÷H(Mon Dec 04 09:49:57 2006) From EPB Familiarity Model R1 Fin.vmfe,Ô$"L"L" (L"  $¡7L¿ì ì ô ¼Ê*)(+&'tu1-,.ö÷yzxv!œÅ``2 ë   €? ñ s À”N¬  @ æ k€ö€ö>¬ €ö  „(€öŠĬ €ö ü |€öª¬ €ö  €ö€ö¼Š)‘€ö€ö¼ ‰9O =ì€ö€ö¼ ‡@Æ( B°T D  FÊ* HÛ]€ö€ö§¼€ö K‘ ,€?=º¼€? RÅ;€ö€ö#±¼€ö \÷ €öT¼€ö „`§Ø;€ö€ö–O¼€ö gA;€ö€ö$¼€ö k" F€ö€öú”¼€ö p¬€ö€ö¼ ‡t¼€ö€ö¼ ‡wk€ö€öj=¼€ö }J €ö€ö`6¼€ö ‚« €ö€öe;¼€ö ‡k  €ö€öI'¼€ö ' ˜€ö€ö›S¼€ö –t  ×£¼ìQ8>l?¼ ×#< ¡$}€ö€ö@¼€ö ¨/Ž€ö€ö•¼€ö ®  €ö€ö‘Ƽ€ö ¶€ö€ö“Ǽ€ö ¾½ N€?ŠH¼ ×#< ÅJ™O€ö€öY5¼€ö Ê[¢€ö€ö錼€ö Õj±€ö€ö— ¼€ö Û}º€ö€ö)¼€ö ám €ö€ö¼€ö çŒË;€ö€ö™Q¼€ö ìn ð€ö¼"ƒòx $€ö€ö¢¼€ö øºâd A&¼? üÆ&ö€ö€öD%¼€ö ÿßû o€ö€öœ¼€ö Éê€?M¾¼€?  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O€ö€öż€ö Lþç€ö€ö¥¼€ö V$€ö€öò‘¼€ö a… {€?QÀ¼€? gv Ë€ö€öÍu¼€ö qêt€ö€öC¼€ö zZ €ö€ö¼€ö ~x. €?O¿¼€? ‰ƒ6€ö€ö ¼€ö ŽD €ö€öW4¼€ö ’. ð€?™¼ÍÌÌ= ˜§N€ö€ö¦¼€ö  ¶b €ö€öc7¼€ö ¥Ûk €ö€öA¼€ö ®™ ˆÅ€ö€ö¢¼€ö À Ž €ö€ö+µ¼€ö ËÈ V é€?2¼ ×#< Õ6  €?š¼ ×#< ÞL ¹ ÍÌÌ=¼c¼oƒ: å# ç ÍÌÌ= ¼ ×£; ï ×zDºb¼? ÷à ¢€?ˆü ×#< ÿ ,;€ö€ö¬μ€ö Ï €?Ü„¼ ×#< Ú €ö€ö狼€ö ¶   5 €ö€ö)´¼€ö (§ = ä€?0¼ ×#< 2è À€ö€ö ȼ€ö 89  €ö€öB¼€ö A² F€?ŽJ¼ ×#< Kÿ €ö¼ŠU[  €ö€ö¼ 4nŠ €ö€ö ¼ 4ƒÁ €ö€ö ¼ 0¼ Ì Ü ì¬¼¬ ¼ì¬ü\¼œŒ¬œl ¼ìœì,üŒÌ üL\Ü<¼L|Ü|ì¬ÌŒÜ,쌌 L, lLœ LÜ||Ì üÌlÜ<üÜL œüÜ|ÜŒ|lü,ü,ŒüLÌ, |Œ¬< Œ<,<Ü\¼œ¬œ\Ì\,<ÌœÌl<¼|¬¼Œl\¬\\ ¬ìÌ ,L<l <,ìl|l lœ¼L\<œ| ì \L  C¡7L¿ôôô™SUMPRODVMINVMAXTimeINITIAL TIMEFINAL TIMETIME STEP SAVEPER".Epb familiarity model r1 fin SSHAPE SSHAPExgblbux0EXPxe -dmnlMaxZIDZABSMin sales 2SW endogeneous drivers&Share of Purchases to Platform i2TechnologyInstalled Base Growth iDiscards iPulse Drivers-vehicles -yearFamiliarity UpdateFamiliarity GainFamiliarity LossExogenous Familiarity ChangeInstalled Base of Others*Fractional Installed Base Growth RateIN Total Installed BaseTotal Familiarity21Total Familiarity Gain 21Total Familiarity Loss 21Initial Familiarity12Familiarity 21*Probability of Contact with NondriverTotal Installed BaseDiscards of OthersDiscard Time LambdaInstalled Base iIF THEN ELSEINCInstalled Base V2Epsilon ' Epsilon"Reference Socialization EffectSW Forgetting On>"Initial Relative Entrant Experience (In case no Learning)""Social Exposure Offset EtaRefKnowledge KjTechnologyToNormal Knowledge K02Effective Knowledge Initialization CorrectionCES parameter rho.Experience to Performance Contribution ij*Knowledge Initialization Correction j"Initial Relative Experience iElasticity of Substiution"Knowledge Share Internal kappa jSw Experience Effect on&Knowledge Share Internal IncumbentENT"Knowledge Share Internal Entrant.Initial Cumulative Production Experience iReference Experience E0"Matrix Incumbent To SelectionPerformance Pj*Sensitivity of Performance to Knowledge*Effect of Performance on AttractivenessPlatform Active i.Sensitivity of Attractiveness to PerformanceRelative Experience iKnowledge Share ijSpillover Strength psi ij*"Off-Diagonal Unit Matrix to from ij"&Weighted Spillover strength psi ijUnit Matrix nXn6"Initial Entrant Experience (in case of learning)"Experience Platform ii*Perceived Experience Other Platforms ij&Cumulative Production Experience i Share ijMatrix Entrant Selection ijMatrix 2 to 1Discards 2 to 1Familiarity of DiscardersSales 2 from 1Perceived Utility ijMatrix 1 to 2&Effective Experience Available to ij2Cumulative Production Experience at Activation iInitial Experience"Relative Initial Experience iProduction Experience Gain&Production Experience Obsolescence&Exogenous Production Experience GainProduction iSW Endogenous Salessales IncumbentPlatform Active at Start iPulse Experience i*Pulse Entrant Experience at Activation PulseEntrant Start Time.Linear Effect of Socialization on Forgetting&Total Social Exposure to PlatformEntrant ActiveSTEP*Effect of Social Exposure on ForgettingNormal Forget Rate PHISW endogenous familiarityInitial Incumbent ExperienceExogenous SalesTEST Market ShareMarketing Start6Entrant Experience Relative to Incumbt at Activation2LogCurve Effect of Social Exposure on Forgetting SMOOTH"Time to Spillover Experience ij&"Relative Installed Base Share V2/N"*Production Experience Obsolescence TimeSW Obsolescence Time&Normal Experience Obsolescence Time"Inf Experience Obsolescence Timediscards 2*Sw Logistic Curve Effect on ForgettingReference Utility F PulsePulse Familiarity 21Relative Social Exposure iFamiliarity ij"indicated net familiarity changeF"Relative Incumbent Experience (in case no Knowledge Obsolescence)"*"socialization effect of non-drivers"&Effective Contact Rate Non Drivers"Pulse Installed Base Fraction 2Marketing Effectiveness&AFV Marketing Effectiveness ShockMarketing DurationTest Market Share EntrantUtility j:Performance Improvement Fraction per Experience Doubling&Probability of Contact with Driverln&socialization effect of drivers cd&Effective Contact Rate Drivers cdTotal Replacements"Indicated Net familiarity gain&Initial Installed Base Fraction 2 .Control SMOOTHINSTb#SMOOTH(EffectiveExperienceAvailabletoij[Technology,TechnologyTo],TimetoSpilloverExperienceij)#R#SSHAPE(TotalSocialExposuretoPlatform,Epsilon,0,1,SocialExposureOffsetEtaRef)#V#xeÿ Jeroen Struben:5 ªõ;ÿ John Sterman‚ Ð]ÿFor detailed Documentation: see paper and appendix; for replication of figures in paper, see appendix.ôø &4>HS^ep{†‘œ§²½ÈÓÞéôÿ  '2=HS^itŠ• ¦±¼ÇÒØÞH¡7L¿ùùôé63 ŒN„ÔSocial Exposure Parameters:8 ŸL„ÔVehicle and Learning Parameters62 }N„ÔInitialization and Shocks&! 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‡ì• &®º¦ÍÌÌ= ‡ì•|&®º•| $•<‡¬'‡¼•¼&®º¦š™™> ‡ì"•| &®º•,•Œ²•l¬°‡¬'‡¼•l?®º•ì±•,•l&®º¦€? ‡ì•ü&®º¦zD ‡¼•<&®º¦€? ‡ì•ì&®º¦ ×£<‡ì'‡¼•\&®º¦ ‡ì2•Œ &®º•ì%¦€?$•|$®º•%•|%•,‡ì'‡¼•&®º•ü'•¼%•L‡¬'‡¼•¼&®º¦A ‡¼.•ü&¸G¸®º#•<$•±®ºº•œ %•œ ‡¬•L&®º¦€? ‡ì•,&®º¦€?‡ì'‡¼•l &®º¦€>‡ì'‡¼•œ &®º¦ ‡ì•l&®º¦ ‡ì•¼&®º¦š™>‡ì'‡¼•ì&®º•Ü#•\ #•¬‡ì'‡¼•Œ¹&¸¦pB ‡¼•|¹&¸$¦ @ ‡¼•¬¹&¸®¹•œ ‡¼•œ¹&¸¦> ‡¼‰¸šš±š&š&Gš$š'š±š œ€üH¡7L¿ô2&Internally defined simulation time.ªdefaults: bl= 0; bu = 1; g = 1;x0=1 this gives a symmetric S-shape from bl to bu through with 1 being the inflection point and derivative = at this point = g*(bu-bl)JAvoid floating point errors at extreme positive / negative values of xRThis is The actual integration takes place in th, as we have a co-flow, this*This would be the dimensionless epsilonReference value to normalizeFormulation used in paperòThis formulation represents a general CES production function. When the CES paramter equals 0, the formulation converges to a constant returns (Cobb-Douglass) function, with the elements lifted to the power of 1/n (check this last part!!)ZTo make sure that the incumbent starts with the same knowledge in different scenariosŠThis assures all runs start with the same knowledge for the incumbent, in case of different knowledge shares, allowing to compare runs.Formulation used in paperZ:MACRO: SSHAPE(x,g,bl,bu,x0) SSHAPE = bl+(bu-bl)*EXP(4*g*xe)/(1+EXP(4*g*xe)) xe=x-x0*To set the initial values for experienceZIf this swtich is set to one we simulate with a piecewise linear approximation of the social exposure effect on forgetting. This allows testing the relevance of the analytical derived nullclines and tipping points for the linear approximation (as we can compare simulations for the linear approximations with the more realistic smooth curves)6Normalizing purpose - at what experience do we achieve the normal improvement cycle time; Could be different for different technologies - default the same. Think of the high end being: Experience to production rate * 2% Market share *Market Size/time to scrap * 20 years experience = 1*.2*50e6/8 *20= 1.6e7zSets the initial experience for the incumbent. If the knowledge obsolescence is on, we use the equilibrium value (of 1).e.g. 0.003 x 100VStrength of word of mouth about AFVs for contacts between ICE and other ICE drivers" Simulation Control Parameters&The final time for the simulation.&The initial time for the simulation..The frequency with which output is stored.&The time step for the simulation.<€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö ×£<€ö€ö€öA€ö€ö€ö€ö€ö€ö€ö€ö€>š™>€ö€ö€ö€ö€ö€öÀ?€ö€ö A€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€?€öpBÀádK€ö€ö¥ÔhS€ö€ö€ö€?€?€ö€ö À€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€?€?€ö€ö€ö€özD€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö A€?€?€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€öš™™>€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€?€ö€ö€ö€ö€@€ö€ö€ö€ö€ö€ö€ö€öš™™>€ö€ö€ö€ö€ö€ö€öÍÌL=€ö€ö€ö€ö€ö€ö€?€?€?€?€?€ö€öÍÌÌ=>A€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö¡7L¿ ô///---\\\ :GRAPH States :TITLE Familiarity and Drivers (long horizon) :SCALE :VAR Familiarity 21|F21 :UNITS dmnl :Y-MIN 0 :Y-MAX 1 :LINE-WIDTH 2 :VAR "Relative Installed Base Share V2/N"|V2/N :LINE-WIDTH 2 :GRAPH States_Short :TITLE Familiarity and Drivers (short horizon) :X-MIN 0 :X-MAX 20 :SCALE :VAR Familiarity 21|F21 :UNITS dmnl :Y-MIN 0 :Y-MAX 1 :LINE-WIDTH 2 :VAR "Relative Installed Base Share V2/N"|V2/N :LINE-WIDTH 2 :GRAPH Phase_Familiarity_1 :TITLE Phase Familiarity (preset range for axes) :X-AXIS Familiarity 21 :X-MIN 0 :X-MAX 1 :SCALE :VAR familiarity gain|F Gain :UNITS dmnl/year :Y-MIN -0.2 :Y-MAX 0.2 :VAR Indicated Net familiarity gain|dFdt :VAR familiarity loss|F Loss :SCALE :VAR Effect of Social Exposure on Forgetting :UNITS dmnl :Y-MIN 0 :Y-MAX 1 :GRAPH Phase_Familiarity_2 :TITLE Phase Familiarity (flexible range for axes) :X-AXIS Familiarity 21 :SCALE :VAR familiarity gain|F Gain :VAR familiarity loss|F Loss :VAR indicated net familiarity change|Net F Gain :GRAPH Familiarity_Drivers_Phas :TITLE Familiarity Drivers Phase Diagram :X-AXIS "Relative Installed Base Share V2/N" :X-MIN 0 :X-MAX 0.5 :SCALE :VAR Familiarity 21 :Y-MIN 0 :Y-MAX 1 :GRAPH Market_Share :TITLE Market Share :X-AXIS "Relative Installed Base Share V2/N" :X-MIN 0 :X-MAX 1 :SCALE :VAR Share of Purchases to Platform 2 :Y-MIN 0 :Y-MAX 1 :VAR "Relative Installed Base Share V2/N"|45d reference :L<%^E!@ 1:base2.vdf 9:base2 22:$,Dollar,Dollars,$s 22:Day,Days 22:Hour,Hours 22:Month,Months 22:Person,People,Persons 22:Unit,Units 22:vehicles,vehicle 22:Week,Weeks 22:Year,Years 18:BASIN_BOUNDARY.vsc 20:Familiarity MDL 2.lst 15:0,0,0,0,0,0 19:5,1 27:2, 4:Time 5:Total Familiarity21 24:-5 25:60 26:60 6:ENT 6:INC