ECON4910 Environmental economics, Spring 2011
Michael Hoel:
Lecture 6: Environmental taxes and other taxes
Revised February 28, 2011
Please bring this lecture note as well as the articles by Bovenberg and Hoel with you to the
lecture.
Reading list:
Bovenberg, A. Lans : Green Tax Reform and the Double Dividend: an Updated Readers
Guide, 1999. International Tax and Public Finance 6. 421-443.
Sections 1 and 2. link.
Hoel, M.: Environmental taxes in an economy with distorting taxes and distributional
concerns, Memorandum No. 04/2008, 2008. Department of Economics, University of Oslo.
Sections 1, 2, 3 (to 3.2) and Appendix B. link.
Outline of lecture:
1. Early literature on the interaction of environmental taxes and other taxes (Hoel,
section 1)
2. A simple model for a one person economy (Bovenberg, section 1 and 2; Hoel, section
2)
3. Extension to a heterogeneous population (Hoel section 3, main points)
4. The Kaplow result (appendix B)
Early literature
Revenue from an environmental tax can be used to reduce other distorting taxes. This gives
rise to the following questions that have been discussed in the literature:
a) Does an environmental tax increase social welfare even if the environmental
improvement is ignored (“double dividend”)? (no)
b) Is it better to use the revenue from an environmental tax to reduce a distortionary tax
rather than reimburse it in a lump-sum manner? (yes)
c) Is the optimal rate of the environmental tax higher than the Pigovian level? (only if the
supply of labor is decreasing in the real after-tax wage)
d) Does the revenue aspect imply an additional advantage of environmental taxes
compared with other environmental policies?
1
A one person economy
In the lecture I will show:
-
A tax on labor gives a distortion in the labor market, with too little labour supplied. To
reduce this distortion labor supply must increase.
-
Labor supply depends on the after tax real wage (and perhaps directly on the amount
of pollution)
-
Even if the tax on labor goes down due to the revenue from the environmental tax, the
real after-tax wage will no go up:
o If the polluting good is a consumer good: The increased price of this good
more than outweighs the tax cut (Bovenberg)
o If the polluting good is a production input: The wage goes down, and this
more than outweighs the tax cut (Hoel)
Bovenberg section 2: The effect of changing an emission tax q when the polluting good is
a consumer good
(All equations will be explained in more detail in the lecture.)
Two consumption goods x (the polluting good) and y (the numeraire good). Labor input is L,
pollution is E=kx and Government consumption is G (exogenous and constant).
Budget equations:
px  y  G  wL
country
( p  q) x  y  (1  t ) wL  s
household
qx  twL  G  s
government
Utility function:
W  u ( x, y,1  L, G, E )
Household behavior:
ux
 pq
uy
and
u1 L
 (1  t )w
uy
giving labor supply function L  L( p  q, (1  t ) w, s)
Welfare effect of changing q (choosing units so k=1)
 u dx dy u dL  u  dE 
dW
 uy  x

 1 L
 E  
dq
 u y dq dq u y dq  u y  dq 
From the country’s budget equation we have
2
p
dx dy
dL

w
0
dq dq
dq
Combining these two equations and using the household equilibrium conditions therefore
gives, when units are chosen so k=1):

u
dW
 u y  q  E

dq
uy

 dx
dL 
  tw 
dq 
 dq
The optimal carbon tax follows from
q opt
dW
 0 , giving
dq



u
w  dL
t
where the term in brackets is positive
 E 
u y   dx  dq
 dq 


We can therefore conclude:
If t=0: q opt 
uE
uy
If t>0: q opt 
uE
u
dL
dL
if
 0 (and q opt  E if
 0)
dq
dq
uy
uy
Assume that increasing q makes it possible to reduce t. This reduction in t will increase L if
L(1t ) w  0 . But the increase in q will have a direct negative effect on L if L p  q  0 . Bovenberg
shows that this direct effect dominates, implying
dL
 0 , if
dq
u( x, y,1  L, G, E)  U  M Q( x, y),1  L  , G, E  and Q is homogeneous of degree 1.
Hoel section 2: The effect of changing an emission tax q when the polluting good is a
production input
(All equations will be explained in more detail in the lecture.)
Assume constant returns to scale or that any profits go to the government. Let w be the wage
rate and q be the emission tax. Then
(1)
F ( L, E )  ( L, E )  pE
(2)
F ( L, E)  C  G  (1  t )wL  s   G
(3)
L  L  (1  t )w, s   L  n, s  (i.e. n  (1  t ) w )
Moreover
E, G and s are exogenous.
3
The welfare effect of changing E:
W  u ( F ( L, E )  G,1  L, E , G )

u
dW
 uF  FE  E
dE
uF

Using
 
u1 L  dL 

   FL 

u F  dE 
 
u1 L
 (1  t ) w , FL  w , and FE  q it follows that
uF

u
dW
 u F  q  E
dE
uF


dL 
  tw 
dE 

The optimal carbon tax follows from
q opt 
dW
 0 , giving
dE
uE
dL
 tw
uy
dE
We can therefore conclude:
If t=0: q opt 
u E
uF
If t>0: q opt 
u E
u
dL
dL
 0 (and q opt  E if
 0)
if
dE
dE
uF
uF
The effect on labor supply of changing E (for given s):
From (2) and (3) we have
(4)
F ( L(n, s), E )  nL(n, s)  G  s
Hold s constant and reduce E
(5)
 L  twLn 
Implying that
dn
 FE
dE
dn
t  n
 0 for  L  twLn   0 , i.e. for
 Ln   1 , which we assume is
dE
1 t  L 
satisfied. A reduction in E hence reduces n, and therefore also L if Ln  0
The effect on labor supply of increasing s (for given E):
From (4) we find
4
-  L  twLn 
(6)
implying
dn
 1  nLs  FL Ls  1  twLs  0
ds
dn
dL
dn
 0 and
 Ln
 Ls  0 (it can be shown that this inequality holds also if
ds
ds
ds
Ln  0 ). Returning the revenue from the emission tax in the form or increased s instead of
reduced t therefore gives an additional reduction in L.
The Kaplow result (see Hoel, Appendix B)
-
separable preferences
-
“rich” tax system, so a change in E can be “compensated” by a change in tax
parameters so everyone is equally well off as before the change in E, whatever labor
supply choice they make
-
If environmental tax ≠ Pigou level, it is possible to change E and taxes as described
above so that the government gets a budget surplus (see Appendix B)
-
This surplus can be used to make every one better off
5