ÃÈÏÅÐÃÅÎÌÅÒÐÈ×ÅÑÊÈÅ ÔÓÍÊÖÈÈ È ÌÎÄÅËÜ … · whittaker and g. n...
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ÓÄÊ 330.42
Âàñèëèé Ìèõàéëîâè÷ Ãîí÷àðåíêî
Íàöèîíàëüíûé èññëåäîâàòåëüñêèé óíèâåðñèòåò«Âûñøàÿ øêîëà ýêîíîìèêè»
101000, ã. Ìîñêâà, óë. Ìÿñíèöêàÿ, ä. [email protected]
Àëåêñàíäð Áîðèñîâè÷ Øàïîâàë
Íàöèîíàëüíûé èññëåäîâàòåëüñêèé óíèâåðñèòåò«Âûñøàÿ øêîëà ýêîíîìèêè»
101000, ã. Ìîñêâà, óë. Ìÿñíèöêàÿ, ä. [email protected]
Ëàðèñà Âëàäèìèðîâíà Ëèïàãèíà
Ôèíàíñîâûé óíèâåðñèòåò ïðè Ïðàâèòåëüñòâå ÐÔ125993, Ìîñêâà, Ëåíèíãðàäñêèé ïðîñï., 49
ÃÈÏÅÐÃÅÎÌÅÒÐÈ×ÅÑÊÈÅ ÔÓÍÊÖÈÈÈ ÌÎÄÅËÜ ÌÍÎÃÎÑÅÊÒÎÐÍÎÉ ÝÊÎÍÎÌÈÊÈÑ ÌÎÍÎÏÎËÈÑÒÈ×ÅÑÊÎÉ ÊÎÍÊÓÐÅÍÖÈÅÉ
 ðàáîòå îïèñàíà ìíîãîñåêòîðíàÿ ìîäåëü ñ ìîíîïîëèñòè÷åñêîé êîíêóðåíöèåé è ðàññìîòðåíûïðèìåðû ôóíêöèé ïîëåçíîñòè, çàäàííûõ ãèïåðãåîìåòðè÷åñêèìè ôóíêöèÿìè, ïðè êîòîðûõâûïîëíÿþòñÿ óñëîâèÿ ñóùåñòâîâàíèÿ è åäèíñòâåííîñòè îáùåãî ðàâíîâåñèÿ â ìîäåëè.
Êëþ÷åâûå ñëîâà: ãèïåðãåîìåòðè÷åñêàÿ ôóíêöèÿ, ìîíîïîëèñòè÷åñêàÿ êîíêóðåíöèÿ, îáùàÿôóíêöèÿ ïîëåçíîñòè, ýëàñòè÷íîñòü çàìåùåíèÿ.
Ââåäåíèå
 ðàáîòå [7] áûëà ïîñòðîåíà è èññëåäîâàíà ìîäåëü ìíîãîñåêîðíîé ýêîíîìèêè ñìîíîïîëèñòè÷åñêîé êîíêóðåíöèåé. Ïðè íåêîòîðûõ îãðàíè÷èòåëüíûõ óñëîâèÿõ áûëîäîêàçàíî ñóùåñòâîâàíèå ñèììåòðè÷íîãî îáùåãî ðàâíîâåñèÿ â ìîäåëè, ïîñòðîåííîéâ ïðåäïîëîæåíèè, ÷òî ðàáî÷èå ìîáèëüíû âíóòðè ñâîèõ ñåêòîðîâ, íî íå ìîãóòïåðåõîäèòü èç ñåêòîðà â ñåêòîð. Ïðè ýòîì ïðåäïî÷òåíèÿ ïîòðåáèòåëåé îïèñûâàëèñüôóíêöèåé ïîëåçíîñòè îáùåãî âèäà.  êà÷åñòâå ïðèìåðîâ ïîëåçíîñòåé,óäîâëåòâîðÿþùèõ óñëîâèÿì ñóùåñòâîâàíèÿ è åäèíñòâåííîñòè ðàâíîâåñèÿ, áûëèðàññìîòðåíû ãèïåðãåîìåòðè÷åñêèå ôóíêöèè.
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ñ âîçðàñòàþùåé ýëàñòè÷íîñòüþ çàìåùåíèÿ .1
12)( A
Ëèòåðàòóðà
1. Abadir, M.K. An Introduction to Hypergeometric Functions for Economists// EconometricReviews. � 1999. � Ñ. 287-330.2. Boucekkine, R., Ruiz-Tamarit, J. R. Special functions for the study of economic dynamics: Thecase of the Lucas-Uzawa model//Journal of Mathematical Economics. � 2008. � Ò. 44. � Ñ. 33-54.3. Albanese, C., Campolieti, G., Carr, P. and Lipton, A. Black-Scholes Goes Hypergeometric//Risk. � 2001. � Ò. 12. � Ñ. 99-103.4. Brida, J. G., Maldonado, E. J. L. Closed form solutions to a generalization of the Solowgrowth model//Applied Mathematical Sciences. � 2007. � Ò. 1. � ¹. 40. � Ñ. 1991-2000.5. Pham-Gia, T. and Thanh, D.N. Hypergeometric Functions: From One Scalar Variable to SeveralMatrix Arguments, in Statistics and Beyond//Open Journal of Statistics. � 2016. � Ò. 6. � Ñ. 951-994.6. L.A. Stole and J.Zwiebel. Organizational design and technology choice under intrafirmbargaining//The American Economic Review. � 1996. � Ñ.195-222.7. A.B. Shapoval, V.M. Goncharenko. A Response of the Economy to Changes in EmploymentStructure//Working paper EERC. � 2016. � ¹. E16/09. � Ñ. 1-54.8. E. T. Whittaker and G. N Watson. A Course in Modern Analysis//Cambridge University Press.� 1990.
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HYPERGEOMETRIC FUNCTIONS AND THE MODELOF MULTISECTOR ECONOMY
WITH MONOPOLISTIC COMPETITION
Vasily Goncharenko
National Research University Higher School of Economics101000, Moscow, Myasnitskaya str., 20, [email protected]
Alexander Shapoval
National Research University Higher School of Economics101000, Moscow, Myasnitskaya str., 20, [email protected]
Larisa Lipagina
Financial University under the Government of the Russian Federation125993, Moscow, Leningradsky prosp., 49, [email protected]
We describe a multi-sector economy model with monopolistic competition and examplesof utility functions given by the set of hypergeometric functions when the conditions ofexistence and uniqueness of general equilibrium in the model are satisfied.
Keywords: hypergeometric function, monopolistic competition, general utility function,the elasticity of substitution.
References
1. Abadir, M.K. An Introduction to Hypergeometric Functions for Economists// EconometricReviews. � 1999. � P. 287-330.2. Boucekkine, R., Ruiz-Tamarit, J. R. Special functions for the study of economic dynamics: Thecase of the Lucas-Uzawa model//Journal of Mathematical Economics. � 2008. � Vol. 44. � P. 33-54.3. Albanese, C., Campolieti, G., Carr, P. and Lipton, A. Black-Scholes Goes Hypergeometric //Risk. � 2001. � Vol. 12. � P. 99-103.4. Brida, J. G., Maldonado, E. J. L. Closed form solutions to a generalization of the Solowgrowth model//Applied Mathematical Sciences. � 2007. � Vol. 1. � ¹ 40. � P. 1991-2000.5. Pham-Gia, T. and Thanh, D.N. Hypergeometric Functions: From One Scalar Variable to SeveralMatrix Arguments, in Statistics and Beyond//Open Journal of Statistics. � 2016. � Vol. 6. � P.951-994.
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6. L.A. Stole and J.Zwiebel. Organizational design and technology choice under intrafirm bargaining// The American Economic Review. � 1996. � P.195-222.7. A.B. Shapoval, V.M. Goncharenko. A Response of the Economy to Changes in EmploymentStructure//Working paper EERC. � 2016. � ¹. E16/09. � P. 1-54.8. E. T. Whittaker and G. N Watson. A Course in Modern Analysis//Cambridge University Press.� 1990.