160
November 2019

Battles between residents and tourists:
On the welfare effects of growing tourism

Takaaki Takahashi(Center for Spatial Information Science, The University of Tokyo)

Battles between residents and tourists:
On the welfare effects of growing tourism

Takaaki Takahashi
Center for Spatial Information Science,
The University of Tokyo.
5-1-5, Kashiwa-no-ha, Kashiwa, Chiba 277-8568, Japan

November 2019

Abstract
This paper examines the impacts of the rise in international tourism on the welfare of local residents. In addition to the positive effect to raise wage, it has two negative effects, namely, theeffect to replace the production of the varieties for consumption of local residents by the production of the varieties for consumption of tourists, and the effect to raise input price, which in turnenhances output price as well. By constructing a simple model, we show that growing tourism
can hurt a worker in the home country when the negative variety shifting effect and price effectoutweigh the positive wage effect.
Keywords: rise in tourism; tourist cost; variety shifting effectJEL Classification Numbers: F1; R1; Z3
E-mail address: takaaki-t@csis.u-tokyo.ac.jp
I appreciate the comments from seminar participants at various institutions. This research is partly supported by the
Grants in Aid for Research by the Ministry of Education, Science and Culture in Japan (No. 18H00841).

1

Introduction

In recent years, world economy has seen a rapid expansion of international tourism, which is a result of the economic growth, particularly in developing economies, combined with the decreases
in transport costs due to the prevalence of less expensive airline services by LCC’s and in accommodation costs due to the spread of shared houses after the launch of Airbnb. For example, Table
1 shows that the number of total international arrivals was steadily increasing from 1995 to 2017,and more than doubled in that period, both in the whole world and in the high income countries(HIC’s). Furthermore, not only the volume but also the value shows a similar trend: the receipts
from the international tourism grew approximately threefold in the same period. For most of thetime intervals, furthermore, the receipts increased more rapidly than GDP, and thus, the ratio of
the total receipts to the total GDP rose both in the whole world and in the HIC’s. Indeed, in the
HIC’s, the ratio grew about 1.4 times in the 12 years.
Table 1: Changes in international tourism

total arrivalsa

samples

1995

2000

2005

2010

2015

2017

world

523.91

677.39808.77956.371206.221341.46

1

1.29

1.54

1.83

2.3

2.56

378.85472.27519.15

574.2

33.06

814.74

1

1.25

1.37

1.52

1.93

2.15

484.9

570.99816.991098.731402.811525.68

1

1.18

1.68

2.27

2.89

3.15

401.49458.49616.84789.691021.58

1109.36

1

1.14

1.54

1.97

2.54

2.76

1.57

1.7

1.72

1.66

1.87

1.89

1

1.08

1.1

1.06

1.19

1.2

1.55

1.66

1.64

1.74

2.13

2.17

1

1.07

1.06

1.12

1.37

1.4

-

-

-

3.12

3.14

3.24

(million persons and relative
size to the figure in 1995)

total receiptsa

HIC

world

(billion US$ and relative
size to the figure in 1995)

ratio of total receipts

HIC

world

to total GDPb(% and relative size to

HIC

the figure in 1995)

average ratio ofOECD

receipts to GDPc (%)
a Source: World Tourism Organization, Yearbook of Tourism Statistics and Compendium of Tourism Statistics.
b Source: Computed by the author from the data in World Tourism Organization, Yearbook of Tourism Statistics andCompendium of Tourism Statistics; and World Bank national accounts data.
c Source: Computed by the author from the data at OECD.stat.

As a result of such expansion, tourism now occupies a non-negligible part of economic activ-

1ities. For one thing, the last row in Table 1 shows that the average ratio of the tourism receipts
to GDP in each 36 OECD country reaches more than 3%. Furthermore, Faber and Gaubert (2018)
reaffirm through a rigorous econometric analysis that tourism has strong positive effects on local
employment, local population, local GDP and wages.
Despite the importance of tourism, however, the impacts of a rise in tourism on the welfare ofresidents have been seldom studied. Notable exceptions are the works by Copeland (1991), Chao
et al. (2006) and Lanzara and Minerva (2018), which examine the impacts of growing tourism,
focusing on the impacts brought about by a change in terms of trade. In those works, international
tourism is interpreted as “export” of non-tradable goods and services from a home country toforeign countries. Then, as a result of the upsurge of international tourists, the price of homecountry’s “export” rises relatively to that of its import, which means that the terms of trade of thehome country improves. The improvement of terms of trade, as is well known in the international
trade theory, makes home country consumers better off.
Having said that, the above line of research is not entirely satisfactory in two points. First,
although the change in terms of trade is certainly an important factor, there are other channels
through which rising tourism affects the welfare of local residents. One of the most important is achange in the composition of varieties. Because of the difference in preference, tourists consume“tourism varieties,” which home country consumers do not consume. As a result of the rise intourism, the demand for tourism varieties increases more than the varieties consumed by local
residents. If the amounts of inputs necessary for the production of varieties are limited in thehome country, therefore, the range of the varieties offered to local residents shrinks, which has anadverse effect on their welfare. We refer to this negative effect as a variety shifting effect. Second,the effect of a change in terms of trade consists of two sub-effects; and it is often more instructive
to analyze those sub-effects than the total effect. On the one hand, the rise in tourism expands thedemand for labor and drives up wage, which has a positive effect on the welfare of workers. We
call this effect an wage effect. On the other hand, the rise in input prices including wage results in
the increase in output price. To the extent that real wage declines, it has a negative effect on thewelfare of workers, which we refer to as a price effect.
The decomposition of the terms of trade effect into the two sub-effects is particularly helpful tounderstand the problems of “overtourism.”1 It is because the negative variety shifting effect andprice effect describe most important aspects of the overtourism, besides the effect of congestion.
First, in a number of cities that are popular touristic destinations, local residents are forced to migrate from a tourist-occupied historical city center to suburbs or other cities. It is because a surgeof tourists boosts the demand of land used for the construction of hotels and shared houses, which
1 For a non-economic review of the overtourism, see Perkumienė and Pranskūnienė (2019), for example.

2

drives up housing prices. This is an example of the price effect. In cities like Barcelona and Amsterdam, this price effect is conceived to be so detrimental that the city governments have initiatedregulations against the construction of hotels in the central districts. Second, in many touristic
destinations, long-established stores that used to offer various goods and services for the necessities of local residents have been replaced by souvenir shops, chain-operated cafes and fast foodrestaurants. Even when the stores continue the business, they attempt to change a merchandise
mix to attract more tourists rather than local residents. For instance, a number of time-honored
stores on the traditional Nishiki food market street at Kyoto in Japan have begun to sell a varietyof take-out food, especially of a ready-to-eat-while-walking type, apparently targeting on tourists.
These are examples of the variety shifting effect.
The purpose of this paper is to examine how the rise in international tourism affects the welfare of local residents, paying attention to the wage effect, variety shifting effect and price effect.
For that purpose, we construct a simple model in which a home country accommodates tourists
from a foreign country. The home country has three sectors, namely, the monopolistically competitive manufacturing and tourism sectors each of which produces manufacturing and tourism
varieties, respectively, and the competitive agricultural sector that produces a homogenous agricultural good. Furthermore, three types of workers are distinguished; the workers who own afixed input used in the manufacturing and tourism sectors, the workers who own a variable input used in those sectors, and the workers who are employed in the agricultural sector. It isshown that growing tourism can hurt a worker in the home country when the negative variety
shifting effect and price effect outweigh the positive wage effect. It occurs when the share of thetype of the worker in question is too large, and when the potential number of foreign tourists
is too small. Finally, we examine the effects of government policies to reduce various costs that
tourists need to pay. There is, it is shown, a possibility that such policies result in the deteriorationof local residents’ welfare depending on parameters.
One reservation is that this paper disregards congestion caused by the upsurge of tourists.
True, congestion is one of the most marked aspects of overtourism; but for at least three reasons,
we abstract it away.2 First, considering the problem of congestion blurs the interplay of the wage
effect, variety shifting effect and price effect. Thus, this paper rather focuses on the welfare effectin the economy with no externalities. Such is also the case in the above-mentioned terms of trade
literature. Second, the problem of congestion is not peculiar to growing tourism: we have a richaccumulation of studies concerning the problem of congestion in various fields of economics.
2 In a number of popular tourist destinations such as Venice, Dubrovnik and Kyoto, congestion in touristic sights andlandmarks, in restaurants and shops, and in public transportation has reached to the level that threatens local residents’
everyday activities. In Venice, for example, the city council has decided to charge an admission fee from July 2020 to limit
the number of tourists entering the city.

3

Third, we could obtain any result by changing the formulation of congestion ad hoc. Because it isdifficult to determine how to formulate it a priori, incorporating congestion to the analysis would
always involve considerable arbitrariness.
The rest of the paper consists of six sections. In the next section, we present a basic framework.
In Section 3, equilibrium is derived. The effects of rising tourism on welfare are discussed in
Section 4. Section 5 extends the model to incorporate the determination of the number of foreign
tourists. In Section 6, some policy implications are obtained. Section 7 concludes.

2

Model

2.1

Basic settings

Consider a small open “Home Country,” or HC, which has three sectors; a manufacturing sector, tourism sector and agricultural sector. The manufacturing sector and the tourism sector aremonopolistically competitive, and produce differentiated products, manufacturing varieties andtourism varieties, respectively. Both the manufacturing and tourism varieties are non-tradable.
The agricultural sector is competitive and produces a homogenous good. The agricultural goodis tradable between countries with 0 transport cost. Thus, its price is fixed at a given level determined in the international market. We normalize it at unity.
In that country, there are three factors of production; human capital, skilled labor and unskilled labor. Both human capital and skilled labor are used for the production of manufacturing
and tourism varieties. The share of human capital used in the manufacturing sector, which is denoted by µ, is endogenously determined. Furthermore, unskilled labor is used for the productionof the agricultural good. Taking a unit arbitrarily, we suppose that one unit of agricultural goodis produced from one unit of unskilled labor. This implies that the wage of unskilled workers isunity.
Human capital, skilled labor and unskilled labor are owned by entrepreneurs, skilled workers
and unskilled workers, respectively. A consumer of each type supplies 1 unit of human capital, 1
unit of skilled labor or 1 unit of unskilled labor, accordingly. The shares of entrepreneurs, skilledworkers and unskilled workers in the total population of HC are λ E , λS and 1 − λ E − λS , respectively, where λ E ∈ (0, 1) and λS ∈ (0, 1). Taking a unit arbitrarily, we normalize the populationof HC at unity. By definition, the number of entrepreneurs employed in the manufacturing sector
is µλ E .
In addition, tourists from “Foreign Country, ” or FC, visit HC. The foreign “country” can beinterpreted as a set of the countries that send tourists to HC. From FC, L consumers visit HC

4and consume manufacturing and tourism varieties produced in HC. For a while, L is consideredgiven. In Section 5, however, this assumption is lifted and we discuss FC consumers’ choice ofthe country to visit.

2.2

Consumers in Home Country

Consumers’ behavior is formulated on the basis of Pflüger (2004), which is one of many New
Economic Geography (NEG) models. Because it is widely used in the literature, we do not give thedetails of the derivation process of a demand function but rather focus on explaining notations.
Consumers in HC have an identical preference, represented by a quasi-linear utility function.
u H = α ln M H + A,
where M H ≡

[∫

σ −1

NM

σ di
qH
M (i )] σ−σ 1

(1)

is a composite of manufacturing varieties, and A is theamount of an agricultural good. q H
M (i ) is the consumption of variety i and NM is the set of manufacturing varieties. σ is elasticity of substitution. A number of studies have found that theelasticity is considerably higher than 2 in the real economy. Thus, we assume that σ > 2, which
will be used in Section 5. Furthermore, (1) indicates that HC consumers consume no tourism
products. That is, the possibility that they visit local places in their own country or abroad for
touristic purpose is abstracted away. One justification is that such simplification does not alter
the main results, although making the analysis much less involved. In addition, we focus on
the case in which there is no congestion, as has been discussed in the introduction. However, it
would be quite straightforward to extend the model to incorporate congestion: we can linearly
add a term that is increasing in L in the right hand side of (1).
H M H + A = y, where y is his/her
Each HC consumer faces a budget constraint given by PM[∫] 1−1 σH ≡income. PM
p M (i )1−σ diis a price index of manufacturing varieties and p M (i ) is aNMprice of variety i. Solving the maximization problem of each consumer yields his/her demandfor each manufacturing variety and the agricultural good:( H ) σ −1
−σPMqH
for i ∈ NM
M (i ) = αp M (i )and

A = y − α.

Because of the specification of the preference, the demand for each manufacturing variety is independent of income.

5

2.3

Consumers in Foreign Country

The preference of FC tourists differs from that of HC consumers. As a result, in addition to
manufacturing varieties, tourists consume tourism varieties, which HC consumers do not consume. The most straightforward example of the tourism varieties is those of lodging and international freight services, on which international tourists spend a large part of their travel budget.
Another example is the varieties of goods and services consumed when tourists visit touristic
sights and landmarks like museums, historical buildings and religious facilities. In the same[∫
] σ−σ 1σ −1q FM (i ) σ dias a composite of themanner as for a HC consumer, we define M F ≡NMmanufacturing varieties that each FC consumer consumes when he/she visits HC. Moreover, let[∫] σ−σ 1σ −1q T (i ) σ diT ≡be a composite of tourism varieties. NT and q T (i ) denote the set ofNTthe tourism varieties produced in HC and the consumption of each tourism variety by a foreign
tourist, respectively. Here, the elasticity of substitution between a pair of tourism varieties is assumed to be equal to that between a pair of manufacturing varieties. This assumption enables us
to keep the analysis tractable, without changing fundamental qualitative results.
The FC consumers who visit HC as tourists have also a quasi-linear preference, given by
u F = β ln M F + γ ln T + Z.
Here, Z is the consumption of goods and services other than the manufacturing and tourism
varieties consumed in HC. Recall that the quasi-linear preference has no income effect. In otherwords, the amount of expenditure on M F and that on T are constant (β and γ, respectively).
Therefore, the size of Z affects neither M F nor T, which saves us from specifying the content of Z
any further.
Tourists incur extra costs to consume varieties abroad. For example, they need to gather information on the basics of a destination country, which is common knowledge to local residents,
such as currency, weather, social system and acceptable behaviors, as well as the informationon the locations of the shops and restaurants that provide the goods and services they want to
consume. To give another example, foreign tourists usually face a language barrier when they
move within a city and when they obtain information regarding the goods and services to buy,
for instance. Such factors become a source of cost to foreign tourists, which we refer to as tourist
cost.
We assume that the tourist cost is of the iceberg form, that is, to consume one unit of a manufacturing or tourism variety, a FC consumer is required to buy more than one unit of it. This
specification is conventional in the literature of international trade theory and NEG, which usually assumes that inter-regional trade entails “trade costs” of the iceberg form. Specifically, we as6

sume that a foreign tourist needs to buy τ units of a variety produced in HC to consume one unitof it. Thus, the consumer prices of a manufacturing and tourism variety are τ p M (i ) and τ p T (i ),respectively, where p M (i ) and p T (i ) are the prices that a producer in HC takes. The tourist costdoes not play an important role up to Section 5, because it does not affect the equilibrium prices
nor the equilibrium sizes of manufacturing and tourism sectors, as long as the number of foreign
tourists is fixed. However, in Section 6, we treat the tourist cost as a policy instrument of the HC
government to promote foreign tourism.
F MF +The budget constraint of a FC consumer visiting HC with income y is given by PM
1
[∫ {
]
}1− σ
1− σ
H and
F ≡
= τPM
PT T + PZ Z = y, where PZ is a price of Z. Here, PMτ p M (i )
di
NM
[∫ {
}1−σ ] 1−1 σPT ≡are the price indexes of manufacturing and tourism varieties forτ p T (i )diNTforeign tourists, respectively. It is straightforward to derive the demand of a FC consumer foreach manufacturing and tourism variety produced in HC:( F ) σ −1
q FM (i ) = βτ −σ p M (i )−σ PM
for i ∈ NM ,2.4

q T (i ) = γτ −σ p T (i )−σ PTσ−1 for i ∈ NT .

Producers

To produce each variety, the manufacturing and tourism sectors in HC need to use f M and f Tunits of human capital as a fixed input, respectively. This implies that the numbers of varieties inthe two sectors are equal to
nM =

µλ E
fM

nT =

and

(1 − µ ) λ E
,
fT

(2)

respectively. In addition, a M and a T units of skilled labor are used to produce each unit of avariety in the two sectors, respectively.
F
Let Q M (i ) ≡ q H
M (i ) + Lτq M (i ) and Q T (i ) ≡ Lτq T (i ) be the total demand for each variety in the

manufacturing and tourism sectors, respectively, and w M and wT be the wages of entrepreneurs inthese sectors. r is a wage of skilled labor. Then, the profit of a firm producing each manufacturing
variety, π M (i ), and the profit of a firm producing each tourism variety, π T (i ), are given by π j (i ) ≡[]p j (i ) − a j r Qi (i ) − f j w j for j ∈ { M, T }. The firm maximizes its profit by setting
p j (v) = p j ≡

σ
ar
σ−1 i

for

i ∈ { M, T }.

Free entry and exit imply that π j (i ) = 0, or, by (2),wM =α + βLσλ E µ

and

7

wT =

γL
.
σλ E (1 − µ)(3)Note that both w M and wT increase with L. It is because increase in foreign tourists brings about
greater demand for human capital at the manufacturing and tourism sectors in HC.

3

Equilibrium

In this section, we derive an equilibrium for a given number of foreign tourists.
To begin, the market for skilled labor must clear at the equilibrium. This necessitates

∫
aM

∫
NM

Q M (i ) di + a T

NT

Q T (i ) di = λS ,(4)

where the left-hand side represents the demand for skilled labor while the right-hand side its
supply.
Furthermore, in a long run, entrepreneurs in HC freely move between the manufacturing andtourism sectors based on the wage difference in the two sectors. Note that w M − wT is a decreasing
function of µ (see (3)), and positive when µ = 0 while negative when µ = 1. Therefore, there ex{
{
> }
< }
ists unique µ∗ such that w M − wT = 0 if µ = µ∗ . Consequently, as long as entrepreneurs<>
have an incentive to move to the sector that offers a higher wage, the stable equilibrium distribution between the two sectors is given by µ∗ .3 This, along with the market clearing condition forskilled labor, (??), gives the following equilibrium values:
w∗ =

B( L)
( σ − 1) λ E Γ ( L )Γ( L),, µ∗ =
and r ∗ =
σλ E
Γ( L)
σλS

where


 B( L) ≡ α + βL

and
 Γ( L) ≡ α + ( β + γ) L.

(5)The ranges of manufacturing and tourism varieties at the equilibrium, denoted by n∗M and n∗T ,respectively, are derived from (2).
Thus, we have established the following result.

Proposition 1

For a given number of foreign tourists, equilibrium is given by (5).

The effects of a change in the number of foreign tourists on the three variables are key to understand this model. Suppose that L increases. First, (5) implies that the wage of an entrepreneur
rises. This is because the demand for human capital increases as a result of the influx of foreign

3 More specifically, one may consider the following replicator dynamics, which is a conventional way to formulate amigration process in the literature of international trade theory and NEG: µ̇ = η (w M − wT ) for some constant η > 0.

8

tourists, who consume manufacturing and tourist varieties. Second, the share of the human capital used in the manufacturing sector declines. As L increases, demand for human capital rises inboth the manufacturing and tourism sectors. However, the rise in the latter sector exceeds that in
the former. Therefore, to recover the wage equality in the two sectors, labor distribution needs toadjust, or, more specifically, the labor supply in the manufacturing sector must shrink while thatin the tourism sector must expand. In addition, this implies that HC ends up with a narrower
range of manufacturing varieties but a broader range of tourism varieties. This is one of crucial
observations. Third, the wage of skilled labor rises because the demand for it increases. Thisimplies that the price of manufacturing varieties also rises, which is another crucial observation.

4

Welfare effects of growing tourism

In this section, we explore how an influx of foreign tourists affects the welfare of HC consumers.
Let us refer to entrepreneurs as type-E consumers, skilled workers as type-S consumers, andunskilled workers as type-U consumers. A HC consumer of type i enjoys the following indirect
utility at an equilibrium:[]αα ( σ − 1)∗∗vi ( L ) = yi +ln n M − α ln r + α ln
−1
σ−1
aM σ

(6)

for i ∈ { E, S, U }. Here, yi is the equilibrium income of the consumer, that is, y E = w∗ , yS = r ∗and yU = 1. Using (6), we can easily derive the effect of a change in L on vi ( L) as follows.
vi ′ ( L ) =

dn∗
dyi
α
α dr ∗· M− ∗+∗dL(σ − 1)n M dL
r dL

(7)

for i ∈ { E, S, U }. This welfare effect of growing tourism consists of three components. The firstterm in the right-hand side of (7) represents the effect through the change in wage, namely, anwage effect. The second term represents the effect through the change in a range of manufacturing
varieties, namely, a variety shifting effect. The last term represents the effect through the change inthe price of those varieties, namely, a price effect.
We have already seen that dw∗ /dL > 0 and dr ∗ /dL > 0. Therefore, the wage effect is positive for entrepreneurs and skilled workers, and 0 for unskilled workers. An influx of tourists
favors the first two types of consumers in HC, because the induced increase in wage income enables them to increase agricultural good consumption. Second, since dn∗M /dL < 0, the variety
shifting effect is negative. As tourists increase, a range of manufacturing varieties shrinks, which
adversely affects HC consumers. Finally, since dr ∗ /dL > 0, the price effect is negative. A rise in9

tourists boosts the input price and, therefore, the price of manufacturing varieties as well.
The first finding is about the welfare of unskilled workers. Since the wage effect is 0 for them,
the total effect is necessarily negative: unskilled workers are always hurt by the rise in the foreign
tourists.
Next, we turn to the welfare effects for entrepreneurs and skilled workers. (7) can be rewritten
as


α2 γ
α( β + γ)
β+γ


−
−
 v E ′ ( L) =σλ E
( σ − 1) B ( L ) Γ ( L )
Γ( L)
2


α( β + γ)
α γ(σ − 1)( β + γ) vS ′ ( L) =
−
.
−
σλS
( σ − 1) B ( L ) Γ ( L )
Γ( L)

(8)

Inspecting the two equations in (8) tells us that both v E ( L) and vS ( L) are convex in L as long as
L ≥ 0. Furthermore, note that the derivative evaluated at L = 0 exhibits
v i ′ (0)
where

{

}
{
}
<
= 0 if λi >
= b
λi
>
<

β+γ
σ−1
b
·
∈ (0, 1)λE ≡σ(σ − 1)( β + γ) + γ

for

and

i ∈ { E, S},(9)b
λ S ≡ ( σ − 1) b
λ E ∈ (0, 1).

Thus, it is useful to consider two cases for each i ∈ { E, S}.
First, suppose that λi > b
λi . Then, (9) implies that vi ′ (0) < 0. Furthermore, vi ′ ( L) approaches
a positive constant as L goes to infinity for i ∈ { E, S}.4 Since vi ( L) is convex, it has a uniqueminimum at a positive value of L. We call such L a pivot number of FC tourists and denote it by b
Li .
It satisfies
vi ′ ( L )

{

}
{
}
<
= 0 if L <
= b
Li
>
>

for L ≥ 0 and i ∈ { E, S}.

(10)

Second, suppose that λi < b
λi . Then, vi ′ (0) > 0. Since vi ( L) is convex, it increases for any L ≥ 0.
We have thus established the following proposition.

Proposition 2i) If λi > b
λi , an increase in foreign tourists hurts type-i consumers in HC when L is smaller
than b
Li , while it benefits them when L exceeds b
Li .
ii) If λi < b
λi , an increase in foreign tourists always benefits type-i consumers in HC.
Let us focus on the case where λ E > b
λ E and λS > b
λS . Since b
λE + bλS < 1, there exists a pair of
4 Indeed, lim v ′ ( L ) = β + γ and lim v ′ ( L ) = ( σ − 1)( β + γ ) .
E
S
σλ E
σλS
L→∞
L→∞

10

(λ E , λS ) with λ E ∈ (0, 1) and λS ∈ (0, 1) that satisfies both conditions. In such a case, it is more
likely that a type-i consumer is hurt by the increase in foreign tourists when b
Li is higher. Now,
consider parameter x that affects b
Li . Since/
dvi ′ ( L) dx
db
Li
=− 2
/
dx
d vi ( L) dL2
and vi ( L) is convex in L, the direction of the change in b
Li is opposite to that of the change in the/welfare effect, given by dvi ′ ( L) dx. Consequently, it is more likely that the increase in foreign
tourists hurts a type-i consumer when the welfare effect is weaker. Thus, what matters is theimpact of a change in parameters on the relative magnitudes of the three sub-effects, namely, thewage effect, variety shifting effect and price effect.
For instance, suppose that α rises and HC consumers spend more money on manufacturing
varieties. First, the wage effect is independent of α for both entrepreneurs and skilled workers,
as the first term at the right-hand side of each line in (8) indicates. Second, the variety shifting
effect strengthens as α rises, since the absolute value of the second term at the right-hand side ofeach equation increases with α. This is because, when HC consumers are inclined more to manufacturing varieties, a given size of reduction in the range of these varieties is more devastating.
Third, the price effect also grows as α rises: the absolute value of the third term also increases with
α. The increase in the demand of HC consumers for manufacturing varieties makes the marketof skilled labor more tight, which raises the wage of skilled workers and, therefore, the price of
manufacturing varieties. Since the positive wage effect remains constant in size but both the two
negative effects, the variety shifting effect and the price effect, grow, the overall impact is negative. Therefore, both entrepreneurs and skilled workers are more likely to be hurt by growing
tourism when α is higher.
Furthermore, when λ E is higher, that is, when entrepreneurs occupy a higher proportion of
the HC population, they are more likely to be hurt by the rise in tourism. This is because the wage
effect is lower when λ E is higher but neither the variety shifting effect nor the price effect dependson λ E . Similarly, skilled workers are more likely to be hurt when their share, λS , is higher. Thisis again because the wage effect is lower when λS is higher but neither the variety shifting effectnor the price effect depends on λS .
Impacts of the changes in other parameters are ambiguous. For example, higher β (higher
expenditure on manufacturing varieties by foreign tourists) expands the wage effect for both
entrepreneurs and skilled workers, and reduces variety shifting effect, both of which work infavor of the welfare of those consumers. However, the price effect grows at the same time, which
has a negative impact. Thus, the sign of the total effect is ambiguous, although we can show that11

it is negative when L is sufficiently small.
To sum up, we have established the following result.

Proposition 3

It is more likely that entrepreneurs and skilled workers are hurt by growing tourism when thewage effect is larger, and the variety shifting effect and the price effect are smaller.

The last question is which group of consumers, entrepreneurs or skilled workers, are more
likely to benefit from growing tourism. To answer the question, we compare the pivot number offoreign tourists for entrepreneurs with the counterpart for skilled workers. The following lemma
is useful.
Lemma 1
b
LE

{

{
}
<
< }
= b
LS if (σ − 1)λ E = λS .
>>Proof of Lemma ??
Note that the variety shifting effect and the price effect are common to the two types of consumers.
dw∗ dr ∗Therefore, the difference stems from the wage effect: v E ′ ( L) − vS ′ ( L) =−, which implies
dL
dL
}
{
}
{
<
>
that v E ′ ( L) = vS ′ ( L) for any L if (σ − 1)λ E = λS . Thus, what remains to do is to prove
>
}
}<
{
{
>
<
′
′
b
b
=
=
vS ( L). We present a proof for the part of the statement with
LS if v E ( L)that L E<>
the uppermost equality/inequality signs, that is, b
LE < bLS if v E ′ ( L) > vS ′ ( L). The other parts canbe similarly proved. Suppose that v E ′ ( L) > vS ′ ( L) for any L. By definition, v E ′ ( L) = 0 at b
LE .
Therefore, it follows from the inequality that vS ′ ( L) < 0 at b
L E . This implies that b
LE < bLS , sincevS ( L) is convex in L. ■If b
LE < bLS , vS ( L) decreases with L whenever v E ( L) decreases with L. Therefore, skilled workers are hurt by the growing tourism whenever entrepreneurs are hurt by it. If b
LE > bLS , parallelreasoning leads to the result that entrepreneurs become worse off as a result of the increase inforeign tourists whenever skilled workers become worse off. Using the result in Lemma ??, we
obtain the following statements.

Proposition 4i) Suppose that λ E (σ − 1) < λS . Then, growing tourism hurts skilled workers whenever it
12hurts entrepreneurs.
ii) Suppose that λ E (σ − 1) > λS . Then, growing tourism hurts entrepreneurs whenever it
hurts skilled workers.

This proposition says that skilled workers are more likely to be hurt by growing tourism thanentrepreneurs, when HC has a relatively small number of entrepreneurs compared to skilledworkers. The parallel result applies to entrepreneurs. In general, the proposition indicates thatthe owners of relatively abundant inputs are more likely to be hurt by growing tourism.

5

Determination of the number of foreign tourists

So far, we have been assuming that the number of the foreign tourists coming to HC, L, is given.
In this section, we relax this assumption and discuss how that number is determined.
Suppose that consumers in FC have two possible tourist destinations, HC and “outer country,”or OC, which may be interpreted as a set of countries. A generalized form of FC consumers’
preference is given by
{
F
= max
u general}ee
β ln M + γ ln T, β ln M + γ ln T + Z.
F

Here, M F and T are the composites of manufacturing and tourism varieties that a FC consumere and Te are those that he/she
consumes when visiting HC, as has been defined earlier, whereas M
consumes when visiting OC.
Consumers in FC choose the destination country that gives the higher utility from local consumption of manufacturing and tourism varieties. Let us denote the difference between the levels of indirect utility that are obtainable when FC consumers visit HC and OC by ∆( L), that is,()()
e + γ ln T/ T
e . A convenient way to define an equilibrium is to look at a∆( L) ≡ β ln M F / M
stable equilibrium of a dynamics, which prescribes the behaviors of L on the assumption that
consumers incur some frictions when changing destination countries. We introduce a simple dynamics given byL̇ = ζ∆( L)forL ∈ [0, F ].

(11)

Here, ζ is a positive constant, representing adjustment speed, and F is the total population of FC.
According to this law of motion, the number of tourists who visit HC increases (decreases, resp.)
if visiting that country gives higher utility (lower utility, resp.) than visiting OC.
To avoid an unnecessary complication, let us focus on the case in which OC has the same13

technologies as HC, that is, a M , a T , f M and f T also apply to the production activities in OC. Then,the difference between the levels of indirect utility is reduced to
[
]
1
nM
nT
τr
β ln
∆( L) =
+ γ ln− ( β + γ) ln ,
e
e
σ−1
τee
r
nM
nT

(12)

eM , neT , ewhere nr, and τe represent the ranges of manufacturing and tourism varieties producedin OC, wage of skilled workers in that country, and tourist cost for the FC consumers who visit
OC, respectively. (12) says that a consumer expects relatively higher utility by visiting HC rather
than visiting OC, when HC offers more manufacturing and tourism varieties, tourist cost to HC
is lower, and the wage of skilled workers and, therefore, the price of varieties are lower in HC.
We assume that OC is so big compared to FC that the FC consumers’ choices of a tourism
destination have only a negligible impact on economic circumstances of OC. In particular, it iseM , neT , eassumed that nr and τe are all fixed. Substituting the equilibrium values in (5), we canrewrite (12) as∆( L) ≡[]
1
β ln B( L) + γ ln(γL) − σ( β + γ) ln Γ( L) + k,
σ−1

(13)

where
[
]
1
σλS τeer
e M f M ) − γ ln(neT f T ) + ( β + γ) lnk≡( β + γ) ln λ E − β ln(nσ−1
( σ − 1) λ E τis a constant.
Let us defineα ( R − 1)
L′ ≡
> 0,
2β

√
where

R≡

1+

4βγ
> 1.
(σ − 1)( β + γ)2

The following lemma characterizes the solution to ∆( L) = 0. Fig. 1, describing ∆( L) as a ∆( L)
curve, may be helpful to understand this lemma.
Insert Fig. 1 around here.

Lemma 2Equation ∆( L) = 0 has{

no solution
one solution
two solutions}

in [0, ∞) if ∆( L′ )

Proof

14

{ < }
= 0.
>

Note that∆′ ( L) =Ω( L),(σ − 1) LB( L)Γ( L)

whereΩ( L) ≡ α2 γ − (σ − 1)( β + γ)2 LB( L).

(14)/
Since Ω( L) is a quadratic function, it has two roots, given by L′ and L′′ ≡ − α(1 + R) (2β). Then,()Ω( L) > 0 if L ∈ L′′ , L′ , and Ω( L) < 0 if L > L′ . Since L′′ < 0 and L′ > 0, (14) implies that ∆( L)[)
increases with L for L ∈ 0, L′ and decreases for L > L′ . Therefore, ∆( L) has a single peak at L′ .
Furthermore, ∆( L) goes to negative infinity, as L approaches 0 from above and as L diverges toinfinity. Consequently, there are only three possibilities about the solutions of ∆( L) = 0. First, if
the peak of ∆( L) lies below the horizontal axis, there is no solution. Second, if the peak happens
to be on the horizontal axis, the equation has one solution. Third, if the peak lies above thehorizontal axis, there are two solutions. ■In the last case in Lemma 2, there are two solutions. However, the lower solution is associated with an unstable equilibrium: If L slightly increases from that solution, the utility difference
becomes positive, which further raises L. Denoting the higher solution by Lo , we derive the following result from Lemma 2, which is illustrated in Fig. 1 above.

Proposition 5

The number of the foreign tourists coming to HC at a stable equilibrium of (11) is given by5

 {0}
{
}
L∗ ∈
 0, min[ Lo , F ]if ∆( L′ ) ≤ 0
if ∆( L′ ) > 0.

(15)

Two properties of the equilibrium are worth mentioning. First, the equilibrium number of foreign tourists does not change continuously when parameters change. Suppose that a parameter
gradually changes and that ∆( L) shifts upward. L∗ remains at 0 as long as ∆( L′ ) lies below thehorizontal axis. As soon as ∆( L′ ) exceeds 0, there appears another equilibrium number, Lo . This
catastrophic change indicates that there is minimal requirement for the number of foreign tourists:
if they want to entice some tourists from FC, they need to entice at least this minimal requirement
number of them.
Second, there are multiple equilibria when ∆( L′ ) > 0. The reason is well-known in the literature of the NEG: increasing returns in production tend to concentrate the tourism destinations of
5 When ∆ ( L′ ) = 0, Lo is an equilibrium but a saddle point: it is stable when L slightly increases from Lo but unstable

when L slightly decreases from Lo .

15

FC consumers into either HC or OC. Furthermore, the existence of multiple equilibria causes indeterminacy of equilibrium. When ∆( L′ ) > 0, whether there are foreign tourists coming to HC or
not is determined for non-economic reasons such as history and expectation, as is often discussed
in the NEG literature.
An important consequence of the proposition is that any change that shifts the ∆( L) curve
upward in parallel causes the increase in the number of the foreign tourists coming to HC. Thisoccurs through two channels (see Fig. 1). First, as the ∆( L) curve shifts upward gradually, ∆( L′ )exceeds 0 at a certain time, which switches the economy from the first case in (15) to the second.
This is accompanied with the emergence of a new equilibrium number, Lo or F. Second, when∆( L′ ) > 0, the parallel upward shift of the ∆( L) curve raises Lo .
The parameters whose changes cause such a parallel shift of the ∆( L) curve are those thateM , neT , eaffect ∆( L) only through k (see (13)). They are nr, τe, τ, λ E and λS . First, the decreases in
eM , neT and τ, and the increases in enr and τe all make OC less attractive as a tourism destination, and,
therefore, raises ∆( L). Second, as λ E declines, ∆( L) increases, as long as σ > 2 (which we havebeen assuming).6 On the one hand, the decrease in λ E reduces the number of varieties producedin HC, which gives a negative impact on ∆( L). On the other hand, the decrease in λ E makes
skilled labor relatively more abundant and reduces the wage of skilled workers and, therefore,
the prices of varieties. This works in favor of the utility differential. Because the latter positive
impact outweighs the former negative impact, ∆( L) rises. Third, as λS falls, wage of skilled laborand prices of varieties rise, which makes HC less attractive for tourists.

6

Policy implication: Effects of the reduction of tourist cost

The tourist cost is one of obvious policy instruments. HC can attract more tourists from FC by
reducing that cost in various ways. Examples are abundant: the HC government can cut down
or eliminate taxes that tourists are to pay, such as entry and exit taxes, accommodation tax, andvalue-added tax; it can spread the charms of the country to people all over the world; and it
can improve communication infrastructure for foreign tourists through the provision of language
interpretation services and free WiFi systems, to name a few. Extreme caution is needed in implementing such policies to make the country more tourist-friendly, because our discussion in
Section 4 indicates that the policies may aggravate the welfare of HC residents. The last task is to
examine this possibility.
To analyze the impacts of a reduction of tourist cost, we put the following two effects together.

6 Note that(σ − 2)( β + γ)
∂k
=−
.
∂λ E
( σ − 1) λ E

16One is the effect on the number of FC tourists coming to HC. For that purpose, we write ∆( L)
as a function of not only L but also τ, as ∆( L; τ ). Obviously, ∆( L; τ ) is decreasing in τ. In otherwords, the decrease in τ brings about an upward shift of the ∆( L; τ ) curve. Since τ affects ∆( L; τ )only through a shift parameter k, L′ does not change. Moreover, the rightmost intercept on thehorizontal axis, Lo , is now considered a function of τ, and thus, denoted as Lo (τ ). Fig. 2 describes
several ∆( L; τ )’s as ∆( L; τ ) curves. The other effect to consider is the welfare effect of growing
tourism. As has been discussed, it is negative when the number of foreign tourists is smaller thanthe pivot number b
Li , and positive when it is larger than the pivot number.
Insert Fig. 2 around here.
The rest of this section focuses on the equilibrium at which at least some foreign tourists cometo HC, that is, the number of foreign visitors to HC is equal to min[ Lo , F ]. Furthermore, we limit
our analysis to the case with F > L′ . If F ≤ L′ , Lo (τ ) would exceed F for any τ since Lo (τ ) > L′ . In
this case, there would be no possibility that the interior equilibrium with L∗ = Lo (τ ) is realized.
To concentrate on interesting cases, such a case is disregarded.
Now, we are ready to examine the impacts of a reduction of tourist cost. We consider threecases. First, suppose that b
Li is smaller than L′ (see the first panel of Fig. 2). Then, Lo (τ ) and F
always exceed b
Li since Lo (τ ) ≥ L′ . Therefore, the welfare effect is positive both at L = Lo (τ ) andat L = F. Second, suppose that b
Li lies in between L′ and F (see the second panel of Fig. 2). Then,the welfare effect is positive at L = F. At L = Lo (τ ), however, it is positive when Lo (τ ) ∈ (bLi , F )whereas it is negative when Lo (τ ) ∈ ( L′ , bLi ). Third and last, suppose that b
Li is larger than F (seethe last panel of Fig. 2). Then, the welfare effect is negative both at L = Lo (τ ) and at L = F.
Let
λoE ≡

1
σ

and

λoS ≡

(σ − 1)( β + γ)(1 + R) + 2γ.
σ ( β + γ)(1 + 2γ + R)

It is easily verified that λoE ∈ (0, 1) and λoS ∈ (0, 1).7 Moreover, it is useful to introduce three
critical values of τ (see Fig. 2). First, let τ ′ be the value of τ for which the ∆( L; τ ) curve touches
the horizontal axis. In other words, τ ′ is a solution to ∆( L′ ; τ ′ ) = 0. Second, we define τ F as thevalue for which the rightmost intercept of the ∆( L; τ ) curve on the horizontal axis is F. That is,τ F solves Lo (τ F ) = F. Third, at the third critical value, τbi , the rightmost intercept becomes b
Li(i ∈ { E, S}). In other words, it is a solution to Lo (τbi ) = b
Li .
The following result immediately follows from the above argument.

7 Note that λo < 1 is equivalent to 2σγ ( β + γ ) + β (1 + R ) + γ ( R − 1) > 0. However, R is greater than 1. Therefore,S

λoS < 1.

17

Proposition 6i) If λi < λio , then the reduction of tourist cost always benefits type-i consumers in HC.
ii) If λi > λio and F > b
Li , then, the reduction of tourist cost benefits type-i consumers in HC
when τ ∈ (τ F , τbi ), while it hurts them when τ ∈ (τbi , τ ′ ).
iii) If λi > λio and F < b
Li , then the reduction of tourist cost always hurts type-i consumers in
HC.

Proof
Remember the property of b
Li described by (10). The necessary and sufficient condition for b
Libeing smaller than L′ is, therefore, that vi ( L) is increasing at L′ . It is straightforward to show that
{
{
> }
< }
vi ′ ( L′ ) = 0 if λi = λio . It follows from this that
<
>
b
Li

{

}
<
= L′
>

if

λi

{

}
<
= λio .
>

Furthermore, note that the conditions Lo ∈ ( L′ , bLi ) and Lo ∈ (bLi , F ) are equivalent to τ ∈ (τbi , τ ′ )and (τ F , τbi ), respectively. These observations along with the above arguments in the text lead tothe lemma. ■The proposition says that the HC consumers’ vulnerability to the reduction of tourist costhinges upon several key factors. First, when the share of a type of consumers in HC is larger, thattype are more likely to be hurt by the reduction. Second, when “potential number” of foreign
tourists is smaller, it is more likely that consumers in HC become worse off by the reduction. The
potential number, in turn, is smaller when FC has a smaller population and tourist cost is higher.

7 Concluding remarks
In this paper, we have examined the impacts of the rise in international tourism on the welfare
of local residents. In addition to the positive effect to raise wage, it has two negative effects,
namely, the effect to replace the production of the varieties for consumption of local residents(manufacturing varieties) by the production of the varieties for consumption of tourists (tourism
varieties), and the effect to raise input price, which in turn enhances output price as well. By
constructing a simple model, we have shown that growing tourism can hurt a worker in thehome country when the negative variety shifting effect and price effect outweigh the positive
wage effect. We have obtained conditions for such an adverse case to occur. Finally, we haveexamined the effects of government policies to reduce various costs that tourists need to pay.

18

This work is one of the few attempts that examine the welfare effect of growing tourism, and, inparticular, the first attempt to explicate its variety shifting effect.
Several agenda are left for future research. First, we have not considered the problem of congestion. To evaluate properly the policies that promote or limit international tourism, it is necessary to pay into account that problem. If the increase in tourists aggravates congestion too rapidly,
the policies to promote tourism will do harm to local residents, especially when the variety shifting effect and price effect are large. Second, empirical research to estimate the wage effect, variety
shifting effect and price effect is necessary. For instance, if the data on the range and amounts ofvarieties provided in a particular area are available, we can estimate the impacts of changes in thenumber of international tourists on the varieties sold.

19

References[1] Chao, C.-C., B. R. Hazari, J.-P. Laffargue, P. M. Sgro, and E. S. H. Yu (2006) “Tourism, Dutch
disease and welfare in an open dynamic economy,” The Japanese Economic Review, 57, 501-15.
[2] Copeland, B. R. (1991) “Tourism, welfare and de-industrialization in a small open economy,”
Economica, 58, 515-29.
[3] Faber, B. and C. Gaubert. (2018) “Tourism and economic development: Evience from Mexico’s coastline,” NBER Working Paper Series, 22300.
[4] Lanzara, G. and G. A. Minerva. (2019) “Tourism, amenities, and welfare in an urban setting,”
Journal of Regional Science, 59, 452-79.
[5] Perkumienė, D. and R. Pranskūnienė. (2019) “Overtourism: Between the right to travel andresidents’ rights,” Sustainability, 11, 2138.
[6] Pflüger, M. (2004) “A simple, analytically solvable, Chamberlinian agglomeration model,”Regional Science and Urban Economics, 34, 565-73.

20

stablestable
L’

O

L

O

∆(L)

∆(L)

F

Lo

L’

L

L’

O

unstable

∆(L)

F

L

unstableFig. 1 Equilibrium number of foregin tourists visiting HC

O

L̂ i

L’

∆(L; τ’)F

L

O∆( L; τ )
F

L’

L̂ i

F

L

O

∆(L; τ’) ∆( L; ˆτi ) ∆(L; τ )F

L’∆(L; τ’)F

L̂ i L∆( L; τF ) ∆(L; ˆτi )Fig. 2 Three cases of the effects of the reduction of tourist cost