Technological Transfers in Global Climate Policy

Technological Transfers in Global Climate Policy Wolfgang Buchholz Lisa Dippl Michael Eichenseer CESIFO WORKING PAPER NO. 5548 CATEGORY 10: ENERGY AND CLIMATE ECONOMICS OCTOBER 2015 An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com • from the RePEc website: www.RePEc.org • from the CESifo website: www.CESifo-group.org/wp T ISSN 2364-1428 T CESifo Working Paper No. 5548 Technological Transfers in Global Climate Policy Abstract Theoretical analysis and empirical evidence show that leadership behavior in climate policy through increased abatement efforts or international transfers cannot be expected to be very successful. In this paper we instead show that pioneering activities, which are based on green technological innovations carried out by a coalition of countries, may be a better approach for combatting global warming through unilateral action. In particular, we examine in an otherwise standard model of private public good supply how the success of such a policy depends on the intensity and scope of technological spillovers. JEL-Code: H410, H870, O310, Q540, Q550. Keywords: climate policy, green technological innovations, voluntary public good provision, leadership. Wolfgang Buchholz* Department of Economics University of Regensburg Germany – 93040 Regensburg [email protected] Lisa Dippl Faculty of Business, Economics and Management Information Systems University of Regensburg Germany – 93040 Regensburg [email protected] Michael Eichenseer Department of Economics University of Regensburg Germany – 93040 Regensburg [email protected] *corresponding author This Version: September 30, 2015 We gratefully acknowledge financial support by the German Federal Ministry of Research through the research project ECCUITY (FKZ 01LA1104B).    1.  Introduction   Progress  in  global  climate  policy  is  impeded  by  the  enormous  difficulties  to  ensure  in-­‐ ternational  cooperation  and  coordination  on  greenhouse  gas  mitigation,  i.e.  to  conclude   an   international   climate   agreement   which   requires   ambitious   and   effectively   binding   obligations  and  which  is  stable  (see,  e.g.,    Sandler,  2004,  and  Finus,  2001,  for  a  detailed   theoretical  analysis  of  these  problems).  The  hope  therefore  is  that  –  following  a  “bottom   up  approach”  -­‐  pioneering  activities  of  a  coalition  of  leading  countries  might  help  mod-­‐ erate  global  warming  and  thus  increase  the  supply  of  this  presumably  most  important   public   good.   When   such   leading   activities   are   considered,   the   focus   normally   is   on   in-­‐ creased  abatement  efforts  or  transfers  to  outsider  countries,  which  in  a  standard  model   of  public  good  provision  have  equivalent  effects  (see  e.g.  Cornes  and  Sandler,  2000,  for   an  analysis  of  this  equivalence).  But  such  unilateral  measures  are  only  of  limited  effec-­‐ tiveness  as  the  countries  outside  the  coalition  can  be  expected  to  show  some  “crowding-­‐ out”   behaviour,   i.e.   to   decrease   their   public   good   contributions   as   a   reaction   to   the   in-­‐ creased   contributions   made   by   the   coalition.   In   Sinn’s   (2012)   figurative   terminology   these  outsider  countries  thus  are  “grabbing  from  the  collection  box”  which  reduces  the   positive   effect   on   public   good   supply   resulting   from   the   pioneering   activities   (see   e.g.   Buchholz,  Haslbeck  and  Sandler,  1998).  Even  worse,  it  is  even  possible  that  total  public   good   supply  falls  when  countries  unilaterally  raise  their  abatement  efforts  before  they   enter  climate  negotiations  (see  Hoel,  1991).                In  the  face  of  these  obstacles  for  successful  leadership  in  public  good  provision  (for   an  overview  see  Buchholz  and  Sandler,  2015)  this  paper  considers  another  type  of  pio-­‐ neering  activities  which  is  not  based  on  an  increase  of  public  good  contributions.  Rather,   leading   behaviour   manifests   itself   in   investments   to   improve   “green”   technologies   (such   as   renewable   energies   or   energy   efficiency   measures)   which   help   reduce   abatement   costs  and  thus  make  the  production  of  the  global  public  good  less  costly.  It  is  well-­‐known   (see  Buchholz  and  Konrad,  1994,  and  Ihori,  1996)  that  in  the  context  of  voluntary  public   good  provision  it  may  harm  a  country  if  it  unilaterally  reduces  its  cost  for  public  good   provision   even   in   the   extreme   case   where   the   innovation   is   completely   costless.   Then   environmentally  friendly  technological  progress  is  blocked  on  the  basis  of  strategic  rea-­‐ sons.   In   this   paper   we   extend   this   analysis   on   the   strategic   choice   of   abatement   technol-­‐ ogy  which  leads  us  to  a  more  optimistic  picture:  If  a  country  or  a  coalition  of  countries  is   –  as  some  kind  of  substitute  for  monetary  transfers  -­‐  able  to  make  the  fruits  of  its  inno-­‐   2      vation  available  to  other  countries  free  of  charge  this  will  not  only  be  beneficial  for  these   countries   but   also   for   the   pioneering   coalition   itself.   This   in   turn   makes   the   coalition   more  prepared  to  engage  in  green  R&D-­‐activities.          The  analysis  will  be  carried  out  in  the  standard  framework  of  voluntary  public  good   provision  (as  exposed  by  Bergstrom,  Blume  and  Varian,  1986,  and  Cornes  and  Sandler,   1996).   But   unlike   these   traditional   contributions   to   the   theory   of   public   goods   we   will       make   use   of   the   more   recent   Aggregative   Game   Approach   (see   Cornes   and   Hartley,   2007).   Application   of   this   approach   considerably   facilitates   the   analysis   of   Nash   equilib-­‐ ria  in  games    of  public  good  provision  which  are  quite  complex  in  the  scenario  consid-­‐ ered  in  this  paper.     2.  The  Framework   Let   there   be   n  countries   i = 1,...,n  be   given   which   all   have   the   same   initial   endowment   w  and  the  same  utility  function   u(xi ,G)  where   xi  denotes  private  consumption  of  coun-­‐ try   i     and   G  is   public   good   supply.   Especially   in   the   context   of   climate   change   G  can   be   interpreted   as   the   amount   of   greenhouse   gases   totally   avoided.   The   utility   function   is   assumed  to  have  the  standard  properties,  i.e.  it  is  twice  partially  differentiable  with  the   first   partial   derivatives   u1 (xi ,G) > 0     and   u2 (xi ,G) > 0  and   quasi-­‐concave.   Moreover,   we   suppose  that  the  private  and  the  public  good  both  are  strictly  non-­‐inferior.              The  crucial  element  for  our  analysis  is  that  the  countries  may  differ  in  their  produc-­‐ tivities   for   generating   the   public   good   which   are   represented   by   the   country-­‐specific   marginal  rates  of  transformation   mrti  between  the  private  and  the  public  good   ai :  This   productivities   indicate   how   many   units   of   the   public   good   country   i  can   produce   if   it   spends   one   unit   of   the   private   good   for   public   good   provision.   The   reciprocal   value   ci   = 1    then  indicates  how  many  units  of  the  public  good  country   i    has  to  give  up  in  order   ai to  get  one  additional  unit  of  the  public  good.  In  the  case  of  environmental  public  goods     ci  thus  represents  the  marginal  abatement  costs  of  country   i .                      Under  these  assumptions  a  feasible  allocation   (x1 ,..., xn ,G)     has  to  satisfy  the  aggre-­‐ gate  budget  constraint       n (1)                                                                                                                     G = ∑ ai (w − xi )     i=1   3        or,  equivalently,       n n i=1 i=1 (2)                                                                                                                     G + ∑ ai xi = ∑ ai w .     In  order  to  describe  the  Nash  equilibria  of  voluntary  public  good  provision  in  this  setting   by  means  of  the  Aggregative  Game  Approach  let   e(G, α i )  be  country   i ’s  (income)  expan-­‐ sion  where   α i     denotes  the  marginal  rate  of  substitution   mrsi     between  the  private  and   the  public  good.  As  non-­‐inferiority  of  both  goods  is  assumed  these  expansion  paths  are   well-­‐defined   and   strictly   monotone   increasing   in   G .   Along   an   expansion   path   e(G, α i )   the   indifference   curves   of   a   country   all   have   the   same   slope   −α i .   As   an   additional   as-­‐ sumption  regarding  preferences  we  assume  that   e(0, α i ) = 0  and   lim e(G, α i ) = ∞ .   G→∞                The   essential   point   for   the   characterization   of   Nash   equilibria   is   that   a   country   which  makes  a  strictly  positive  public  good  contribution  is  in  an  individual  equilibrium   position   only   if   its   mrsi  coincides   with   its   mrti ,   i.e.   α i = ai  holds.   Otherwise,   country   i   could   attain   a   higher   utility   level   either   by   slightly   increasing   (if   α i > ai )  or   by   slightly   decreasing  (if   α i < ai )  its  public    good  contribution.  This,  however,  means  that  in  an  in-­‐ terior  Nash  equilibrium   ( x̂1 ,..., x̂n , Ĝ)  with  positive  public  good  contributions  of  all  coun-­‐ tries,   country   i ’s   position   ( x̂i , Ĝ)  has   to   lie   on   the   expansion   path   e(G,ai )  such   that   x̂i = e(Ĝ,ai ) .                          As   a   benchmark   we   consider   the   case   in   which   the   productivity   parameters   ai  are   fixed   and   no   country   undertakes   efforts   to   improve   public   good   productivity.   Then   no   R&D-­‐costs  have  to  be  taken  into  account,  and  the  budget  constraint  (1)  for  an  interior   Nash  equilibrium  becomes     n (3)                                                                                                       Ĝ = ∑ ai (w − e(Ĝ,ai ))   i=1   n Given   our   assumptions   the   function   Φ(G) := ∑ ai (w − e(G,ai )) ,   whose   value   at   Ĝ  ap-­‐ i=1 pears  on  the  right  hand  side   of  eq.  (3),  is  strictly  monotone  increasing  and  continuous   and,  given  our  assumptions  on  expansion  paths,  has   Φ(0) = 0     and   lim Φ(G) = ∞ .  Hence,   G→∞   4      by  the  intermediate  value  theorem  there  exists  exactly  one  level  of  public  good  supply   Ĝ ,  which  fulfils  condition  (3).  If   e(Ĝ,ai ) < wi  holds  for  each  country   i = 1,...,n ,  the  Nash   equilibrium   is   interior   with   public   good   supply   Ĝ  and   private   consumption   levels   x̂i = e(Ĝ,ai ) .  In  this  Nash  equilibrium  country   i = 1,...,n  spends   ẑi = wi − x̂i  on  the  public   good  thus  inducing  an  increase  of  public  good  supply  by   ĝi = ai ẑi .       3.  Technological  Interdependencies   We  start  from  a  situation  in  which  all  countries  have  the  same  productivity  parameter   a0 .  Public  good  supply   Ĝ(a0 )  in  the  Nash  equilibrium  -­‐  which  is  clearly  interior  in  this   initial  state  of  full  symmetry  and  without  any  R&D-­‐costs  -­‐  then  is  given  by     (4)                                                                     Ĝ(a0 ) = na0 (w − e(Ĝ(a0 ),a0 ))                                                                           Now   the   possibility   arises   that   a   subgroup   of   countries   undertakes   some   R&D-­‐efforts   aimed  at  improving  “green”  technologies  (such  as  better  insulation  of  houses,  renewable   energies,  smart  grids  and  new  methods  for  power  storage)  through  which  the   reduction   of  carbon  emissions  becomes  cheaper  or,  in  other  words,  the  productivity  of  the  global   public  good  climate  protection  is  increased.  Through  intended  or  unintended  technolog-­‐ ical   spillovers   other   countries   may   also   benefit   from   these   productivity   enhancing   ef-­‐ fects   even   if   they   do   not   incur   any   of   the   costs   associated   with   developing   these   ecologi-­‐ cally  friendly  technologies.                  For  a  precise  description  of  this  scenario  we  divide  the  whole  group  of   n  countries   into  three  subgroups  K,  L  and  M  whose  members  are  playing  a  two-­‐stage  game.     Subgroup  K  consisting  of   k  countries   The   members   of   subgroup   k  are   forming   a   technological   coalition   which   is   willing   to   play  a  pioneering  role  in  climate  policy  by  collectively  promoting  green  innovations.  In   the  framework  of  our  model  this  means  that  at  the  first  stage  of  the  game  coalition  K  is   able  to  choose  an  improved  production  technology  for  the  public  good  which  exhibits  a     higher   public   good   productivity   a  than   the   original   technology.   Choosing   some   a > a0 ,   however,  is  not  costless  but  results  in  R&D-­‐costs  of   ck (a)  for  each  country  in  coalition  K.     This   cost   function   is   assumed   to   be   differentiable   in   a  and   has   ck (a0 ) = 0 .   If,   as   in   the     5      case   of   basic   research,   R&D-­‐costs   can   be   divided   among   the   members   of   the   coalition   ck (a)     will  –  for  any   a > 0  -­‐  fall  when   k  increases.  However,  if  technological  progress  is   based   on   learning-­‐by-­‐doing   activities,   which   have   to   be   carried   out   in   each   country   of   the  coalition  at  an  equal  scale,  then     ck (a)    will  not  be  affected  by  the  size  of  the  coalition.                    While   the   coalition   cooperates   at   the   innovation   stage,   the   coalition   members   still   act  independently  in  the  second  stage  of  the  game  at  which  the  coalition  members  de-­‐ cide  on  their  contributions  to  the  public  good.  This  assumption  reflects  the  notion  that  in   climate  policy  cooperation  on  abatement  levels  is  harder  to  achieve  than  technological   cooperation.     Subgroup  L  consisting  of     l    countries   The  members  of    subgroup  L  do  not  have  a  share  in  the  spillover:  They  stick  to  the  origi-­‐ nal   technology   with   the   productivity   parameter   a0  irrespective   of   the   technological   choice  made  by  coalition  K.  This  inability  to  make  use  of  the  better  environmental  tech-­‐ nologies  may  arise  from  specific  physical  or  meteorological  conditions.  E.g.  countries  in   the   tropical   zones   obviously   do   not   benefit   from   improved   efficiency   in   the   heating   of   buildings,  and  countries  like  Canada  with  fewer  sunshine  hours  than  Florida  cannot  gain   much  from  the  development  of  solar  technology.  But  it  is  also  possible  that  in  developing   countries  the  capacities  for  adopting  the  improved  technologies  are  lacking.  In  contrast   to   the   physical   limitations   these   obstacles   can   be   removed,   e.g.   through   education   and   the  formation  of  human  capital.     Subgroup  M  consisting  of   m  countries   For   subgroup   M   there   is   a   technological   spillover   from   the   technological   innovations   provided   by   coalition   K   so   that   they   become   more   productive   in   generating   the   public   good     -­‐   but   possibly   to   a   different   degree   as   the   coalition   members.   The   differentiable   function   b(a)  describes  which  productivity  parameter  results  in  each  country  in  M  when   the   productivity   parameter   chosen   in   coalition   K   is   a .   This   function   measuring   the   in-­‐ tensity   of   the   spillover   effect   is   monotone   increasing   in   a  with   b(a0 ) = a0 .   The   normal   case   will   be   b′(a) ≤ 1 ,   which   means   that   the   countries   in   M   benefit   not   more   from   the   innovation   than   the   countries   in   K.   Nevertheless,   situations   are   conceivable   in   which   b′(a) > 1  holds   so   that   the   productivity   increase   for   subgroup   M   is   even   larger   than   in   K.     6      An   example   for   this   might   be   solar   energy   when   in   the   countries   of   subgroup   M   solar   radiation  is  stronger  than  in  the  countries  of    subgroup  K.     Like   the   countries   in   coalition   K   also   the   countries   in   the   outsider   subgroups   L   and   M   determine  their  public  good  contributions  non-­‐cooperatively  at  the  second  stage  of  the   game.                    Applying  the  Aggregative  Game  Approach,  it  now  is  straightforward  to  describe  the   interior  Nash  equilibrium  which  results  when  coalition  K  has  chosen  some  productivity   parameter   a ≥ a0  as  we  know  that  in  the  Nash  equilibrium   • the  position  of  all  countries  in  K  is  on  the  expansion  path   e(G,a) .   • the  position  of  all  countries  in  L  is  on  the  expansion  path     e(G,a0 ) .   • the    position  of  all  countries  in  M  is  on  the  expansion  path     e(G,b(a)) .     Based   on   condition   (3)   public   good   supply   Ĝ(a)  in   the   Nash   equilibrium   if   coalition   K   has  chosen  the  productivity    parameter   a  is  characterized  by  the  following  equation:     (5)           Ĝ(a) = ka(w − e(Ĝ(a),a) − ck (a)) + la0 (w − e(Ĝ(a),a0 )) + mb(a)(w − e(Ĝ(a),b(a)) )  .           Private  consumption  of  the  countries  in  subgroups  K,  L  and  M  thus  is   x̂K (a) = e(Ĝ(a),a) ,   x̂ L (a) = e(Ĝ(a),a0 )  and   x̂ M (a) = e(Ĝ(a),b(a)) ,  respectively.  Note  that  in  eq.  (5)  it  is  taken   into   consideration   that   the   members   of   group   K   do   not   spend   the   whole   residual   be-­‐ tween  income  and  private  consumption  for  public  good  provision  because  they  have  to   spend     ck (a) > 0    for  R&D-­‐efforts  when  choosing  some   a > a0 .              Since   the   initial   Nash   equilibrium   is   interior   it   follows   from   a   standard   continuity   ar-­‐ gument  that  the  Nash  equilibrium  will  stay  interior  when  the  productivity  parameter   a     chosen   by   coalition   K   is   sufficiently   close   to   a0 .   The   analysis   to   follow   only   considers   these  cases.     4.  The  Change  in  Public  Good  Supply  through  Technological  Progress   Let   the   partial   derivative   of   any   expansion   path   e(G, α )  w.r.t.   public   good   supply   G  be   denoted   by   e1 (G, α )  which   describes   how   private   consumption   changes   if   one   is   moving     7      along   an   expansion   path.   Analogously,   e2 (G, α )  is   the   partial   derivative   of   the   expansion   path  w.r.t.  to  the  marginal  rate  of  substitution   α .  This  derivative  indicates  the  change  of   private  consumption  which  results  when  –  for  a  given  level  of  public  good  supply  –  the   move  is  to  another  expansion  path  corresponding  to  a  higher  marginal  rate  of  substitu-­‐ tion.   From   the   non-­‐inferiority   assumption   on   preferences   we   have   e1 (G, α ) > 0  and   e2 (G, α ) < 0 .   ∂Ĝ              To  calculate  the  effect  on  public  good  supply   Gˆ ′(a) =     which  is  driven  by  a  mar-­‐ ∂a ginal  change  of  its  productivity  parameter  by  coalition  K  we  first  consider  the  total  dif-­‐ ferential  of  eq.  (5)  at    some  arbitrary   a  for  which  interiority  holds  which  yields     (6)       Gˆ ′(a) =     − k(w − e(Ĝ(a),a) − ck (a)) − ka(e1 (Ĝ(a),a)Gˆ ′(a) + e2 (Ĝ(a),a) − ck′ (a))                                                           − lae1 (Ĝ(a),a)Gˆ ′(a)                                                           +   mb′(a)(w − e(Ĝ(a),b(a))) − mb(a)(e1 (Ĝ(a),b(a))Gˆ ′(a) + e2 (Ĝ(a),b(a))b′(a)) .     We  now  apply  eq.  (6)  to  infer  the  effects  on  public  good  supply  which  result  from  a  mar-­‐ ginal   change   of   a  starting   from   a0 = b(a0 ) .   Without   loss   of   generality   we   can   assume   a0 = 1 and,   to   simplify   notation,   we   use   abbreviations   as   follows:   Gˆ ′ = Gˆ ′(1) ,   ẑ = w − e(Ĝ(1),1) ,   κ k = ck′ (1) ,   β = b′(1) ,   γ 1 = e1 (Ĝ(1),1)  and   γ 2 = e2 (Ĝ(1),1) .   Since   ck (1) = 0     by  assumption  condition  (6)  then  turns  into     (7)                                                                 Gˆ ′ = k( ẑ − γ 1Gˆ ′ − γ 2 − κ k ) −lγ 1Gˆ ′ +m(β ẑ − γ 1Gˆ ′ − γ 2 β ) .     Solving  (7)  for   Gˆ ′  and  observing   k + l + m = n  gives  the  following  result.     Proposition  1:  If  coalition  K  marginally  increases  its  productivity  parameter   a  starting   from  the  symmetric  Nash  equilibrium  with   a0 = 1      then  public  good  supply  changes  by       (k + mβ )( ẑ − γ 2 ) − kκ k (8)                                                                                   Gˆ ′ =  .   1+ nγ 1     8      Public  good  supply  hence  increases  if  and  only  if     (9)                                                                                               kκ k < (k + mβ )( ẑ − γ 2 )                               Since   γ 1 > 0     and   γ 2 < 0  condition   (9)   directly   shows   that   –   for   a   given   partition   into   the   three   subgroups   –   an   increase   in   public   good   supply   results   if   the   aggregate   marginal   costs  for  the  technological  improvement   kκ k  are  not  too  high.  A  high  spillover  parame-­‐ ter   β  and   a   high   public   good   contribution   ẑ  in   the   original   Nash   equilibrium   are   also   favourable   for   an   increase   of   public   good   supply   as   both   help   to   make   the   increase   of   public  good  productivity  more  effective.                  If,  however,  the  R&D-­‐costs  are  sufficiently  high,  so  that   kκ k > (k + mβ )( ẑ − γ 2 )     holds,   public   good   supply   is   reduced   by   the   innovation.   The   reason   for   this   adverse   effect   is   that  due  to  the  costly  R&D-­‐efforts  coalition  K’s  resources  available  for  public  good  provi-­‐ sion  are  reduced  while  at  the  same  time  the  spillover  effect  is  too  weak,  either  because   only  few  countries  are  positively  affected  or  the  intensity  of  the  spillover  is  small.              In  addition  we  can  infer  from  conditions  (8)  and  (9)  how  for  a  fixed  total  number  of   countries   n  the   size   of   the   different   subgroups   affects   the   change   of   public   good   supply.   In  this  context  we  first  note  that   ẑ ,   γ 1  and   γ 2  refer  to  the  original  fully  symmetric  Nash   equilibrium  and  thus  do  not  depend  on   k, l  and   m  as  long  as  the  total  number  of  coun-­‐ tries   n = k + l + m    is  fixed.     Proposition  2:  Assume  that   Gˆ ′  is  positive.  Then   Gˆ ′    is  the  larger     • the    larger  the  coalition  K  is  when  aggregate  marginal  costs   kκ k  of  the  technolog-­‐ ical  improvement  are  not  rising  in   k .   • the    larger  the  group  M  is.   • the  smaller   γ 1    and  the  larger   −γ 2    are.     In  a  Nash  equilibrium  public  good  supply  normally  is  too  low  as  compared  to  Pareto  op-­‐ timal   levels   (see   Buchholz   and   Peters,   2001,   for   a   treatment   especially   of   exceptions).   Against  this  background  Proposition  2  says  that  this  “underprovision”  is  mitigated  both   through  a  spatial  expansion  of  the  technological  spillover,  i.e.  an  increase  of   m ,  and  an     9      increase  of  its  intensity   β .    The  same  positive  effect  on  public  good  supply  occurs  if  the   coalition  K  is  enlarged  given  that   β ≤ 1  and   kκ k  is  decreasing  in   k .              For  a  further  interpretation  of  Proposition  2  note  that  a  small   γ 1  means  that  in  a   xi -­‐ G -­‐diagram  the  income  expansion  path   e(G,1)  is  relatively  steep.  Then  along  this  expan-­‐ sion  path  an  increase  of  public  good  supply  is  accompanied  by  a  small  increase  in  pri-­‐ vate  consumption  which  is  favourable  for  an  increase  of  public  good  supply  when   a  is   increased.  The  same  holds  true  for  a  large  value  of   −γ 2  which  represents  a  strong  shift   of  the  expansion  path  to  the  left  and  thus  a  large  increase  of  the  willingness  to  pay  for   the  public  good.                  As  a  next  step  we  examine  the  incentives  the  coalition  K  has  for  making  a  green  in-­‐ novation  through  which  its  public  good  productivity  is  increased.     5.  The  Incentives  for  Coalition  K  to  Make  the  Technological  Improvement   Given   some   productivity   parameter   a  utility   of   a   member   of   coalition   K   is   ûK =   u(e(Ĝ(a),a), Ĝ(a))  in   the   Nash   equilibrium   as   e(Ĝ(a),a) = x̂K (a)  is   its   private   consump-­‐ tion.  A  marginal  variation  of   a  changes  this  utility  by     (10)                         uˆ K′ (a) =   u1 ( x̂K (a), Ĝ(a))(e1 (Ĝ(a),a)Gˆ ′(a) + e2 (Ĝ(a))) +u2 ( x̂K (a), Ĝ(a))Gˆ ′(a) .     Without  loss  of  generality  we  can  assume  that  at  the  original  Nash  equilibrium  for   a0 = 1   we  have   û1 ( x̂K (1), Ĝ(1)) = û2 ( x̂K (1), Ĝ(1)) = 1 .  With  the  abbreviations  as  introduced  before   and  additionally  letting   uˆ K′ = uˆ K′ (1)  eq.  (10)  then  is  reduced  to           (11)                                                                                                     uˆ K′ = (1+ γ 1 )Gˆ ′ + γ 2 .     Based  on  eq.  (11)  a  precise  condition  for  an  increase  of  utility  for  countries  in  the  coali-­‐ tion  K  is  provided  by  the  next  result.  In  its  first  part  this  Proposition  is  a  direct  conse-­‐ quence  of  eq.  (11)  and  in  its  second  part  it  follows  from  plugging   Gˆ ′  as  given  by  eq.  (8)   into  eq.  (11).       10      Proposition  3:  Starting  from  the  Nash  equilibrium  with   a0 = 1    the  members  of  coalition   K  benefit  from  an  increase  of  their  public  good  productivity  if  and  only  if         −γ 2 > 0               (12)                                                                                                           Gˆ ′ > 1+ γ 1 holds  or,  equivalently,  if  and  only  if     (13)                                                                                 kκ k <   (k + mβ )( ẑ − γ 2 ) + γ 2 1+ nγ 1 .     1+ γ 1   As   γ 1 > 0    and   γ 2 < 0    it  follows  from  condition  (12)  that  a  higher  public  good  supply  is  a   necessary  but  not  a  sufficient  condition  for  an  increase  of  a  coalition  member’s  utility:   The  coalition  members  only  benefit  from  their    R&D-­‐efforts  when  the  increase  in  public   good  supply  is  strong  enough.            The  factors  which  determine  the  right  hand  side  of  inequality  (13)  are  similar  to  those   characterizing   the   change   of   public   good   supply:   An   enlargement   both   of   the   coalition   K   and  of  the  group  M  are  favourable  for  an  increase  of  utility  for  the  members  of  K.  Con-­‐ cerning  the  incentives  for  innovation  in  K  this  in  particular  shows  how  important  it  is  to   ensure   a   broad   dissemination   of   the   improved   technologies.   Giving   patents   for   green   technological   innovations   to   other   countries   away   free   of   charge   thus   may   be   a   clever   strategic  move  for  coalition  K.              Concerning  the  second  term  we  note  that   1+ nγ 1  is  increasing  in   γ 1 .  Hence,  a  utility   1+ γ 1 increase  for  countries  in  coalition  K  is  more  likely  if   γ 1    is  small.  The  effect  of   γ 2 ,  howev-­‐ er,  is  ambiguous.       6.  Utility  Effects  for  the  Outsiders   We  now  examine  how  utility  of  the  countries  in  the  groups  L  and  M  is  changed  by  the   innovative  activities  of  coalition  K.            Differentiating   utility   û L (a) = u( x̂ L (a), Ĝ(a)) = u(e(Ĝ(a),a0 ), Ĝ(a))  of   a   country   in   L   and     utility   û M (a) = u( x̂ M (a), Ĝ(a)) = u(e(Ĝ(a),b(a)), Ĝ(a))     of   a   country   in   group   M   w.r.t.   the   productivity  parameter   a  yields       11      (14)                             u ′L (a) =   u1 ( x̂ L (a), Ĝ(a))e1 (Ĝ(a),a0 )Gˆ ′(a) + u2 ( x̂ L (a), Ĝ(a))Gˆ ′(a) .     (15)   u ′M (a) = u1 ( x̂ M (a), Ĝ(a))(e1 (Ĝ(a),b(a))Gˆ ′(a) + e2 (Ĝ(a),b(a))b′(a))                                                              +   u2 ( x̂ M (a), Ĝ(a))Gˆ ′(a)       Assuming   again   a0 = 1 and   u1 ( x̂(1), Ĝ(1)) = u2 ( x̂(1), Ĝ(1)) = 1  and   abbreviating   uˆ ′L = uˆ ′L (1)   and   uˆ ′M = uˆ ′M (1)  a   marginal   change   of   productivity   at   the   initial   Nash   equilibrium   thus   results  in  utility  changes  as  follows:     (16)                                                                                                                   uˆ ′L = (1+ γ 1 )Gˆ ′       (17)                                                                                                                     uˆ ′M = (1+ γ 1 )Gˆ ′ + βγ 2 .     Comparing   the   utility   changes   for   the   three   groups   K,   L   and   M   as   described   by   eqs.   (11),   (16)  and  (17)  leads  to  the  following  result:     Proposition  4:  If  coalition  K  marginally  increases  its  public  good  productivity  starting   from   the   Nash   equilibrium   with   a0 = 1  the   countries   in   K   benefit   least   while   countries   in   the  group  L  benefit  most,  i.e.   uˆ K′ ≤ uˆ ′M < uˆ ′L .       The   interpretation   of   Proposition   4   is   as   follows:   Through   the   change   of   public   good   productivity   in   coalition   K   utility   of   countries   in   each   subgroup   is   equally   affected   by   (1+ γ 1 )Gˆ ′ ,  which  is  positive  if  public  good  supply  increases.  For  countries  in  K  there  is,   however,  a  negative  partial  effect  on  utility  which  is  expressed  by   γ 2 < 0  and  which  re-­‐ flects  the  increased  willingness  to  pay  for  the  public  good  when  productivity  improves.     The   same   effect   hits   the   group   M   but   to   a   lesser   degree   if   the   spillover   is   incomplete,   i.e.   β < 1 .     If,   however,   β = 1  the   utility   change   is   the   same   for   group   K   and   group   M   even   though  only  the  members  of  the  coalition  K  initially  bear  the  cost  of  the  green  innova-­‐ tion.  This  means  that,  due  to  equilibrium  repercussions,  R&D-­‐costs  can  be  shifted  to  oth-­‐ er   countries.   This   indirect   redistribution   effect   is,   in   a   certain   sense,   similar   to   the   fa-­‐ mous   Warr   neutrality   in   voluntary   public   good   provision   (see   Warr,   1982,   and   e.g.     12      Cornes   and   Sandler,   1996)   which   in   particular   implies   that   in   an   interior   Nash   equilibri-­‐ um  an  increase  of  income  in  some  country  will  increase  utility  not  only  in  that  specific   country  but  in  all  countries.              The   negative   effect,   which   arises   from   the   change   of   the   willingness   to   pay   for   the   public   good   implied   by   the   technological   improvement,   is   completely   absent   for   coun-­‐ tries  in  group  L  whose  technology  is  unaffected  by  the  innovation.  Therefore,  the  mem-­‐ bers   of   this   group   benefit   most.   This,   however,   creates   an   incentive   problem   because   countries  in  group  K  attain  a  higher  utility  level  if  they  do  not  adopt  the  better  technolo-­‐ gy  for  public  good  provision.  This  strategic  effect,  however,  is  avoided  if  the  technologi-­‐ cal   spillover   occurs   automatically   which,   e.g.,   is   the   case   if   firms   in   coalition   K   are   the   dominant   producers   of   energy   technology   and   thus   can   set   environmentally   friendly   standards   worldwide   (see,   e.g.,   Barrett,   2003).   For   the   countries   in   group   M   also   co-­‐ benefits  from  climate  friendly  may  arise  which,  on  the  one  hand,  may  be  caused  by  im-­‐ proved  possibilities  to  abate  locally  damaging  pollutants  as,  e.g.  particulate  matter  from   power  plants  (see,  e.g.,  Finus  and  Rübbelke,  2013)  and,  on  the  other  hand,  by  the  pro-­‐ spect  of  initiating  a  sustainable  growth  process  implied  by  the  transition  to  a  low-­‐carbon   economy  (see  Stern,  2015).  In  this  way  the  adoption  of  green  technologies  is  promoted.   In  the  sense  of  “issue  linkage”  the  coalition  may  also  introduce  separate  incentive  mech-­‐ anisms  (as,  e.g.,  additional  financial  aid)  to  ensure  broad  dissemination  of  its  green  in-­‐ novation.              Moreover,  the  countries  outside  the  coalition  K  may  notice  that  their  unwillingness  to   apply   the   new   technology   can   undermine   the   willingness   of   coalition   K   to   make   the   R&D-­‐efforts.  To  prevent  this  undesirable  outcome  the  outsiders  also  may  form  a  sepa-­‐ rate  coalition  in  which  they  commit  themselves  to  adopt  the  improved  technology.     7.  An  Example   We  now  specifically  assume  that   w = 1  and  that  all  countries  have  the  Cobb-­‐Douglas  util-­‐ ity  function   u(xi ,G) = xiρ G .  For  some  marginal  rate  of  substitution   α  the  expansion  path   is  given  by   e(G, α ) = ρ ρ ρ G     which  gives   e1 (G, α ) =     and   e2 (G, α ) = − 2 G .    According  to   α α α eq.  (4)  the  symmetric  Nash  equilibrium  at   a0 = 1 is  given  by  the  public  good  supply  level     13      Ĝ(1) = n nρ ,   the   private   good   consumption   levels   x̂(1) =     and   country-­‐specific   nρ + 1 nρ + 1 public  good  contributions   ẑ(1) = 1 nρ  .    Since   γ 1 = ρ    and   γ 2 = −    we  get   nρ + 1 nρ + 1   k + mβ − kκ k (18)                                                                                                                   Gˆ ′ =     nρ + 1   (19)                                                                                               uˆ K′ = ( ρ + 1)(k + mβ − kκ k ) − n ρ     nρ + 1   (20)                                                                                                 uˆ ′L = ( ρ + 1)(k + mβ − kκ k )   nρ + 1     (21)                                                                                                     uˆ ′M = ( ρ + 1)(k + mβ − kκ k ) − n ρβ   nρ + 1   We  now  especially  look  at  eq.  (19)  and  consider  the  extreme  case  when  there  is  only  a   single   pioneering   country,   i.e.   k = 1 .   The   innovation   is   profitable   for   this   country   if   its   R&D-­‐costs  are  below  a  certain  threshold  level,  i.e.     (22)                                                                                                     κ 1 < 1+ mβ − nρ .     ρ +1   Now  let  either   m = 0  or   β = 0  so  that  there  are  no  technological  spillovers.  Then,   even   if   the   innovation   is   completely   costless,   the   potentially   pioneering   country   has   no   incen-­‐ tive   to   increase   its   public   good   productivity   if   1− nρ ρ +1 < 0     or,   equivalently,   n > ,   ρ +1 ρ which   is   always   the   case   if   the   total   number   of   countries   is   sufficiently   large.   A   single   country   then   would   even   have   an   incentive   to   choose   a   technology   with   higher   abate-­‐ ment  costs,  which  is  the  paradoxical  effect  described  by  Buchholz  and  Konrad  (1994).                But  if  in  contrast  there  is  a  technological  spillover  the  innovation  will  be  profitable  for   the  country  if  the  technological  spillover  extends  to  sufficiently  many  countries,  i.e.  if         14      (23)                                                                                                                         m> (n − 1) ρ − 1 ( ρ + 1)β       Some   values   for   m  which   satisfy   condition   (23)   exist   if   the   right   hand   side   of   this   ine-­‐ quality  is  smaller  than   n − 1 ,  i.e.  if  the  spillover  is  sufficiently  strong  so  that       (24)                                                                                                                           β > β := 1 nρ ( − 1)     n −1 ρ +1   holds.   In   the   case   of   a   perfect   spillover   condition   (24)   is   always   fulfilled.   The   example   thus   clearly   illustrates   how   a   single   country’s   incentive   to   innovate   depends   on   the   number  of  followers  and  the  strength  of  the  spillover  effect.  For  a  further  specification   consider  the  case  where   n = 10  and   ρ = 1 .  Then  without  a  spillover  a  costless  marginal   increase  of  public  good  productivity  does  not  pay  for  a  single  country.    But  if  there  is  a   spillover  with   β = 1 ,  which  benefits  at  least  five  other  countries,  condition  (24)  implies   that  the  innovation  becomes  worthwhile  for  the  country  which  undertakes  it.  Moreover,   the   lower   threshold   for   the   productivity   parameter   which   is   obtained   from   condition   (24)    is   β = 4 .     9   8.  Conclusion   In  this  paper  we  have  shown  how  the  provision  of  a  global  public  good  such  as  climate   protection  may  be  improved  through  unilateral  action  of  a  group  of  countries  which  col-­‐ lectively  carry  out  a  green  technological  innovation  lowering  the  costs  of  providing  the   global  public  good,  i.e.  in  the  case  of  climate  change  the  costs  of  greenhouse  gas  abate-­‐ ment.  The  success  of  such  a  specific  form  of  leading  behaviour  not  only  is  more  likely  if   the  cooperating  coalition  is  large  but  also  if  there  is  a  steep  rise  of  public  good  produc-­‐ tivity   in   as   many   other   countries   as   possible,   i.e.   if   the   technological   spillover   effect   is     strong  both  at  the  intensive  and  at  the  extensive  margin.  A  basic  message  of  this  paper  is   that   it   is   not   only   favourable   for   the   climate   but   also   for   the   coalition   if   these   follower   countries   get   free   access   to   the   improved   technology   and   thus   receive   some   indirect   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