = a ±
yt = a +
(27)
(28)
(29)
According to calculations, for this economic motivation mechanism we has the
following:
r(y) = j/ + J^E?=1ß " (32)
= A + Jf^ I) _ ÎL 11 _ fc.Y (33,
We use Kendall's concordance coefficient (see. Table 2) in order to confirm the absence of links between the economic interests of market relations agents in conditions of pricing and state pricing regulation.
According to the simplified formula, excluding connected ranks we have following
results:
W = 912!S = 0,0611; S = Y d2-(Yd)2/n = 5,5 , m\n3 - n) Y ' VY ''
Results of calculations are indicating the lack of communication between contractors.
Evaluation of Kendall's concordance coefficient by the criterion ofx2. According to calculations. We have received following results:
xX = 12 'S = 0,733; m(n2 - n)
For each of the four systems (1- HH- HH; 2 - HH, E,E-E; 3- E-S; 4 - HH- E - S) there were developed and formulated following model parameters:
- For 1) - (7), (8) and (9);
- For 2) - (14) (15) (16) and (17);
- For 3) - (22) (23) (24) and (25);
- For 4) - (30) (31) (32) and (33).
Conclusions. Designed models are enabling the possibility to use the most flexible pricing policy, price discrimination and state pricing regulation. In its turn, it enables us to provide economic interests of producers, consumers and the state on the maximal degree. Thus, the every case is checked by Kendall's and Spearman's coefficients. Coefficients show a weak link between economic interests of agents. When we talk about state - there is lack of communication.
References
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3. Pinishko, V. Prices and pricing [Text]: Tutorial / VS Pinishko - Lviv: Intelligence-west, 2006. - 488 p.
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