• No results found

Adoption of a clean technology using a renewable energy

N/A
N/A
Protected

Academic year: 2020

Share "Adoption of a clean technology using a renewable energy"

Copied!
15
0
0

Loading.... (view fulltext now)

Full text

(1)

Adoption of a clean technology using a

renewable energy

Ben Youssef, Slim

Ecole Supérieure de Commerce de Tunis

September 2010

Online at

https://mpra.ub.uni-muenchen.de/25576/

(2)

, $

- ! ! .# !

! ! # # ! !

! / . # # #

# ! # .

. ! - # # #

.# ! # .# !

0 ! # ! # # ! # .#

1 2 . # 1 ! # .#

# ! # ! # #

. # # 1 3 # #

! ! # ! #

# ! # ! #

Keywords$ ! # ! . !

(3)

! "

! ! # . ! # ! . !

! # ! #

0 # ! ! #

. / ! # # !

# ! # # . #

. !

4 % (()' # ! .# # . #

! # ! ! # # !

. # / # . !

! # ! . # # 1 7 8

! # # # ! # #

! # ! #

# . # ! # !# % +'

9 # / : # !

.# # .# # ! 1 # !

.# # 2 # #

! # # 3 ; % ('

! 1 # # 9 # 9 !

. ! # # $

! # # 9 # ! 1 3 #

: < = % '

# # ! . # !

2 # . # # 1

. # #

-# # # % )' # # !

. # ! ! ! 3 # > " 7 #

<# % (' # . # #

# ! ? et al. % (' # . # # # .

(4)

% (' # 7

. ! # / + # 7

# .# "# %">'. 7

# # ! #

!# ! # !

7 # 7 ! # # ! . #

! # ! " < B % (' . #

. % / ' 0 # #

! !

# # . 7 # # # ! # .

# # ! . # 1

# # ! 1 !

- ! ! ! % !'

# ! - # 7 7

8 ! 9 % C' .# # # . !

! # ! ! #

# ! . # !

! / # # . !

# ! # 9 .

. ! - # .#

# ! # 1 / .# #

# ! .# # ! # !

-# .# # !

! # ! # ! # !

# .# # ! # #

# # 1

3 # # 1 ! # # !

# .#

0 .# # ! . # # ! # ! !

(5)

: # 8 .#

# # ! 0 # #

. # !

. 2 . # # !

# ! # # # , # # #

# ! # .# -# # 1 !

# ! # ! :

# #

# . # # # 1 !

# !# # .#

D . # # < = % ' .#

# ! # #

! # 8 .# # # # !

E 4 % (()' #

! B # # ! # !

# ! F8 88 .# # # !

/ 9 # . # #

# .# # !

# . # *

# ! 6 # 1 !

0 + . # # &

E /

#!

- ! ! : q #

7 p(q)=a bq, a,b>0

# # ! ! :

2 0 ( ) ( ) 2 )

(q p z dz p q q bq

(6)

E # ! ! # ! 0 # !

# ! ! # 9

G e>0

# # # E=eq .# # ! #

: D=αE .# α>0 # ! ?

# # . # ! #

# . # 7

- # # ! # ! # d>0 # #

1 p q q dq

d = −

Π ( )

# # # 9 .

# ! . # τ # # !

. ! % ! ' # #

. c ! 0<c<d # # #

. ) (q q cq p

c = −

Π

E ! # . # ! #

# @A4 G # : #

! # ! # . . #

# !

# ! # # ! τ 9 0 $

τ

θ

τ e mr

V( )= − % '

.# θ>0 # # ! # ! r>0 #

m>1 # # .# m !

, V ! # / 1

# ! # # .#

/ # @A4 .# #

# ? 8 7 # τ=+∞ # #

(7)

$!

0 # . # .# # ! #

@ # # 7 ! # 1 ! .

. # 1 : 3 / . #

!

-# # # # ! # . $

) ( ) ( )

(q D q q

CS

Sd = − +Πd % '

/ 9 ! # / ! % ' . # q ! # 1

. # # ! # ! $

b e d a

qˆd = − −α %*'

- # . ! # : $

e d

a> +α %6'

# # / . ! # ! # !# # #

! # ! !

# ! ! E 1 / 1

t # 1

0 # # $

) ( ) (q tE q

Udd − %+'

# 1 1 1 / # # qˆd $

e q b d a

t = − −2 ˆd %&'

! # / qˆd . # . # $

e d a

t >0⇔ < +2α %)'

# # 1 / .# # ! !

# !# !# D # . ! ! # # ! 9

. # #

-# # # # ! # . $

) ( )

(q q

CS

(8)

/ 9 ! # / ! %H' . # q ! # 1 . # # ! # ! $

b c a

qˆc = − %('

0 # qˆc >qˆd # # # !

. #

# # 1 !

1 s # 1

0 # # $

sq q

Ucc( )+ % '

# 1 1 # # qˆc $

a c q b

s=2 ˆc + − % '

! # / qˆc . # . # s>0

%! & '

0 # . . # .# # !

.# # # !

-# # # ! # / 9 Πd ! #

$ 2

b d a qdn

2

= % '

-# # ! # ! # / 9 Πc ! #

$

b c a qcn

2

= % *'

0 # # . # # # !

.

(

qcn >qdn

)

- # # $

(9)

e d a q

qˆd > dn ⇔ − >2α % 6'

0 . # # ! # ! # 1 7

# ! # # !#

# # .# # ! ! . !# 2 .

. # # # ! # . . # qˆc >qcn

7 .

(! )

# . # !

1 ! $

τ τ τ θ mr rt c c rt d

d q e dt S q e dt e

S

IS

+∞

+

=

(ˆ )

(ˆ )

0 % +'

τ τ τ θ mr rt c c rt d

d q e dt U q e dt e

U

IU =

(ˆ ) − +

+∞ (ˆ ) − − −

0 % &'

τ τ τ θ mr rt n c c rt n d d

n q e dt q e dt e

IU =

Π ( ) − +

+∞Π ( ) − − −

0 % )'

0 # . # . ! .# #

. # !θ G m# !# !#$

mr q

U q

Ucc)− dd)<θ % H'

# ! # / 9 # . #

τ ! # 0 # E / . #

1 # # !

# 1 ! .# # $

0 ) ˆ ( ) ˆ ( ln ) 1 ( 1

ˆ >

     − − = mr q S q S r m d d c c θ τ (19) 0 ) ˆ ( ) ˆ ( ln ) 1 ( 1

* >

     − − = mr q U q U r m d d c c θ τ (20) 0 ) ( ) ( ln ) 1 ( 1 * >       

Π Π

(10)

We have the following ranking for the optimal adoption dates:

* * ˆ

0<τ <τ <τn (22) Therefore, the optimal adoption date for the regulated firm is earlier than the socially optimal one. However, the optimal adoption date for the non regulated firm is later than the socially optimal one.

Proof. See the Appendix.

# # # #

! # ! # # 1 ! #

# # : % (' 0 .# # ! #

# ! !

/ # .

: # ! # ! # ! , #

# # ! !

# 8 .# # 1 ! #

# : ! # . # ! #

3 # # 1 ! # !

# ! . #

" / # ! # # !

# 1 # # # #

#

0 # # ! IU(τ*) IU(τˆ).# #

*

τ τˆ # #

% ' $

0 ) ˆ ( )

( * − >

=IU τ IU τ

g % *'

(11)

*!

0 # . ! ! !

# ! 2 . # # ! . #

! ! / #

# ! # ! # 9

. . ! - #

.# # ! # 1 / .#

# # ! .# # !

-# .# # !

-# # ! . # # ! # ! !

/

: ! 0 #

# . #

! . 2 . #

# ! # ! # # # -# #

1 ! # ! # !

:

# # # . , # .

# . !

# 1 ! # # ! #

.# 1 0 ! # ! # !

# ! # .# # !

# # # # #

# 1 2 . # !

! # ! # #

(12)

+

, "

ISc qc Sd qd a b(qˆd qˆc) c (qˆc qˆd) (d c)qˆd eqˆd 2 ) ˆ ( ) ˆ

( − + − +α

    − + − = −

< ! # / qˆd qˆc # 7 / :

. 2

e c d− +α

# . # $ 0 ) ˆ ˆ ( 2 ) ˆ ( ) ˆ

( cd d = − + c + d >

c q q

e c d q S q

S α % 6'

IUc(qˆc)−Ud(qˆd)=

[

ab(qˆc +qˆd)

]

(qˆcqˆd)+(sc)qˆc +dqˆd +teqˆd

< # ! ! # /t # s # /

d

qˆ qˆc . $

0 ) ˆ ˆ ( ) ˆ ( ) ˆ

( − = 2− 2 >

d c d

d c

c q U q b q q

U % +'

c(qcn)−Πd(qdn)=

[

ab(qcn+qdn)

]

(qcnqdn)+dqdncqcn

< ! qcn qdn . # 7 # . ! $

0 ) ( 2 ) ( )

( −Π = − + >

Π n d n c n d d n c

c q q

c d q q % &' # # # ! # . .#

# 1 0 #

# # ! 1 !

,

I< ! / % 6' % +' . # $

(

c c d d

) (

c c d d

)

(

c d

)

(

qc qd

)

e c d q q b q S q S q U q

U ˆ ˆ

2 ˆ ˆ ) ˆ ( ) ˆ ( ) ˆ ( ) ˆ ( +     − + − − = − − − α

< ! # / qˆd qˆc # 7 / . $

(

) (

)

(

ˆ ˆ

)

0

2 ) ˆ ( ) ˆ ( ) ˆ ( ) ˆ

( cd dc cd d = − + c+ d >

c q q

e c d q S q S q U q U α % )'

(13)

(

)

(

)

(

)

(

)

[

c d cn dn

]

(

c d

)

n d n c d c n d d n c c d d c c q q e q q q q c d q q c d q q e c d q q q S q S ˆ ˆ 2 ˆ ˆ 2 2 ˆ ˆ 2 ) ( ) ( ) ˆ ( ) ˆ ( + + − − + − = + − − + + − = Π − Π − − α α

< ! qˆd qˆc, qcn qdn # # 7 . $

(

c c d d

)

(

c cn d dn

)

(

qc qd

)

e b e d c a c d q q q S q

S ˆ ˆ

2 2 2 2 2 ) ( ) ( ) ˆ ( ) ˆ ( + +     − − − − = Π − Π −

− α α

! %6' # 7 ! $

(

)

(

)

(

ˆ ˆ

)

0

2 4 ) ( ) ( ) ( ) ˆ ( ) ˆ ( 2 > + + − > Π − Π −

n c d

d d n c c d d c

c q q

e b c d q q q S q S α % H'

# . # # . ! 7 !$

) ˆ ( ) ˆ ( ) ˆ ( ) ˆ ( ) ( ) (

0<Πc qcn −Πd qdn <Sc qcSd qd <Uc qcUd qd % ('

# ! ! # # ! ! # !

# # .# # # # 1 !

, )

I ! # 1 # ! / 9 #

. ! % +' . # τ$

(

(ˆ )− (ˆ )

)

+ =0

= ∂

τ θ τ

τ Sd qd Sc qc e r mre mr

IS %* ' : %* ' : $ ⇔ = +

− (ˆ ) − 0

) ˆ

( d c c θ (1 m)rτ

d q S q mre

S       − − = mr q S q S r m d d c c θ

τ ln (ˆ ) (ˆ )

) 1 (

1

ˆ %* '

< m>1 % H' : % (' τˆ>0

- # $

(

)

τ θ τ

τ mr r d d c

c q S q e mr e

S r

IS

− − = ∂ ∂ 2 2 2 ) ( ) ˆ ( ) ˆ ( ! # ! %* ' . ! $ 0 ) 1 ( ) ˆ

( 2 ˆ

2 2 < − = ∂

θ − τ

τ

τ m m r e mr

IS

(14)

I # ! / 9 ! % &' . #

τ$

(

(ˆ )− (ˆ )

)

+ =0

= ∂

τ θ τ

τ Ud qd Uc qc e r mre mr

IU %* ' : %* ' : $ ⇔ = +

− (ˆ ) − 0

) ˆ

( d c c θ (1 m)rτ

d q U q mre

U       − − = mr q U q U r m d d c c θ

τ ln (ˆ ) (ˆ )

) 1 ( 1 * %**'

< m>1 : % H' τ* >0

- # $

(

)

τ θ τ

τ mr r d d c

c q U q e mr e

U r

IU

− − = ∂ ∂ 2 2 2 ) ( ) ˆ ( ) ˆ ( ! # ! %* ' . $ 0 ) 1 ( )

( 2 *

2 * 2 < − = ∂

θ − τ

τ

τ m m r e mr

IU

# #

I # 1 ! / 9 ! % )' . #

τ$

(

Π ( )−Π ( )

)

+ =0 =

∂ − τ θ − τ

τ d dn c cn r mr

n mre e q q IU %*6' # : $ ⇔ = + Π −

Πd(qdn) c(qcn) θmre(1−m)rτ 0

  

 

Π Π

− = mr q q r m n d d n c c n θ

τ ln ( ) ( )

) 1 ( 1 * %*+'

< m>1 : % H' % (' τn* >0

- # $

(

)

τ θ τ

τ mr r n d d n c c n e mr e q q r

IU

− Π − Π = ∂ ∂ 2 2 2 ) ( ) ( ) (

! # ! %*6' . $

0 )

1 ( )

( 2 *

2 * 2 < − = ∂

n nmr n

e r m m

IU θ τ

τ τ

#

-,

(15)

* * ˆ 0<τ <τ <τn

# ! # .# .# # 1

!

< = % ' F8 E # !

0 0 88 Economics Bulletin * )*61 )6*

C % (' F8C ! ! # , @ . !

88 Energy Economics * 66*166(

4 % (()' F8 " E , 0

" 0 # ! # ! " < 88

Environmental & Resource Economics H+1*

? 2 2 J 7 1 # ? @ " < K C 2 % (' F8"

@ ! @ , , $ 0 ! ! 2 #

- ! 1 1" ! @ # 4 88 Ecological Economics &H )* 1)6

3 , C ; % (' F8 E / C 1 # E <

C # 88 Energy Policy *) 6+ 616+

" 0 @ @ < B % (' F8@ . ! 0 $ " 88

Energy *6 () 1(H

4 " > % +' F8 # 0 " 0 # !

E ! 1 ! # ! 88 Resource and Energy Economics ) *+1 6)

> @ " 7 # 0 K <# % (' F8 !

0 @ . ! 88 Renewable and Sustainable Energy Reviews * ) &1 )

-# # J ? # % )' F8 - ! " C !

" ! $ E /1E /1" 2 # < !

References

Related documents

The use of sodium polyacrylate in concrete as a super absorbent polymer has promising potential to increase numerous concrete properties, including concrete

Florian Kohlmayer*, Fabian Prasser*, Claudia Eckert, Klaus A. A flexible approach to distributed

Given the fact that the governance mechanism has an interactive effect to moderate the relationship between tax avoidance and firm value, this study will investigate further on

Based on the result of the statistical analysis in this study, TBL and STAD equally had a positive impact on students' motivation and reading achievement. Both methods were

Step 2 : During a Self-Registration, a player will confirm they last played football in another country. other

To determine if data available from national and local microbiology surveillance systems can be utilised for outbreak detection of infectious diseases within the acute

Having a visual sequence beside the toilet can help your child understand what is expected of them, for example: trousers down, pants down, sit on the toilet, wee/poo in the

Conclusions: Compared with non-Xp11.2 translocation RCCs, the Xp11.2 translocation RCCs seemingly showed a higher tumor grade and pathologic stage and have similar