Theoretical Economics Letters, 2013, 3, 262-266
http://dx.doi.org/10.4236/tel.[phone] Published Online October 2013 (http://www.scirp.org/journal/tel)
Consumption Tax, Nontraded Goods and Welfare
Wataru Johdo
Faculty of Economics, Tezukayama University, Nara, Japan
Received July 3, 2013; revised August 3, 2013; accepted August 13, 2013
Copyright © 2013 Wataru Johdo. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
This paper studies the welfare effects of a consumption tax rise based on the two-sector small open economy model of
Obstfeld and Rogoff (1995) and Lane (1997). The main findings of our analysis are that 1) in the case of free trade, the
consumption tax rise has no effect on welfare, 2) when there is the nontraded goods sector, the consumption tax rise has
a negative effect on welfare, and 3) the larger the share of nontraded goods in consumption is, the larger the negative
welfare effect of consumption tax will be.
Keywords: Consumption Tax; Nontraded Goods; Trade Openness; Small Open Economy; Welfare
1. Introduction
In the new open economy macroeconomics literature
pioneered by Obstfeld and Rogoff [1], the relationship
between monetary expansions and aggregate economic
activity has been studied extensively at the theoretical
level.1 This literature has focused on how the macroeco-
nomic activity and welfare of multiple countries are in-
fluenced by unanticipated monetary shocks in one coun-
try under monopolistic distortions and price rigidities.
The benchmark model of Obstfeld and Rogoff [1] shows
that a domestic monetary expansion raises consumption
in both countries by lowering the world interest rate,
which results in an increase in world consumption de-
mand, and thereby improves foreign and domestic wel-
fare. At the same time, in the appendix, Obstfeld and
Rogoff [1] also sketch a small open economy model that
incorporates a nontraded goods sector and show the pos-
sibility of exchange rate overshooting. Then, Lane [5]
extends the small open economy model in Obstfeld and
Rogoff [1] to include government behavior and shows
how variation in trade openness affects the welfare ef-
fects of expansionary monetary policy shocks. Further-
more, Cavallari [6] and Lee and Chinn [7] also take the
two-sector small open economy model of Obstfeld and
Rogoff [1] (or Lane [5]) and study how the current ac-
count and exchange rate are influenced by monetary pol-
icy shocks. Johdo [8] also generalizes the two-sector
small open economy model of Lane [5] to include habit
formation, and examine how the strength of habit forma-
tion affects the response of welfare to monetary policy
shocks.
However, no studies have attempted to examine the
welfare effects of an increase in a consumption tax by
using the two-sector small open economy model. The
purpose of this paper is to contribute theoretically to the
new open economy macroeconomics literature by gener-
alizing the small open economy model of Obstfeld and
Rogoff [1] and Lane [5] to include a consumption tax
rate and examining the question of how the degree of
trade openness (or the share of nontraded goods in con-
sumption) affects the response of welfare to an increase
in the consumption tax rate.
The main findings of our analysis are that 1) in the
case of free trade, the consumption tax rise has no effect
on welfare, 2) when there is the nontraded goods sector,
the consumption tax rise has a negative effect on welfare,
and 3) the larger the share of nontraded goods in con-
sumption is, the larger the negative welfare effect of con-
sumption tax will be.
The remainder of this paper is structured as follows. In
Section 2, we outline the features of the model. In Sec-
tion 3, we present the symmetric equilibrium with flexi-
ble nominal prices. In Section 4, we present a log-lin-
earized version of this model. In Section 5, we analyze
the welfare effect of a permanent consumption tax rise
and examine how the degree of trade openness affects the
responses of welfare to the consumption tax shock. Sec-
tion 6 gives the conclusion.
1For surveys of the new open economy macroeconomics models, see
Lane [2], Sarno [3] and Lane and Ganelli [4].
C
opyright © 2013 SciRes. TEL

W. JOHDO 263
2. A Two-Sector Small Open Economy
Model
Following Obstfeld and Rogoff [1] and Lane [5], we
consider a small open economy with two sectors, a
traded goods sector and a nontraded goods sector, with
nominal price rigidities. The traded goods sector is char-
acterized by a single homogeneous endowment, and the
price of traded goods is determined in perfectly competi-
tive world markets. Meanwhile, the nontraded goods
sector is a monopolistically competitive market with dif-
ferentiated goods. In this model, a unit mass of agents is
characterized as both consumers and producers, where
each agent produces a unit of nontraded differentiated
goods. The agents have perfect foresight, derive their
utility from consuming a homogeneous good and a group
of differentiated goods and from holding real money
balances, and incur the cost of expending labor (or pro-
duction) effort.
The intertemporal objective of a typical agent at time 0
is to maximize the following lifetime utility:


00
2
log1 log
log ,
2
tTt Nt
t
tNt
t
UC
Myi
P
 











C
(1)
where is a constant subjective discount factor,
Nt

0, 1  

y
it is the agent’s output of nontraded goods in pe-
riod is the share of the consumption of
traded goods, Tt is consumption of the traded good,
and

,0,1  C
N
t is composite nontraded goods consumption,
defined as:
C




1
11
0d
Nt Nt
CCi i




, (2)
where  () is the elasticity of substitution between any
two differentiated goods and CNt(i) is the consumption of
nontraded good i. The second term in (1) represents real
money balances

tt

M
P, where M
t denotes nominal
money balances held at the beginning of period t  1, and
Pt is the consumption price index, which is defined as:


1
1
1,
1
tTtNt
t
PP
P









 (3)
where t

is the consumption tax rate and PNt is the price
of nontraded goods and is defined as:



11
11
0d
Nt Nt
PPii




, (4)
and PTt is the domestic currency price of traded goods.
Because there are no trade costs, the law of one price
holds for traded goods; i.e., , where Et is the
nominal exchange rate and P
Tt* is the exogenously de-
termined world price. A typical agent faces the following
budget constraint:
*
Ttt Tt
PEP




 
11
1
1,
Tt ttTtttNtNt
Tt TtTtTtNtNtt
PBMPrBMPi yi
PyPC PCT 

 

 (5)
where Bt+1 denotes real bonds denominated in traded
goods in period 1t

, r denotes the world real interest
rate in traded goods on bonds that applies between peri-
ods 1t

and t, and Tt denotes lump-sum transfers from
the government. In the government sector, we assume
that government spending is zero. Hence, the government
budget constraint is


1tTtTt NtNtttt
PCPCM MT 
 .
In addition, in this model, each agent is endowed with a
constant amount of the traded good in each period.
Therefore, as shown in (5), we can delete the subscript t
from yTt, i.e., yTt = yT, t.

At the first stage, agents maximize the consumption
index (2) subject to a given level of expenditure on non-
traded goods
 
1
0d
Nt NtNtNt
P
CPiCii
by optimally
allocating differentiated nontraded goods. This static
problem yields the following demand function for good i:
 
,
Nt
N
t
Nt
Pi
yi C
P
 



NAt
(6)
where C
NAt is aggregate consumption. At the second
stage, agents maximize (1) subject to (5). For simplicity,
we assume


1r  1

. Then, the first-order conditions
for this problem can be written as:
1Tt Tt
CC


, (7)
1Tt
N
t
Nt
P
C
P









Tt
C , (8)
1
11
1
1
1,
1
tTt
tTtt t
Tt
Ttt Tt
MP
CPP
P
PC






 

 

 
 
 

 



(9)




1
1
11 11 ,
1
Nt
NAt
tNt
yi
C
C



 

 



 
(10)
and the terminal condition is
 
1
lim1 10
T
tTtT tT
TrB MP
 
 



.
3. Steady-State Flexible Price Equilibrium
Henceforth, we assume that initial net foreign assets are
zero (B  ). In the steady state, all exogenous variables
are constant. Substituting (8) into (10) and considering

W. JOHDO 264
the symmetric equilibrium CN  yN  CNA, we obtain:

12 12
11 1
1
NN
Cy

 








. (11)
Equation (11) shows that all agents produce the same
output of nontraded goods. Meanwhile, from (7) and a
fixed endowment of traded goods output, the consump-
tion of traded goods remains constant in each period; i.e.,
CTt  yT, t. This implies that the current account is
always balanced.
4. A Log-Linearized Analysis with Nominal
Rigidities
To examine the effects of an unanticipated permanent
consumption tax rise, we solve a log-linear approxima-
tion of the system around the initial, zero-shock steady
state. Following Obstfeld and Rogoff [1] and Lane [5],
we assume nominal price rigidities under which the price
of nontraded goods in period t is predetermined at time t
 1. In addition, the price of nontraded goods is assumed
to be fully adjusted after one period. For any variable Xt,
we use to denote the short-run (long-run)
percentage deviation from the initial steady-state value.
The short-run percentage deviation is proportional to the
degree of the nominal price rigidity under which the
output of nontraded goods is determined by demand. In
the long run, the price of nontraded goods adjusts per-
fectly to the new steady-state value to be consistent with
the optimal conditions (10).

1
ˆˆ
tt
XX


First, in the short run, as the price of nontraded goods
is sticky, we obtain . In addition, as the con-
sumption of traded goods remains constant in each pe-
riod, we obtain 1Tt Tt. By log-linearizing Equa-
tions (8) and (9), and considering and
ˆ0
Nt
P
ˆ0CC


ˆ
ˆ0
Nt
Pˆ0
Tt
C

,
respectively, we obtain:
ˆ ˆ
Tt Nt
PC, (12)

1
1
ˆˆ ˆd
11
TtTt Tt
PPP





 



. (13)
Equation (12) shows that the consumption of non-
traded goods is affected positively by the price of traded
goods in the short run. Equation (13) shows that the price
of traded goods is affected by the consumption tax rise.
With , the short-run response in the consumption
price index is
ˆ0
Nt
P
1
ˆ
d
1
t
Pˆ
Tt
P







 . (14)
In the long run, the economy reaches a steady state.
Therefore, for the price of traded goods, we obtain
12
. Substituting
ˆˆ
Tt Tt
PP

1
ˆˆ
Tt Tt
PP
1
1
ˆd
1
Tt
P 


0






. (15)
In addition, from the consumption price index, we ob-
tain

11
1
ˆˆˆ
d1
1
tTt
PP  

1Nt
P






 
1
. (16)
Furthermore, from (8), we obtain
11
ˆ ˆˆ
Tt Nt Nt
PPC




. (17)
Substituting (17) into (16), we obtain

11
1ˆ
ˆˆ
d1
1
tTt
PP 

1Nt
C






 
. (18)
From (11), we obtain
11
11
ˆˆd
21
Nt Nt
Cy 


0

 


 . (19)
Substituting (15) and (19) into (18), we obtain
1
11
ˆd
21
t
P




0




 . (20)
Equation (20) shows that the consumption tax rise al-
ways increases the consumption price index in the
long-run. Meanwhile, in the small open economy model,
because the world price of traded goods is determined
exogenously and always holds, we obtain
*
Ttt T
PEP
ˆ
Tt t
PE
ˆ

in the short run. This implies that the price of
traded goods reacts proportionately to the exchange rate.
By substituting ˆˆ
Tt t
PE

into (13), the short-run re-
sponse of the exchange rate to a consumption tax rise is
given by:
1
ˆd
1
t
E 

0






. (21)
Equation (21) shows that a rise in the consumption tax
rate appreciates the exchange rate. Therefore, from
ˆˆ
Tt t
PE

, (14) and (21), the consumption tax rise always
increases the consumption price index in the short-run,




ˆt
P11 d0 

 
 . Finally, from (12) and (21),
we obtain:
1
ˆd
1
Nt
C 

0





 . (22)
Equation (22) shows that the consumption tax rise de-
creases the consumption of nontraded goods in the short
run. In addition, from (6) and

1
NN
PiP, we obtain
ˆ
ˆ
N
tNt
y
C. Therefore, by linking this to (22), we obtain:
1
ˆ
ˆd
1
Nt Nt
yC 

0

 


 . (23)
2


 into the long-run
case of (13), we obtain:
Equation (23) shows that the consumption tax rise also
decreases the output of nontraded goods in the short run.

W. JOHDO 265
5. Welfare Analysis
Our interest here lies in exploring the welfare effects of a
consumption tax rise. Recalling that , we
can rewrite Equation (1) as:
1
ˆˆ 0
Tt Tt
CC


R
M
UU U , (24)
where


2
0
2
101
ˆˆ
1
ˆˆ
1
1
RNtNNt
NtN Nt
UCyy
Cyy








,


 
11
ˆˆˆˆ
1
Mtt t
UMP MP





 


 t
,
where yN0 denotes the initial steady-state output of non-
traded goods. The short-run and long-run results for non-
traded consumption, output and price index can be used
to derive the impact of a consumption tax rise on welfare.
By substituting these results into (24), we obtain:


11
121
1
1d
1
U







 










 





0.

(25)
The first term of the right hand side in square brackets
of Equation (25) reflects the net welfare effect, composed
of the welfare loss from a decrease in the consumption of
nontraded goods and the welfare gain from a decrease in
the production effort of nontraded goods. From   and
  , we find that the first term of Equation (25) is al-
ways negative. The second term is the welfare loss from
a decrease in the real balances through and
1. Therefore, the impact of a consumption tax rise
on welfare is always negative.
ˆ0
t
P
ˆ0
t
P
The intuitive explanation is as follows. The welfare
effect is determined by two mechanisms. On the one
hand, an unanticipated permanent consumption tax rise
requires an instantaneous decrease in the price of traded
goods to restore the traded goods market equilibrium for
a given constant endowment of tradable output. With
fixed nontraded goods prices, the decrease in the price of
traded goods in turn raises the relative price of nontraded
goods and thereby decreases the consumption of non-
traded goods. The importance of this negative nontrad-
able consumption effect depends positively on the share
of nontraded goods in consumption, ( −  ). On the other
hand, the consumption tax rise also increases the price
index and thereby decreases real balances. Here, recall
from , (14) and (21) that the impact of a con-
sumption tax rise on the price index depends positively
on the share of nontraded goods in consumption, (  ),
from
ˆˆ
Tt t
PE

ˆt
P11
d0
  


. Therefore, the scale
of this negative real balance effect depends positively on
( − ). Thus, for reasons mentioned above, the larger
the share of nontraded goods in consumption, the larger
the negative welfare effect of consumption tax.
Here, remember that the parameter


01 


measures the degree of trade openness, where  ap-
proaches one as the degree of trade openness increases
and approaches zero when trade is extremely costly.
Therefore, Equation (25) also shows that the larger the
size of trade cost, the larger the negative welfare effect of
consumption tax.
Incidentally, in the extreme case of free trade 
 = 1,
the impact of a consumption tax rise on welfare is:
10U  

. (26)
Thus, under free trade, the consumption tax rise has no
effect on welfare. Intuitive explanation of this result is as
follows. First, the negative nontradable consumption
effect disappears when  = 1 as shown in the above. Sec-
ond, recall that the consumption tax rise has two oppos-
ing effects on the consumption price index. On the one
hand, a rise in the consumption tax increases the price
index directly from (3). On the other hand, the consump-
tion tax rise decreases the price index through an appre-
ciation in the nominal exchange rate (see (21)). Therefore,
there are two conflicting price index effects of a con-
sumption tax rise. However, from , (14) and
(21), when  = 1, these two changes in the price index
offset each other, and hence, the negative real balance
effect also disappears. Thus, under free trade, the con-
sumption tax rise has no effect on welfare.
ˆˆ
Tt t
PE
6. Conclusion
We have used the two-sector small open economy model
of Obstfeld and Rogoff [1] and Lane [5] to consider the
response of welfare to a consumption tax rise. The main
findings of our analysis are that 1) in the case of free
trade, the consumption tax rise has no effect on welfare,
2) when there is the nontraded goods sector, the con-
sumption tax rise has a negative effect on welfare, and 3)
the larger the share of nontraded goods in consumption is,
the larger the negative welfare effect of consumption tax
will be. In particular, the latter results indicate the fol-
lowing policy implication: when trade is costly, the con-
sumption tax rate must be decreased from a welfare point
of view. Further, the actual data suggest that the second
result in the above is consistent with the impacts of a
consumption tax rise in Japan and the UK. Indeed, in
Japan, the consumption tax rate was raised from 3% to
5% in 1997, while the real GDP growth rate was 2.6% in
1996 but it fell to 1.6% in 1997 (IMF, 2013 [9]). In addi-
tion, recently, in the UK, the consumption tax rate was
raised from 17.5% to 20% in 2011, while the real GDP
growth rate was 1.8% in 2010 but it fell to 0.9% in 2011

W. JOHDO 266
(IMF, 2013, [9]). Therefore, the main result of this paper
is supported with the actual data, because, in both Japan
and UK, the real GDP growth rates fall after the con-
sumption tax rise.
7. Acknowledgements
The author would like to thank an anonymous referee for
valuable comments and suggestions. The author is also
grateful to have received financial support from Tezuka-
yama University.
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