Construction of a fuel demand function portraying interfuel substitution, a system dynamics approach
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(2) !! ". Avril 2011 Les cahiers de l'économie - n° 81. Série Recherche. [email protected] [email protected]. La collection "Les cahiers de l’économie" a pour objectif de présenter des travaux réalisés à IFP Energies nouvelles et à IFP School, travaux de recherche ou notes de synthèse en économie, finance et gestion. La forme peut être encore provisoire, afin de susciter des échanges de points de vue sur les sujets abordés. Les opinions émises dans les textes publiés dans cette collection doivent être considérées comme propres à leurs auteurs et ne reflètent pas nécessairement le point de vue d’ IFP Energies nouvelles ou d'IFP School. Pour toute information sur le contenu, prière de contacter directement l' auteur. Pour toute information complémentaire, prière de contacter le Centre Économie et Gestion: Tél +33 1 47 52 72 27 The views expressed in this paper are those of the authors and do not imply endorsement by the IFP Energies Nouvelles or the IFP School. Neither these institutions nor the authors accept any liability for loss or damage incurred as a result of the use of or reliance on the content of this publication.. IFP Energies nouvelles - IFP School - Centre Économie et Gestion 228-232, av. Napoléon Bonaparte, F-92852 Rueil-Malmaison Cedex, FRANCE.
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(91) &(')$*,+.-0/1"243657+985;:,+=<>3?(@A. +BC3ED$+=*F)G3 H. 2. D. '8:,+9I. JKMLONQPQREKMNTSVU XY2E57+9I@BC+92;@Z:2[2 e. H. Xj2 n. +=*VIAQ'8a+9If:2[2 I@a'**`+9D[)$H$82. +=8b+. \.d930I@rw,?mH. :|?'2Ec7s. 3 2. :`If@bA. CCi. +=8a'@:2. +=<Z*cg:2. J"WVNQPQREKMNTSMU. :2$\C+^]7H$:`_$BC+=2E@. :,If@A. P B Ti. Dd6'8)G3 2[d937Ip@f+=xvd9*H nZ{. +. nf{. 3?. AQ' If2. @:`3 2. +=*FBg'8i7+=@Z_$8:`d9+^I. :_$BC+=2E@. +t'0IIb3Ed=:,'@b+9D[_T'9cE)Q' dai@:BC+0s. D$+9DQy=s. :`Il@A. Pi. +9B.:`IbIp:,3 2g?Y' d=@b3 8Z3?M?}HQ+=*. +"?mH. s. +=*G_. :,Iq@bA. i Ei. +zBC:`Id^+=**,'2. d93 2QIpH$BC_$@:`3 24:2Q+=8@:,'vs. 3 @Z)T+^+=2[@a'i;+=2[:2E@b3h' d9d93 H. H. IH$B._. +=*,I. 2 2i _$8b+=BC:H$B4sv@AQ'@f:`I^s$'t_T'8a'Bh+=@b+=8f@AQ'@f8b+Q+9d=@aIq@bA IpHQdbA' IlT+xE:`)$:*:@kc7sQ'950':*}')$:*:@kc7s. e. +=8b\0cd93 2. +=*V30_$@:`3 2. @:`3 243 ?O@AQ+50'8:`3 HQIq?mH. +rd^'_$:@'*Md930I@^s +=*M'2. :`Il@A. QCO. IH$B._. &O3 @a' *V+=2. I@a'**`+9D4+9];H$:_$Bh+=2;@. :2$\Cd^' _Q' d=:@kcg_G+=8l?mH. '_Q' d=:`@jcgH$@:`*:o6'@:`302?Y' d=@b3 8aIf3 ?O:2QIp@'**`+9D[+^]7H n. <fA. +=<>)$H$82. 8:`d9+0s. +z)$H +^3 H. 82. D$+=2. O O. i. :`Iq@bA. PCO. 2 +=8f+=~hd=:`+92. IlH$2$Bh3;D. +=@bd7Xj23^xv2. 3 @b+^If@AQ+30_vu nf{. +z_$8:,d9+3?. d=c7s. '2. D. :`IZ'. PR. i. +=*`+9Dg?m+^' @H$8b+9If3?M?mH. +9Itwp-6 07Es-6 0 07ys$@A. 2. +=*. i. +_$8b:`d9+. 2;@^. 2 &lA. + IAQ'8b+. d930I@Z3?(@A. <fA. +=8b+. Ip@8bH. α. 3 ??mH. si. +=*(3 _$@:`302. +@A$8b+9+?}HQ+=*V3 _$@b:`3 2. :`I"'w}2. d=@:`302Vs @bA. :`2@bA. +t2. +=<)$H$8b2$:2$\+9];H$:_$Bh+=2E@":,IzD$+=@b+98B.:2. I^&lAQ+z?3 **`36<f:2$\CBtH. 3 2$uY2. +=\;' @:57+6yl_Q'8a'Bh+=@b+=8^sT'2. 'D$+9d98b+^' I:2$\?mH$2. IpAT'8b+9Iz'8b+rD$+9@b+=8B.:`2. +9D43 2@A. d9+_G3 :2E@^/A. D. +z?mH. +)Q'0Ip:`I"3?Dv:|F+=8b+92. D$+98*:2. w7y. +@a3 @a'*Md^30I@bI"D$+ D. 2. i =1 i s l+^Ip:`D Pi. d9+9IZ:24@b3 @'*Md930I@bIz'2. +9I9s$302. +f3?. B.:2. 308D$:|F+=8b+=2. '**c7s7@A BC+^'2 :2. α. @8'2. + @AQ'@@AQ+t_$8a+9I+92. PR. AQ'0If@AEH. 1. d9+3?q+xv_G3 2. I*,'@b+9I:2;@a3+^]7HQ' *$IAQ'8a+9IO?3 8'**v?}HQ+=*`I^s <ZA d9+^I:2h@b3 @'*Td930I@*`+^' DC@b3rBg'6p308qDv:|F+=8b+=2. +f50'*:`D$:@jc.3?G@A. :2$\@AQ'@t@bA. +h+=2. :`I*`3 \7:@BC3ED$+=*Qd93 2 +=8\7cIcEI@b+=B H$2. D4@A;HQIZDv:G+=8a+=2. d9+9IZ:24@bA. If)G+9+=2Ib+=@"+9];HQ'*V@b3. +=8b+^'0I'z*,'8\7+l50'*H. d^+9I:2h@bA. d^+=_$@HQ'*`*c _$8a+9IpH. D$+=8 Ibd=8H$@b:2;cB H. 0. +. +=*daA +f3?. +Z8b+9IH$*@:2$\r?mH. +. XY@Z:`I. +=2E@bIz:`2@AQ+t*,3 \0:@z?m308B H$*,'h@b+=2. D$I@b3. 3 :`d^+9I9C1IpBg'**. α. :2. Dv:`d^' @b+9I(@AT'@. +=*TIAQ'8a+9I9 g1fd=@bHvu. _$_G30I+^I'CBh' d98b30Ibd93 _$:`d7l_G+=8bI_G+9d=@:5;+0s. I@ d93 2E@a':2'[*,'8\;+h+=2. 3 H$\7A¡2;H. Bt)G+=8 3?. Dv:5E:`DvHT'*VD$+9d9:`Ip:,3 2vuYBh' i7+=8bI^. XY2@A$:`I BC3ED$+=*jsd^'_$:`@a'*q:`I Bh+^' IH$8b+9D:2H$2$:`@bI3?zd^'_Q' d9:@jc¢@b3)$H$82?}HQ+=*`I[w}@AQ'@:`I^s(:2+92 H$2$:@C_T+98.H$2$:`@C3?@:Bh+6y&lAEH 2. si. +Bh'^ch2Q3 @:`d9+@AT'@. I@a')$*`+Z_T'8a'BC+9@b+=8bI^s7:`@Bh'9c.)G+"+^' I:`+=8@b3tD$+9@b+=8B.:`2. ' d9d9+=2E@HQ' @b+@AQ+.Dv:|F+=8b+=2Qd9+9I:2@b30@a'*d937Ip@bIt' I@AQ+=c'8b+.d9302;5;+=8@b+9D:2;@a3g?mH 5 ' *H. +^D[:2w-6yqqc[d9302vu. (XY2h' D$D$:@:`3 2Ms @AQ+lIAQ'8a+. P. +=*F_$8:`d^+. +98b+^'6?m@b+=8^s$@AQ+_$8a+=B.:H$B ?3 8"d937'*. '*`Ib3h:`2;@b+98b+9I@:2$\@b3gH$2. +t8b+=*,'@b:57+. Ib+9DF/. s. '8b+r@A. d=@b:`3 243?(@A. +^D4)Ec[@bA. 3 BC:,'*F*`30\0:@fBh3;D$+9*F:`IfH. Ci '2 ∀i, si ∈ [0, 1]. +9Iq3?F@AQ+Z_$8b+=B.:`H$BCI^(1zI@AQ+9I+z' 8b+z' DpH. ' 8a+?m+98b+=2. *@:2. e−αCi si = P −αC i ie. +l30)$@a':2Q+9DIAQ' 8b+9IIa'@:`Ip?}c. :`I9sV9j,q$0=;=s. 5 ' *H. i. +=<£)$H$82$:`2$\h+9];H$:`_$BC+=2E@^l&lA 3 _$@:`302. i. :,IfD. +=2. 3 @b+9D. Ii. I9s@AQ+@b30@a'*f:2E57+9I@Bh+=2;@ +r@b3 @a' *V:2E57+9I@BC+=2E@":242. Ip@8bH. d=@H$8a+l:`IH. +gD$c;2Q' B.:`d9I3?f?mH. Ib+9D.@b3_G3 8@b8a'9c @bA. d^'_$:@'*O'8a+i7+=_. 8b+9_$8b+9Ib+=2E@bI.@A. +43^57+98a'**Zd6'_Q' d=:`@jc3?. BC+=2E@z' IbIb3Ed=:,'@b+9D4<f:@A@A. +?}HQ+=*. '2QD[Ia'@:`IpQ+9I^/. Ii = s i I ¥¢+gd^'22Q3^<¦D$+9@a':*q@A. I. +9<£+9];H$:_. +=8\0c. +Z'\7:2$\_. +=*lIH$). . I@:@H. 8b3Ed9+9IbI3?G:2. w¤7y. @:`3 2V1zI BC+=2E@:`3 2. +^D')G3^57+7s'45E:2E@a'\0:`2$\. I@a'**`+9DC+9];H$:_$Bh+=2E@^O§z+=8b+7s0@k<q35E:2E@a'\7+9I3?. @Z@8' dbi43?pl1Bh3 8b+r_$8b+9d=:`Ib+tD$+9Ibd=8:_$@b:`3 23?@A. ¨k©}ª«¬6ª6®¯°m±²=²³9´jµ ¶ªz· ª6¸|¬a¹jºl®»z· ª9¼®p¹Y½^¹j®k¼j¶b¼Y· ¬=ª· ¯V¾=· ¿=®pªz¸|¬a¹. + '\0:2$\h_$8b3Ed9+9IbI"IA. 3 H$*`Dd93 2QIp:`D. +=8. · ¸$¼YÁ6®¼¬¼j¶aÂEÃp¬¯¼Y¯F¸|¬=  ¬Ä¶qÅ®p· ÆÇ ÂE»6· ¯m¼¹Y· È αÀ · ¯V· ª9¿=®k¹Y¯®Â É"½6¹Y¬½0¬¹¼Y· ¬ª ¶Â0¼Y¬q¼YÁ®¯m¼j¶ª»¶b¹j»»^®¿9· ¶b¼Y· ¬=ªz¬¸v¼Á· ¯V»6· ¯m¼¹Y· ÆÇ6¼Y· ¬ª;Ê. Æ6Ç6¼Y· ¬=ª;µ. α Ë.
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(94) ;õ Ø^ÔÒøìGÏÔ0ÖÖÙ$ÌhÏ9ðF×TÓbç. . 1 Ti /2. ÏCÓÎÔÒ Í èqÓç. Ú KO i Ti /2. ÌCÏ9ð[ÓbÍìGÏÏ^ô7ÙTÔîFÓbÍ. ÖpèmÍ ÎbÌhÔÓÑ`Í0Ò¡Í èfÒ. Ti 2. ÖbÏ Íè. ÔÒQðÓç. Ï=ÜlêYì. Í6Ü Ï. Ï. Ï=ÜÏ9ô;Ù$Ñë$ÌhÏ=ÒEÓrÑÒEÓbÍÍ î`ð¡Í ÒQÏ9ÖtØ^ÔÒ¡ìGÏ. Ï.Í6Ð7Ï=ÎaÔîîØ^ÔëTÔ Ø=ÑÓkíÍèlÒ. ÌCÏ=ÒEÓzÑ`ÖÖØ=ÎÔë$ëGÏ9ðøÔ6èmÓbÏ=ÎÔCÙ. Ô ÖlèmÍ0îî`Í^Ü"Ö. ðgÓç. Ï"Ø^ÔëTÔ Ø=ÑÓkí.ÍèFÎbÏ9Ø^Ï=ÒEÓîíÑÒ. Ð0ÔÎÑ}Ôì$î`ÏgÔ ÖbÖÍEØ=Ñ,Ô ÓbÏ9ð¢ÜfÑÓç¡Óç. Ô ÖbÖpÙ$ÌhÏ9ðøÓbÍìTÏ.Ï9ô;ÙQÔîÓbÍ. ò. Óç. Ï9Ü£Ï^ô7Ù$Ñ`ë$ÌCÏ=ÒEÓ^Úf÷zÏ=ÜÏ9ô7Ù. Ô ÖzÑÒÝÍ^ÞEÒ. Í6Ü. Ïzî,Ô ØaïhÍèMë$ÎbÏ9Ø=Ñ`ÖbÏzðQÔÓaÔv×$ÔÒ. ÖpÓbÑ|æQÏ9ÖÓç$Ñ`ÖrØbçQÍ Ñ`Ø9Ï.ÍèZÔ[é6ê. ÏzÒEÙ$Ì ìGÏ=ÎfÍèOÌCÍEð$Ï=î`Ï9ðgÐEÑÒEÓaÔÕ;Ï9Ö9ÚòZØ9Ø9Í ÎbðvÑ`Ò$Õ0îí7×vÓjÜlÍÖÓbÍEØbïhÐ0ÔÎÑ,Ôì. Ï=îTÍ ë$ÓÑ,Í Ò. Í7ÖÏfÍèTÓç. Ï^ÖCßpà^á7â7ã0äåpÙ. ÑÓç[ÓçQÏ9ÖbÏrÔ ÖbÖÙ$Ì.ë$ÓÑ,Í Ò. Ù$ÎÒ. Ï=ÎbÖ. KN. Ú ;Ñ`Ì.Ñî,ÔÎî`í7×MÔÒ. i. Í èÖbØ=ÎaÔë$ëGÏ9ðøÍ î`ðÏ9ô;Ù$Ñë$ÌhÏ=ÒEÓ. DO. i. Ö^×vÓçQÏðvíEÒQÔÌCÑ`Ø9ÖZØ^ÔÒ4ìGÏzèÍ ÎÌ Ù$î,ÔÓaÏ9ð. ó. ÖÑÌ.ë$î`ÏrÑÒEÓbÏ=Îë$ÎaÏ=ÓaÔÓÑ`Í0ÒÍèÓç. d KN dt. i. d KO dt. i. KN. = Ii − KN. =. i. ß Eä ×. Ti 2 i. −. Ti 2. KO. i. ß 7ä Ú. Ti 2. Ö"Ø6ÔÒ4ìGÏrë$ÎbÍ6ÐEÑ`ð$Ï9ðFÚ"!QÍ ÎzÏ^Ô Øaç[èmÙ. Ï9ÖbÏrÏ9ô;ÙQÔ ÓÑ`Í Ò. Ï=î. i. ÔÓ"ÓÑÌCÏ. t ×$Óbç. Ï. ØbçTÔÒ$Õ7Ï ÑÒøÓç ÏÍ6Ð7Ï=ÎaÔ îîÖpÓbÍEØaïÍèqÒ Ï=Ü Ï9ô;Ù$Ñë$ÌhÏ=ÒEÓzÜZÑÓçøÎbÏ9ÖëGÏ9Ø=ÓÓbÍgÓÑÌCÏ Ñ`ÖÕ0ÑÐ7Ï=ÒøìEí4ÓçQÏtÑ`Ò 6 Í Ü ÍèfÒ Ï9Ü Ï^ô7Ù$Ñ`ë$ÌCÏ=ÒEÓÔ ÖbÖÍEØ=Ñ,ÔÓaÏ9ð¢ÜfÑÓç¡ÑÒEÐ7Ï9ÖÓÌCÏ9Ò;Ó ×ÔÒ ð¢Óç ÏhÍ Ù$Ó Í^ÜØ^Ô Ù ÖbÏ9ð¢ì;í¡ÔÕ0ÑÒ$Õß}ÓçTÔÓ Ñ`Ö9×TÓçQÏ Ï9ô;Ù$Ñë$ÌhÏ=Ò;ÓÓçQÔÓzÑ`ÖzÒ. Ii. Ígî`Í Ò$Õ7Ï=ÎzÒQÏ=Ü. ÔÒQðçQÔ ÖzÓbÍhìGÏtÎbÏ^Ô îî`ÍEØ^ÔÓbÏ9ðÑÒ;ÓbÍgÓç. Ï Í î,ðØ^ÔÓbÏ=Õ;Í Îí. äÚ. Ó ç ÏhÑ`Ò 6 Í Ü¦Íè. ;ÑÌ.Ñî}ÔÎîí7×(Óbç ÏhÓbÏ=ÌCëTÍ0ÎaÔîqÐ0ÔÎÑ,Ô ÓÑ`Í ÒÍ èZÓçQÏgÖÓbÍ;Øaï¡ÍèzÍ î`ð¡ì Ù$ÎÒ Ï=ÎbÖ ÎbÏ^ÖpÙ$î`ÓbÖrèmÎbÍ Ì ó Ï9ÖbÏhë$ÎaÏ=ÐEÑ`Í Ù Öîí¢Ò Ï=Ü Ï9ô7Ù Ñë$ÌCÏ=ÒEÓ^×ÔÒ ð¡Óbç ÏgÍ Ù Ó Í6ܦØ9Í0ÎÎbÏ9ÖëTÍ0Ò ðvÑÒ$ÕøÓbÍÓçQÏgÖbØ=ÎaÔë$ë ÑÒ$ÕøÍ è"Í0î`ð. Óç. Ï9ô;Ù$Ñë$ÌCÏ9Ò;Ó^Ú. # ç. Óç. Ï[Ò. Ï=ÞEÓhÖÓbÏ=ëÑ`ÖCÓbÍÌCÍEð$Ï=îZÓçQÏ4ð$Ï=ëGÏ=Ò. ÖÓaÔîî,Ï9ð¡ì$Ù$ÎÒ$Ñ`Ò$ÕÏ^ô7Ù. ÑÒ. ÑÒ$ÕCÏ9ô;Ù$Ñ`ë$ÌCÏ=ÒEÓ. ÖÓaÔîî`Ï9ð[ì$Ù$ÎÒ. òlÓfÓÑ`ÌCÏ. ó. Ø9Ï[ìGÏ=ÓjÜlÏ9Ï9ÒÓç. ÌCÏ=ÒEÓ^Ú$ ¢ÏtØ^Ô Ò4æ. ÏtÍ6Ð7Ï=ÎaÔ îîOÖÓbÍ;Øaï4ÍèÏÞvÑ`ÖpÓÑ`Ò$ÕgÏ9ô;Ù$Ñë. Ø^ÔëQÔ Ø9ÑÓjí¡ÍèZÑÒ. ð$Ï9Ò. Ñë$ÌCÏ=ÒEÓ ÜfÑÓç¡èmÙ. K=. P. i Ki. t ×vÓçQÏÍ6Ð7Ï=ÎaÔîîMØ^ÔëQÔ Ø9ÑÓjíÍèÖbØ=ÎaÔë DO = ED. ëQÔÎaÔÌhÏ=ÓbÏ=ÎOÑÒtÓç. Óç. Ï4Í6Ð7Ï=ÎÔîî"ð$Ï=ÌgÔÒ. ìTÏÎbÏ=î}ÔÓbÏ9ðÑÒÖÍ ÌhÏgÜfÔ^í¡ÓbÍøÓç Ø^ÔëQÔ Ø9ÑÓjíÍèÏÞvÑ`ÖÓÑÒ$ÕÏ9ô;Ù$Ñë ßpà^á0â7ã7äCÑÒEÓÎbÍEðvÙ. ðèÍ ÎCÓç. Ñ`ÖMÌCÍEð$Ï=îYÚ 'qÍ ÌCÌCÍ ÒÖÏ9Ò. Ø^Ï9ÖÓç. Ï[Í ì. DO. i. =. X KO. Ki = (KN i K Óç ×ÔÒQð. i. + KO i ). ×"Óç. Óç. ð. ÏrÓbÍ ÓÔî. ÏhÓbÍ ÓaÔ îqØ^Ô ëQÔ Ø=ÑÓkí¢Íè. Ï4Óç$ÎbÏ9ÏèmÙ. ó. i. ß %7ä Ú. Ï=î,ÖhÔÓCÓbÑÌCÏ. t ×qÜfç$Ñ`ØaçÑ`ÖgÔÒ. ÖÏqÖÙ$Õ0Õ7Ï9ÖÓbÖMÓçQÔ ÓMÑÒEÐ7Ï9ÖÓÌCÏ9Ò;ÓOÑÒtÒQÏ=ÜÏ9ô;Ù$Ñë. ÖbÏ=ÎÐ7Ï^ððvÑ,ÖØ=ÎaÏ=ëQÔÒ. TI. Ï. Ô Ò. I. Ti 2. i. ÌCÏ=ÒEÓ^ÚzòzÖ"Óç$Ñ`ÖÔ ðåpÙ. ÏøëQÔÎaÔÌhÏ=ÓbÏ=Î. Ò. ÍèÓbÍ ÓaÔîZÑÒEÐ7Ï9ÖÓÌhÏ=ÒEÓ. Ú. i. & Ï=Ó^ñ ÖCØ^Ô îî. ÎbÖÓzð$Ï=æ. Ï=îlÍ ë$ÓÑ`Í0Ò. ëTÏ^ð[Ï9ô;Ù$Ñë$ÌhÏ=ÒEÓfÑ`Ö. X. Í6Ü Ï. Ø9í¡ìTÏ9ÓjÜlÏ9Ï=Òð$Ï=ÌgÔÒ. ÖÓÌCÏ=ÒEÓzÑ`Ö"ÙQÖpÙQÔ îîí[Ò. ÏøÓÑÌCÏøÓbÍ. Í0Ó"Ñ`Ò. ðÔÒ. ÏÞ$Í Õ7Ï9Ò ÌCÏ=ÒEÓOÖç. ðÓç. ÖpÓÔÒ;ÓÔÒ. ÏÑÒ. Í Ù Í Ù. Ö î`ð. ÖÓaÔîî,Ï9ð. Ï9Í ÙQÖ9×GÝÍ9ÞvÒ. Ï9Ö. Ô0ðåkÙQÖpÓ[ÑÒEÐ7Ï9ÖÓÌCÏ=ÒEÓbÖÓçTÔÓ)(*+,ü
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