Theoretical Economics Letters, 2011, 1, 28-32
doi:10.4236/tel.[phone] Published Online August 2011 (http://www.scirp.org/journal/tel)
Tourism, Terms of Trade and Welfare to the Poor
Bharat Raj Hazari, Jian Jing Lin
Department of Economics and Finance, City University of Hong Kong, Hong Kong, China
Received April 11, 2011; revised June 7, 20 11; a c cepted June 20, 2011
Abstract
The paper investigates the impact of an increase in tourism and a change in the terms of trade on the welfare
of different classes in an economy. We set up a three-sector, three-factor (one specific) model of general
equilibrium to derive the results. The most important result we obtain is that tourism can immiserize the poor.
In the concluding section we argue that a tax on tourism (a non-distortionary tax) should be used to subsidize
the poor and restore their welfare level.
Keywords: Tourism, Terms of Trade, General Equilibrium, Welfare
1. Introduction
There exist two interesting and important results in the
theory of internation al trade. The first result is associated
with Bhagwati and states that in the presence of a distor-
tion growth may be immiseri zing. Although this result is
very old the interest in it is still alive as is shown by a
recent paper by Sonnenschein et a l. (2009) [1]. They d em-
onstrate that immiserizing growth occurs in the presence
of monopoly power in trade and reverse Rybczynski ef-
fect. Bhagwati (1 958) [2] had shown that in the presence
of monopoly power in trade growth may be immiserizing.
The second important result in trade theory is due to
Sonnenschein (1967) [3] that an improvement (deteriora-
tion) in the terms of trade raises (lowers) welfare. In both
these results it is generally assumed that there is a repre-
sentative agent. In this paper we relax the assumption of
a representative agent and divide the society in two
groups of households: poor and rich. These households
differ from each other in terms of their endowments of
capital, labour and a specific factor. Given this disaggre-
gation we analyse the impact of an increase in tourism
and a change in the terms of trade on the welfare of these
groups. This provides an extension of immiserizing
growth theorems, that is, immiserization of a partcular
class of indiviuals or households as a result of a pa ramet-
ric change.
We consider a model in which there are two types of
households: rich and poor. Each type of household is
characterized by expenditure functions and they also
provide factors of production. The economy produces
three goods: an importable, an exportable and a non-tra-
ded good. In this type of framework we introduce tour-
ism where tourists consume the non-traded good. Tour-
ism is defined as a temporary movement of consumers to
consume non-traded goods, for example, white beaches,
monuments of national heritage, art galleries and so on
(Hazari et al. 2004 [4]). The consumption of non-traded
goods by tourists creates a nontraded goods terms of
trade effect. This movement in the terms of trade may be
immiserizing to the rich or the poor (and in representa-
tive agent models to the n ation as a whole). Our analysis
is important given that tourism is one of the most impor-
tant growth industries in the world and is promoted
heavily by various governments both in developed and
third world countries. The most important result we ob-
tain is that tourism can immiserize the poor. In the con-
cluding section we argue that a tax on tourism (a
non-distortionary tax) should be used to subsidize the
poor and restore their welfare level.
2. Model
We set up a three-sector, three-factor (one specific) mode l
of general equilibrium to analyze the impact of tourism
on the welfare of the poor and rich. The assumption of a
representative agent is relaxed and instead we assume
that there are two groups of individuals: poor and rich.
These groups differ in terms of their factor endowments
and therefore may not have the same welfare conse-
quences as a result of an increase in tourism.
The economy produces three goods: 1
X
, 2
X
and
N
X
. It is assumed that both 1
X
and 2
X
are intertion-
ally traded goods. 1
X
is importable and 2
X
is ex-

B. R. HAZARI ET AL29
portable. The go od
N
X
is the non-traded good wh ich is
consumed by domestic consumers and tourists. Its price
must be determined endogenously, that is, local plus
tourist demand must equal its supply. All commodities
are assumed to be substitutes in consumption. These
goods are produced by the following neo-classical pro-
duction function s:


1111
,
X
FLK (1)


2222
,
X
FLK (2)


,,
NNNN
X
FLKZ (3)
where i and i L
K
denote the labor and capital allo-
cated to the ith sector respectively while

1, 2,iN
Z
is specific to the non-traded goods sector. The non-traded
goods sector is assumed to be labor-intensive. The
economy is considered to be small in the traded goods
sector s. Therefor e, the terms of trade are given from
outside. However, the price of the non-traded good is
determined endogenously. The commodity 1 is assumed
to be the numeraire.
P
We assume that the markets are competitive. The
pricing equations are given below:
11
1
LK
araw
aw
(4)
22LK
ar P (5)
L
NK
a
NZN
aw raP
N

  (6)
where denote the Leontief variable input coeffi-
cients, P and
'
ij
as
N
P denote the relative price of good 2 and
the non-traded good respectively, w and r are wage rate
and rental on capital respectively, and

is the price of
the specific factor Z. Note that w, r,

and
N
P are
determined endogenously.
Both the poor and rich supply labor. There are house-
holds in each group and each of them is assumed to pos-
sess one unit of labor. The rich income group is denoted
by R and the poor by P. However, only the rich class
supplies capital and the fixed factor Z. The resources are
fully employed:
11 22
p
R
LNN
aXa XLL 
LL
aX
2KK
aX
(7)
11 2R kNN
aXaX Lk  (8)
R
ZN N
aX Lz (9)
where
P
L and
R
L are the labor supply of the poor an d
rich class respectively, k is capital endowments per
household and z is the specific factor possessed by each
household. Both the labor and capital are assumed to
freely mobile among the three sectors while factor Z is
specific to the non-traded goods sector. This is a three-
good, three-factor model with factor specificity.
It is now appropriate to discuss the structure of the in-
come classes: rich and poor. Each class is represented by
an expenditure function. In equilibrium, the expenditure
of each class must equal their income so that:


,,
PPP P
N
LEPP ULw (10)



,,
RRR R
N
LEPP ULwrkz



ii
(11)
where represents expenditure and the utility of
each class
E U


1, 2,iN.
The economy-wide budget constraint is given by the
equality between revenue an d expenditure:





,,,,,,
,,
PP P
NN
RRR T
N
N
GPP LKZLEPPU
LEPP UEP


(12)
where G represents the revenue function and


T
N
EP
is the total expenditure of the tourists. This function is
convex in prices and concave in factor endowments. By
differentiating Equation (12) with respect to
N
P and
adding tourists’ demand to local demand, we obtain the
following equation:

,
NNN
PP R
PPRPTN
GLELEDP


 (13)
The left-hand side of this equation shows the output of
commodity
N
X
and the right-hand side the demand for
this good. At the point of equilibrium demand must equal
supply. This equation determines the relative price of
N
P. The term T denotes the demand for the non-
traded goods by tourists and
D

is a shift parameter. It
is assumed that:
0
TT
DD


 (14)
At a later stage, we will analyze the impact of a shift
in tourism demand on the welfare for each group.
We will be using the reciprocity condition at a later
stage. These are given below:
N
P
L
N
wG
P

, N
P
k
N
rG
P

, N
P
z
N
G
P
 
,
P
L
wG
P

,
P
K
rG
P

 and
P
Z
G
P
 
.
We assume that the non-t raded good i s la bor-intensitve
while the traded goods are capital-intensive:
12
N
kkk Therefore:
0
N
PL
G

, 0
N
Pk
G

, , , 0
N
PZ
G0
PL
G
0
PK
G

, and 0
PZ
G

In the next session, we are going to analyze the impact
from the change of tourism demand (

) and the impact
of terms of trade (P) respectively. As usual, when we do
the comparative statics analysis, we only allow one ex-
ogenous variable to change each time and then see what
happens to other endogenous variables, i.e., the welfare
of different classes.

B. R. HAZARI ET AL. 30
P

RR
3. Results and Analysis
3.1. An Increase in Tourism and Welfare of the
Poor
In this section, we analyze the impact of a shift in tour-
ism demand on the welfare of the poor and rich using the
method of comparative statics. By totally differentiating
equations (10) and (11) , we obtain:

0
NN
PP
PPLNU
EGdPEdU (15)

0
NN NN
P
PPLPK PZNU
EG kGzGdPEdU  (16)
The excess demand functions of the non-traded good
for each class are denoted by:
N
PP
P
NP
EG  
L
N NN
RP R
P
NPLPK P
EG kGzG   Z
In general,
P

and
R

cannot be of the same sign
as everyone cannot be on the same side of the market.
However, in this model there are tourists who consume
this good. Therefore,
P

and
R

can both be nega-
tive but both can not be positive, that is: 1) 0
P


,
; 2) , and 3) , 0
R
 0
P
 0
R
 0
P
 0
R


.
Due to the reciprocity condition, we can conclude that
, .
0
P
 0
R

By totally differentiating equation (13), we obtain:

NNNNNN N
NN
PP RR

P
PPPPPTP
PP PRR R
PUPU T
GLELEDd
LE dULE dUDd

N
P


 
(17)
Let
NNNNN NN
PP RR
P
PPPTPP
LELED G  
P
.
It is obvious that 0

. Using this definition, we can
rewrite equation (17) as
NN
PPP RRR
NPUPU T
dPLEdULEdUD d


 (17’)
Equations (15), (16) and (17’) provide us with three
equations in three unknowns
N
dP ,
P
dU and
R
dU as
functio ns of d

. The system is given below:
0 0
0 0
NN
UN
RR
P
U
R PP RRT
PU PU
EdP
EdU
Dd
dU LE LE



PP



 

 







 
 


(18)
By solving the above system, we obtain: (1) the
change in the relative price of the non-traded goods and
(2) the impact on welfare of poor and rich of an increase
in tourism. The determinant of the left-hand side of the
system in equation (18) is given below:
NN
P
PP RRRR PPR
P
UUPUU UU
DLEE LEEEE  
By the assumption of Walrasian stability this is posi-
tive.
The solutions for
N
dP ,
P
dU and
R
dU are given
below:
RR
UUT
N
EED
dP d
D


 (19)
PR
UT
PED
dU d
D



 (20)
RP
UT
RED
dU d
D



 (21)
Proposition 1: An increase in tourism raises the rela-
tive price of the non-traded good.
This is a very straightforward result. An increase in
demand for tourism represents a shift in the demand for
the non-traded good. An increase in demand in general
raises the relative pr ice of the non-traded good . Note that
this is a trade model and there exist demand shifts in
trade literature in which demand shifts do not necessarily
raise the relative price o f a particular commod ity. In this
context see the paper by Bhagwati and Johnson (1960) [5]
and also the textbook by Kemp (1969) [6] where many
kinds of demand shifts are considered. We will assume
that the demand shifts invariably lead to an increase in
the relative price of th e non-traded good.
Proof: , , and
Note that and from the properties of
the expenditure function.
0D0
P
U
E
0
P
U
ER
U
E0
R
U
E0
T
D


0
Proposition 2: For and , an increase
in tourism necessarily immiserizes the poor but improves
the welfare of the rich.
0
P
 0
R
 
The model we have set up captures demand and sup-
ply effects for each class of individuals. An increase in
the relative price of the non-traded good has both supply
and demand effects. The poor and rich both demand and
supply the non-tr aded good. If the excess demand for the
non-traded good is positive as is the case we are demon
strating then the demand effect dominates the supply
effect. In other words the poor do not earn enough from
increase supply of the non-traded good to cover the out-
lay on the demand for this good as its price increases.
Therefore, their welfare level must fall when their excess
demand is positive. By the same logic the welfare of the
rich must increase when their excess demand is positive.
Proof: Obvious from equations (20) and (21).
In the case of Propositions 2 the government must de-
vise compensation mechanisms such that the losing
groups are not hurt by an increase in tourism. This is
very important for economies that are heavily dependent
on tourism and tourism is an important earner of foreign
exchange.

B. R. HAZARI ET AL31
P
P
3.2. Terms of Trade and Welfare of the Poor
In this section we analyze the impact of a change in the
terms of trade on the relative price of the non-traded
good (which has a an additional terms of trade effect in
this model) and on welfare of the poor and rich. Does
disagregation matter for the result of Sonneneschein and
Krueger (1967) [3] that an improvement in the terms of
trade is always welfare raising? By differentiating equa-
tions (10) and (11) with respect to P the terms of trade,
we obtain:


NN
RPP
PPLNU PLP
EGdPEdUGEd (22)


NN NN
R
RR
PPLPK PZNU
R
PLPKPZ P
EG kGzGdPEdU
GkGzGEdP
 
  (23)
The excess demand functions for commodity 2 for
each class are now denoted by:
PP
P
PL
EG  
RR
P
PL PKPZ
EG kGzG   .
These excess demand functions are different from
those used in the previous section of the paper. Since
commodity 2 is assumed to be an exportable good, the
aggregate excess demand

P
R


0
must be negative.
From the reciprocity and factor intensity conditions we
know that , PK, and , 0
PL
GG0
PZ
G
P

and
R

can both be negative or of opposite signs, that is: 1 )
; 2) , and 3) ,
. We will assume that both the poor and rich class
are net suppliers of commodity 2. Therefore, we will
only focus on the case: .
00
P

R

0
R
 00
R
 
0R  
P

P

0
P

0
By totally differentiating equation (13) with respect to
P the terms of trade, we obtain:



NNNNNNN
NN NNN
PP RR
PP PP PPTPN
PP PRRRPPRR
PUPUPPPP PP
GLELEDdP
L
EdU LEdULELEGdP

 
(24)
Let
0
NNN
PP RR
PPPP PP
LELE G  
i


.
Note that N
PP on the assumption
that goods are substitutes in consumption. Then we can
rewrite equation (24) as
0E

,iPR
NN
PP PRR R
NPU PU
dPL EdUL EdUdP    (24’)
Equations (22), (23) and (24’) provide us with three
equations in three unknowns
N
dP ,
P
dU and
R
dU as
functions of terms of trade . The system is given
below: dP
0
0
NN
PP P
UN
RRP
U
R PPRR
PU PU
EdP
dP
EdUdP
d
dU
LE LE


R











 

 







(25)
By solving the above system, we obtain: (1) the
change in the relative price of the non-traded goods and
(2) the impact on welfare of poor and rich as a conse-
quence of an improvement in the terms of trade. The
determinant of the left-hand side of the system in Equa-
tion (25) is given below:
NN
P
PP RRRR PPR
P
UUPUU UU
DLEELEEEE  
.
By the assumption of Walrasian stability this is posi-
tive.
We first analyze the impact of an improvement in
terms of trade on the price of the non-traded good. The
solution for
N
dP is given below:
NN
PP PRRR RPPR
PU UPU UU U
N
LE ELE EEE
dP dP
D
 

(26)
Proposition 3: An improvement in terms of trade
necessarily increases the relative price of the non-traded
good.
Proof: 0
P


, 0
R


, , , ,
, , , and
0
P
L
00
N
P
PU
E
00
R
L
0
N
R
PU
E0R
U
E
P
U
E

 Note that
N and N. from the properties of the ex-
penditure function.
0
P
PU
E0
PU 
R
E
An improvement in the terms of trade raises domestic
income which spills over to increase the consumption of
non-traded goods. This increase in the demand results in
an increase in th e re lative price of the non-traded good.
Therefore, both the mathematics and intuition are con-
sistent with each other.
We now present the results of the welfare for the poor
and rich households.


NN
RPPPPPRPPRP
PU UPUU
RLE ELEE
dU dP
D
   

(27)


NN
PRRRRRPRRPR
PU UPUU
PLE ELEE
dU dP
D
   

(28)
Proposition 4: An improvement in terms of trade
necessarily improves the welfare of the rich.
Proof: , 0
R
 0
R


, , , , 0
P
 0
R
 0
P
L
, , , 0
N
P
PU
E0
R
L0
N
R
PU
E0

, , 0
P
U
E
and 0
R
U
E0


.
In the previous section we had established that an in-
crease in the relative price of the non-traded good raises

B. R. HAZARI ET AL. 32
the welfare of the rich group (of course under certain
conditions). Here, also the price of the non-traded good
increases so the result of the previous section must hold
in this parametric shift also. However, there is an addi-
tional terms of trade effect which is also positive. This is
nothing other than the normal terms of trade effect. So
the rich gain from two favourable movements in the
terms of trade; one movement from the commodity terms
of trade and the second movement from the tourism
terms of trade.
Proposition 5: An improvement in terms of trade im-
proves the welfare of the poor provide d that

NN
R
PP PPRR RRPR
P
UPUU
LELE EE
U
 


 .
Proof: , , , , , 0
P
 0
R
 0
P
 0
R
 0
P
L
, , , 0
N
P
PU
E0
R
L0
N
R
PU
E0

, , 0
P
U
E
and 0
R
U
E0

.
In the case of Proposition 4 and 5, both the rich and
poor classes are better off due to an improvement in the
terms of trade. This is consistent with Sonnenschein’s
theorem that an improvement (deterioration) in the terms
of trade raises (lowers) welfare. Hence, even in a disag-
gregated framework under certain conditions the Kruger-
Sonnenschein result holds.
Proposition 5’: An improvement in terms of trade
immiserizes the poor provided that

NN
R
PR RPRR RRPR
P
UPUU
LELE EE
U
 


 
Proof: Can be derived by changing the inequality in
Proposition 5.
It is clear from Propsitions 2 and 5’ that the welfare of
the poor can fall as a result of an expansion in tourism
and from an improvement in the terms of trade.
4. Conclusions
The results about the immiserization of the poor as result
of an increase in tourism and/or an improvement in the
terms of trade must be taken very seriously. As noted
earlier many countries rely heavily on tourism both as an
engine of growth and as an earner of foreign exchange.
Many of these countries are third world countries with a
lot of poor people. Therefore from the policy point of
view it is important to devise a scheme for compensating
the poor. There are obvious gains from tourism for cer-
tain section in the community. In this model subsidizing
the poor (losers) is an easy task. It can be done in a
non-distrotionary way. The correct way of subsidizing
them would be to tax tourism, for example, camera tax,
hotel bed tax, discriminatory pricing (as done for Taj
Mahal in Agra), higher Visa fees and so on. The fees
raised here should be used to at least make the poor as
well off as they were in the pre-expansion position.
There is no need for taxing the rich. As there is monop-
oly power in trade in this model the tax would also cor-
rect this distortion. A good example of correcting this is
provided in simulations in the paper by Hazari et al.
(2008) [7].
5. References
[1] M. M. Opp, H. F. Sonnenschein and C. G. Tombazos,
“Rybczynski’s Theorem in the Heckscher-Ohlin World
-Anything Goes,” Journal of International Economics,
Vol. 79, No. 1, 2009, pp. 137-142.
doi:10.1016/j.jinteco.2009.05.005
[2] J. N. Bhagwati, “Immiserizing Growth: a Geometrical
Note,” The Review of Economic Studies, Vol. 25, No. 3,
1958, pp. 201-205. doi:10.2307/2295990
[3] A. Krueger and H. F. Sonnenschein, “The Terms of Trade,
the Gains from Trade and Price Divergence,” Interna-
tional Economic Review, Vol. 8, No. 1, 1967, pp. 121-
127.
[4] B. R. Hazari and P. M. Sgro, “Tourism, Trade and Na-
tional Welfare,” Amesterdam, Elsevier, 2004.
[5] J. N. Bhagwati and H. G. Johnson, “Notes on Some Con-
troversies in Theory of International Trade,” The Eco-
nomic Journal, Vol. 70, No. 277, 1960, pp. 74-93.
doi:10.2307/2227483
[6] M. C. Kemp, “The Pure Theory of International Trade
and Investment,” Prentice-Hall, Englewood Cliffs, 1969.
[7] C. C. Chao, B. R. Hazari, J. P. Laffargue and S. H. Yu,
“Is Free Trade Optimal for a Small Open Economy with
Tourism?” International Trade and Economic Dynamics,
Springer, 2008.