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Bogatyrev Vladimir Dmitrievich, Ivanov Dmitry Yurievich, Kurilova Anastasia Alexandrovna APPROACHES TO MANAGING THE DEVELOPMENT OF HIGH-TECH ...
economic sceinces
УДК 330.43
ПОДХОДЫ К УПРАВЛЕНИЮ РАЗВИТИЕМ ВЫСОКОТЕХНОЛОГИЧНОГО ПРЕДПРИЯТИЯ НА ОСНОВЕ ЭКОНОМИКО-МАТЕМАТИЧЕСКОЙ МОДЕЛИ ЦЕНОВОЙ КОНКУРЕНЦИИ НА РЫНКЕ ЛЕГКОЙ АВИАЦИИ
© 2018
Богатырев Владимир Дмитриевич, доктор экономических наук, профессор Иванов Дмитрий Юрьевич, доктор экономических наук, профессор Самарский государственный аэрокосмический университет им. академика С.П. Королева (национальный исследовательский университет) (443086, Россия, Самара, Московское шоссе, д. 34, e-mail: [email protected]) Курилова Анастасия Александровна, доктор экономических наук, доцент, профессор кафедры «Финансы и кредит» Тольяттинский государственный университет (445667, Россия, Тольятти, ул. Белорусская, 14,e-mail: [email protected])
Аннотация. Авиационная промышленность наряду с отраслью по производству автомобилей является локомотивом развития национальной экономики. Занятость одного человека в отрасли авиапрома обеспечивает наибольшую дополнительную занятость в других отраслях до 9 человек на одного занятого в авиапромышленности. Это делает важным и необходимым эффективное развитие этой отрасли. Помимо обеспечения занятости авиапромышленность дает значительный толчок к развитию смежных отраслей, таких как нефтехимия, электронная промышленность и т. д. Также развитая авиапромышленность обеспечивает значительный оборонный потенциал страны, позволяя обеспечить вооруженные силы качественными и современными летательными аппаратами. Наибольшую роль в мировой экономике играет производство пассажирских самолетов. На этом рынке лидируют такие крупные производители летательных аппаратов как Boeing и Airbus. Значительную долю в мировом производстве летательных аппаратов занимают также канадская компания Bombardier и бразильская Embraer. Несмотря на безусловное лидерство больших летательных аппаратов в сфере пассажирских перевозок во всем мире большое значение и развитие получила легкие и сверхлёгкие летательные аппараты позволяющие сделать полеты доступнее. В настоящее время этот сектор летательных аппаратов недостаточно сильно развит в России. Однако существующая динамика национального рынка летательных аппаратов демонстрирует рост интереса к лёгким и сверхлегким летательным аппаратам в России. В настоящее время на российском рынке сформировался значительный отложенный спрос, который потенциально может быть реализован, в том числе за счет производства лёгких и сверхлёгких летательных аппаратов российскими авиапроизводителями. При этом российские авиастроительные предприятия вынуждены функционировать в условиях развивающегося рынка и растущей конкуренции, что делает необходимым разработку специальной экономической модели рынка легких летательных аппаратов с учетом специфики российской авиационной отрасли. Данная модель должна определять влияние отдельных параметров на спрос на производимую продукцию и на этой базе обеспечивать формирование устойчивой стратегии развитие предприятия российской авиационной промышленности.
Ключевые слова: легкие и сверхлегкие летательные аппараты, моделирование конкуренции, оптимальная стратегия, равновесие на рынке, ценовая конкуренция
APPROACHES TO MANAGING THE DEVELOPMENT OF HIGH-TECH ENTERPRISES ON THE BASIS OF THE ECONOMIC AND MATHEMATICAL MODEL PRICE COMPETITION ON THE MARKET OF EASY AVIATION
© 2018
Bogatyrev Vladimir Dmitrievich, Doctor of Economics, Professor Ivanov Dmitry Yurievich, Doctor of Economics, Professor Samara State Aerospace University academician S.P. Koroleva (National Research University) (443086, Russia, Samara, Moskovskoe shosse, 34, e-mail: [email protected]) Kurilova Anastasia Alexandrovna, Doctor of Economics, professor of «Finance and Credit» Togliatti State University (445667, Russia, Togliatti, Belorusskaya street, 14,e-mail: [email protected])
Abstract. The aviation industry, along with the automobile industry, is the locomotive of the national economy. Employment per person in the aviation industry provides the largest additional employment in other industries up to 9 people per person employed in the aviation industry. This makes it important and necessary for the effective development of this industry. In addition to providing employment, the aviation industry gives a significant impetus to the development of related industries, such as petro chemistry, electronic industry, etc. Also, the developed aviation industry provides a significant defense potential of the country, allowing providing armed forces with high-quality and modern aircraft. The largest role in the global economy is the production of passenger aircraft. Leading aircraft manufacturers such as Boeing and Airbus are leading in this market. The Canadian company Bombardier and the Brazilian Embraer also occupy a significant share in the global production of aircraft. Despite the undoubted leadership of large aircraft in the field of passenger transport throughout the world, light and ultra-light aircraft have gained great importance and development, making flights more accessible. Currently, this sector of aircraft is not well developed in Russia. However, the current dynamics of the national aircraft market shows a growing interest in light and ultra-light aircraft in Russia. Currently, the Russian market has formed a significant pent-up demand, which can potentially be realized, including through the production of light and ultra-light aircraft by Russian aircraft manufacturers. At the same time, the Russian aircraft manufacturing enterprises are forced to operate in an emerging market and growing competition, which makes it necessary to develop a special economic model of the light aircraft market, taking into account the specifics of the Russian aviation industry. This model should determine the influence of individual parameters on the demand for manufactured products and, on this basis, ensure the formation of a sustainable strategy for the development of the enterprise of the Russian aviation industry.
Keywords: Light and ultra-light aircraft, competition simulation, optimal strategy, market equilibrium, price competition
The largest role in the global economy is the production of passenger aircraft. Leading aircraft manufacturers such as Boeing and Airbus are leading in this market. The
Canadian company Bombardier and the Brazilian Embraer also occupy a significant share in the global production of aircraft. Despite the undoubted leadership of large aircraft in
экономические науки
Богатырев Владимир Дмитриевич, Иванов Дмитрий Юрьевич, Курилова Анастасия Александровна ПОДХОДЫ К УПРАВЛЕНИЮ РАЗВИТИЕМ ВЫСОКОТЕХНОЛОГИЧНОГО ...
the field of passenger transport throughout the world, light and ultra-light aircraft have gained great importance and development, making flights more accessible. Currently, this sector of aircraft is not well developed in Russia. However, the current dynamics of the national aircraft market shows a growing interest in light and ultralight aircraft in Russia. Currently, the Russian market has formed a significant pent-up demand, which can potentially be realized, including through the production of light and ultra-light aircraft by Russian aircraft manufacturers. At the same time, Russian state-owned and private aircraft manufacturers are forced to operate in an emerging market and growing competition, which makes it necessary to develop a special economic model for a light aircraft market, taking into account the specifics of the Russian aviation industry. This model should determine the influence of individual parameters on the demand for manufactured products and, on this basis, ensure the formation of a sustainable strategy for the development of the enterprise of the Russian aviation industry.
When forming this model, it is necessary to use elements of game theory and the mechanisms of functioning of multi-level organizational systems, discussed in the works of D.A. Novikov, V.N. Burkova, A.G. Chkhartivili, and A.A. Vasin [1, 4, 3,10], as well as the models and optimization methods considered by S.A. Barkalov [6, 8, 9].
As a result of competitive interaction, the light aircraft market tends to equilibrium. Additional difficulties arise if the demand for products is determined by their value. In order to ensure efficient operation in a stable market environment, manufacturers need to choose the optimal pricing strategy, taking into account the positions of competitors and their chosen competitive strategies. The problem of modeling the choice of pricing strategy for given target functions of participants in the light aircraft market is reduced to determining equilibrium states and determining the stability parameters of the competitive environment [1, 2, 3].
Given that the main product of production is a multi-purpose light aircraft in various versions, we will form a model for determining the price for each modification, subject to profit maximization.
In the case of price competition, the demand functions q..(p),i=1,n, where p - is the price vector, impose the following requirements: dqi dqi that is, the — < 0; —- > 0; i, j = 1, n, i * j, dPi dPj
higher the price of manufactured products by the i -th manufacturer, the lower the demand for them, and the higher the price of the product from a competitor, the higher the demand for the products of the i -th manufacturer. This condition is a requirement for demand functions in the formation of competitive interaction between manufacturers in the light aircraft market [4].
Let "n" enterprises producing "m" different modifications of light aircraft participate in the light aircraft market, each enterprise is interested in obtaining maximum profit with a known demand function and a known cost function for production volumes. The task of choosing a competitive pricing strategy is determined in accordance with the following set of equations:
m
В i (p) = Y [p q(Pj, p-j) - С )]
^ max„
,i = 1, n,
q..(pj,p-j ) = q-p-afpj +ZLkipPfJ =1 n;j =1 m, (1) (q) = c^j(Pj )
where B t (p) - is the profit of the i-th manufacturer; qf (pf , p— ) - demand function;
ap, kp - coefficients characterizing the rate of increase
and decrease of the demand function with respect to price changes for the products of the i-th manufacturer and prices of competitors;
c j (q j ) - the cost of production of the i-th enterprise for
the j-th modification;
Pj = ( Pi j , P2 j ,..., Pi-1,j , Pi+1,j ,
, p¿ ) - the vector of
the situation at the price of the j-th modification of the product for the i-th manufacturer.
The high price of its own products reduces demand, and vice versa, with the high price of competitors, the demand of the i-th manufacturer increases [5].
If the demand exceeds the production capacity of the enterprise producing light aircraft q¿ (p}, p— ) > q0 , then the
optimum output corresponds to the current demand for light aircraft and is equal to qj (P) = q0 .
In such a situation, enterprises determine the optimal competitive strategy in accordance with the restrictions on the volume of output from the allowable values. The range of permissible decisions on the choice of the optimal price for products, based on the production capabilities of the enterprise, is represented by the following set of inequalities:
yeqj M,k = i,к,i = i,n,
j=i m
y j qj <T, i = i, l, i = i, n,
j
m
Y aSj q¡ ,s = 1,S,i = 1,n,
j
m
Y wjqj <Wi, ,v = 1,V,i = 1,n,
(2)
where в, tj , as, wv ■
the standards of resources and
materials by type i-m manufacturer per unit of j-th product; Mk - available materials;
T - the total complexity of the release of products in the
amount of q. <ji;;
A t - the total area of production sites required for the
release of a given volume of light aircraft; Wf - total number of tooling for molding.
If, qj (pj, p_) < q0 then the solution of the problem of
determining equilibrium strategies for choosing the price of a product is reduced to the calculation of partial derivatives of the profit equations and the subsequent formation of a system of equations for unknown prices of products subject to non-negative values of the assumed variations
dPj
dPt
< 0, j, k = 1, m, j ф k
The solution of the problem of determining equilibrium strategies for choosing the price of a product is reduced to the formation of the following system of equations for unknown aircraft prices:
1 T , p V"1" , p 0
0 p j
2a P
J
qP
;i = 1, n, j = 1, m. (3)
Bogatyrev Vladimir Dmitrievich, Ivanov Dmitry Yurievich, Kurilova Anastasia Alexandrovna APPROACHES TO MANAGING THE DEVELOPMENT OF HIGH-TECH ...
economic sceinces
Each equation (3) is the line of reaction of the enterprise to the pricing strategy chosen by competitors [6-11].
Let us consider an example of a decision-making model for price selection by enterprises producing light aircraft in conditions where two companies are participating in the market, whose objective function is to ensure maximum profit in a separate segment corresponding to a certain modification of light aircraft:
Б i (Pi ) = Pi q (P)- ci (q ) ^ max q(p) = 4i0 - apPi + bpPj, i =1,2 ci (4i) = c?4i(P) i = 1,2
(4)
where Б i (Pi ) is the profit of the i-th manufacturer;
We will solve this system with respect to optimal prices:
p = q» + ciaiP + x
2a1P 2af
q0 + C2 aP bP
2a P
2ap
x P
(10)
Find the equilibrium values of prices, the equilibrium price for the 1st and 2nd manufacturer:
pe = Papq + CiaiP) + bP (qB + Cpa2P)
1 = 4a1PaP -b1Pb2P :
e _ 2af (qB + C2 a2P ) + b2P (qc + C1a1P ) P2 = •
2 4a1PaP - b1Pb2P
(11)
qt (p) - demand function;
C (qt ) - the cost of producing one modification of a light aircraft;
ap, bp - coefficients characterizing the rate of increase
and decrease of the demand function with respect to price changes for the products of the i-th manufacturer and the price of competitors.
The decision-making models (4) interconnected through the demand function characterize competitive interactions between the two enterprises in the light aircraft market. Each manufacturer determines the price level for its products p1 > 0 and p2 > 0 in accordance with the condition of profit maximization. The task of the enterprise to determine the equilibrium price is reduced to finding the maximum value of profit for given functions of demand and costs. The necessary condition for the existence of a maximum is determined from the following inequality:
дБ i (Pi )
dPi
= 0, i = 1,2.
(5)
From equations (11), which determine the equilibrium values of the prices of light aircraft under duopoly conditions, it follows that there are equilibrium prices for each market participant if the following inequalities are fulfilled for the parameters of the demand function and the production system for producing light aircraft:
(12)
¡2aP > bP }л {2aP >b2Pj
When inequalities (12) are fulfilled, the numerators and denominators in each equation (11) become positive numbers, which provides non-negative prices for the production of light aircraft at the equilibrium point. The economic sense of inequalities (12) lies in the fact that for the sustainability of a competitive market for each product name it is necessary that the impact of prices on the demand of the i-th manufacturer is not less than the influence of the prices of competitors on this demand.
Point E is the equilibrium point of the two manufacturers with coordinates (p.E, p2E), determined at the intersection of the reaction lines. The upward character of the reaction lines means growing profits as producers increase the prices of light aircraft produced (Figure 1).
Substituting the equations of the function of demand and cost into the equation of profit, we obtain the following system of equations:
b , (p,) = p,q,o- p,app, + p,bppj- c,q,o + c,app,- c,bpPj ^ max,i = 1,2 (6)
Based on the maximum conditions, we calculate the private derivative of the profit and obtain the equation:
(Pl) = q,0 - 2a,pp, + bPpj + c,ap = 0,i = 1,2. (?)
dp,
The solution of the problem of determining equilibrium strategies for choosing the price of a product is reduced to the formation and solution of the following system of equations for unknown aircraft prices:
1 i V v \ (8)
Pi = — (q,0 + c, ap + bpp}),, = 1,2.
2a i
Each equation (8) obtained characterizes the reaction of the enterprise to the chosen strategy by the competitor, as a result of which the equilibrium price values are determined for a separate modification of light aircraft for manufacturers under duopoly conditions.
Transform the system to the following form:
p1 = * + ciap x p
2aP
2aP
(9)
P2 = q° + C2 a2P +i2L x p.
2a 2
2a2
Figure 1 - Graphic solution for determining the equilibrium prices in conditions of price competition for two participants
Equilibrium price values, determined in accordance with equations (11), make it possible to establish equilibrium volumes of light aircraft production. Thus, substituting the obtained equilibrium prices p1E and p2E into the demand function q (p1E,p2E), q2(pE,p2E), one can find the equilibrium values of the output q1(pE), q2 (pE).
We illustrate the results obtained in a numerical example. Let the market capacity of the light aircraft of the j-th modification be qo = q» = qn = ' , coefficients
экономические науки
Богатырев Владимир Дмитриевич, Иванов Дмитрий Юрьевич, Курилова Анастасия Александровна ПОДХОДЫ К УПРАВЛЕНИЮ РАЗВИТИЕМ ВЫСОКОТЕХНОЛОГИЧНОГО ...
ap = 1, 1 •
-5, ap = 1, 1 •
-5, bp = 3 •
-6,bp = 3•Ф -6,
В E (p2) = 7124631,5-Т - 5,5 •
•Т =21420000
the price coefficients for light aircraft p1,p2, the cost of production of the aircraft by the first and second manufacturers:
cq = 5,4 •§ 6,cq = 5,5 •
6
Then the demand functions for the products produced by the first and second enterprises will be
q(p) = qo _ appi + bpp2 = 5 _ 1,1 -D _5 • pj + 3 • ® _6 p2;
q2(p) = q0 - app2 + bpp1 = 5 -1,1 • p2 + 3 • ® p1.
With a known demand function by each market participant, the model of the problem of choosing the price level according to the condition of profit maximization is:
Based on the necessary conditions for the existence of a maximum, we determine the price values that ensure maxi-
ci (qo- appi + bppp)
В i(Pi) = Pi(q0 - apPi +1
p,(s -1,1 •O -5 • p1 + 3•«> -6p2)-5,4•» 6(з -1,1 •О -5 • p1 + 3^0 -6p2maxp1; В 2(p2) = P2 (q0 - a2 P2 + bpp1 )- c2 (q0 - app2 + ¿2^1 ) =
p2(з -1,1 •O -5 • p2 + 3 •» -6p1 )-5,4 •» 6 (з -1,1 •О -5 • p2 + 3 •«> -6p1 maxp, ;
mum profit:
дВ '(p1 ) = q0- 2a1pp1 + b\ p2 + c1a1p =0;
Ф1
дВ 2(pI)
dp 2
= q0 - 2app2 + bpp1 + c2ap = 0.
The solution of the problem of determining equilibrium strategies for choosing the price of a product is reduced to the formation of the following system of equations for unknown aircraft prices
Pi = (qo + bfp2 + ciaip) lap
In the conditions of price competition in the case of duopoly, with known functions of demand for light aircraft, as a result of competitive interaction, equilibrium in the market of light aircraft is achieved at the values of prices p = 7080631,5 and p2 = 7124631,5 and production volumes qx = 8 , q2 = T .
In this case, the price of light aircraft at the first company is lower than the price of a competitor, which provides a larger volume of production and, as a result, greater profits: Пр =23800000 and Пр2=21420000. Reducing the price of light aircraft at the first; company is possible due to lower costs for the production of one light aircraft.
СПИСОК ЛИТЕРАТУРЫ:
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Статья поступила в редакцию 09.11.2018
Статья принята к публикации 27.11.2018
р2 =-- (q0 + b2pp1 + c2 a2p)
2
Determine the equilibrium price values:
e = 2ap (q0 + с ^ ) + q + c2 a{ ) = 4apap -bpbp
2•1,b® "5 (5 + 5,4•« 6 ab® 5) + 3^® -6(3 + 5,5•« 6 ab® 4•1,Ь® -5 аь®-5 -3^® -6 • 3^® -6
- = 7080631,5
PE = 2a1 q + C2 a2 ) + b2 q + C1< ) _
2 •!,!
4 •U • 1,1 • 4J
4-1,1 -B -5 -1,1-» -5 -3-D -6 ■ 3-D -6
Substitute the equilibrium values of prices in the demand function and determine the equilibrium level of output for each manufacturer:
qE(p) = - app1 + bP p2 = 3 -1,1-0 -5 ■ 7080631,5 + 3-B -6 ■ 7124631,5 = 8
qE(p) = q0 - aiPPi + bPp2 = s -1,1-® -5 -7124631,5 + 3-b -6 -708063i,5 = 1
We determine the equilibrium values of the profits of producers:
B f (p1) = 7080631,5•$ _5,46 •$ = 23800000
= 7124631,5
