Understanding tourist behavior, demand elasticities, and the purchasing power of regular tourists visiting a destination is of great interest to the tourism industry for business strategy and to governments for tourism public policy. Here, we propose a new method to empirically estimate the own-price and cross-price elasticities of demand for tourist goods and services, as well as an innovative way to measure the average tourist's marginal utility of income. In the tourism sector, we consider that there are two relevant markets: one for tourist goods and services and the other for accommodation. These are separate but interrelated because of the feedback between demands for lodging and tourism products through a vertical relationship of complementarity. The optimal solution to the tourist choice problem consists of a primary demand for tourist services and a derived demand for overnight stays. We focus on obtaining robust estimates of the elasticities corresponding to the former by forecasting the latter. Most of the empirical modeling of tourism demand consists of ad hoc equations that are not directly attached to a specific theoretical framework. Our paper provides a solid characterization of the empirical linkages between the demands for tourist goods and services and accommodation using economic theory. This paper extends existing theory and makes an important contribution to the empirics of tourism economics, with an application to the tourism database of Australia, Canada, Spain, and the United States that quantifies demand elasticities and identifies the socioeconomic status of their respective tourists.
Citation: Asensi Descals-Tormo, María-José Murgui-García, José-Ramón Ruiz-Tamarit. A new strategy for measuring tourism demand features[J]. National Accounting Review, 2024, 6(4): 480-497. doi: 10.3934/NAR.2024022
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Understanding tourist behavior, demand elasticities, and the purchasing power of regular tourists visiting a destination is of great interest to the tourism industry for business strategy and to governments for tourism public policy. Here, we propose a new method to empirically estimate the own-price and cross-price elasticities of demand for tourist goods and services, as well as an innovative way to measure the average tourist's marginal utility of income. In the tourism sector, we consider that there are two relevant markets: one for tourist goods and services and the other for accommodation. These are separate but interrelated because of the feedback between demands for lodging and tourism products through a vertical relationship of complementarity. The optimal solution to the tourist choice problem consists of a primary demand for tourist services and a derived demand for overnight stays. We focus on obtaining robust estimates of the elasticities corresponding to the former by forecasting the latter. Most of the empirical modeling of tourism demand consists of ad hoc equations that are not directly attached to a specific theoretical framework. Our paper provides a solid characterization of the empirical linkages between the demands for tourist goods and services and accommodation using economic theory. This paper extends existing theory and makes an important contribution to the empirics of tourism economics, with an application to the tourism database of Australia, Canada, Spain, and the United States that quantifies demand elasticities and identifies the socioeconomic status of their respective tourists.
The definition of impulsive semi-dynamical system and its properties including the limit sets of orbits have been investigated [1,9]. The generalized planar impulsive dynamical semi-dynamical system can be described as follows
{dxdt=P(x,y),dydt=Q(x,y),(x,y)∉M,△x=a(x,y),△y=b(x,y),(x,y)∈M, | (1) |
where
I(z)=z+=(x+,y+)∈R2, x+=x+a(x,y), y+=y+b(x,y) |
and
Let
C+(z)={Π(z,t)|t∈R+} |
is called the positive orbit of
M+(z)=C+(z)∩M−{z}. |
Based on above notations, the definition of impulsive semi-dynamical system is defined as follows [1,9,23].
Definition 1.1. An planar impulsive semi-dynamic system
F(z,(0,ϵz))∩M=∅ and Π(z,(0,ϵz))∩M=∅. |
Definition 1.2. Let
1.
2. for each
It is clear that
Definition 1.3. Let
Denote the points of discontinuity of
Theorem 1.4. Let
In 2004 [2], the author pointed out some errors on Theorem 1.4, that is, it need not be continuous under the assumptions. And the main aspect concerned in the paper [2] is the continuality of
In the following we will provide an example to show this Theorem is not true for some special cases. Considering the following model with state-dependent feedback control
{dx(t)dt=ax(t)[1−x(t)K]−βx(t)y(t)1+ωx(t),dy(t)dt=ηβx(t)y(t)1+ωx(t)−δy(t),}x<ET,x(t+)=(1−θ)x(t),y(t+)=y(t)+τ,}x=ET. | (2) |
where
Define four curves as follows
L0:x=δηβ−δω; L1:y=rβ[1−xK](1+ωx); |
L2:x=ET; and L3:x=(1−θ)ET. |
The intersection points of two lines
yET=rβ[1−ETK](1+ωET), yθET=rβ[1−(1−θ)ETK](1+ω(1−θ)ET). |
Define the open set in
Ω={(x,y)|x>0,y>0,x<ET}⊂R2+={(x,y)|x≥0,y≥0}. | (3) |
In the following we assume that model (2) without impulsive effects exists an unstable focus
E∗=(xe,ye)=(δηβ−δω,rη(Kηβ−Kδω−δ)K(ηβ−δω)2), |
which means that model (2) without impulsive effects has a unique stable limit cycle (denoted by
In the following we show that model (2) defines an impulsive semi-dynamical system. From a biological point of view, we focus on the space
Further, we define the section
y+k+1=P(y+k)+τ=y(t1,t0,(1−θ)ET,y+k)+τ≐PM(y+k), and Φ(y+k)=t1. | (4) |
Now define the impulsive set
M={(x,y)| x=ET,0≤y≤YM}, | (5) |
which is a closed subset of
N=I(M)={(x+,y+)∈Ω| x+=(1−θ)ET,τ≤y+≤P(yθET)+τ}. | (6) |
Therefore,
According to the Definition 1.3 and topological structure of orbits of model (2) without impulsive effects, it is easy to see that
However, this is not true for case (C) shown in Fig. 2(C). In fact, for case (C) there exists a trajectory (denoted by
If we fixed all the parameter values as those shown in Fig. 3, then we can see that the continuities of the Poincaré map and the function
Theorem 2.1. Let
Note that the transversality condition in Theorem 2.1 may exclude the case (B) in Fig. 2(B). In fact, based on our example we can conclude that the function
Recently, impulsive semi-dynamical systems or state dependent feedback control systems arise from many important applications in life sciences including biological resource management programmes and chemostat cultures [5,6,10,12,17,18,19,20,21,22,24], diabetes mellitus and tumor control [8,13], vaccination strategies and epidemiological control [14,15], and neuroscience [3,4,7]. In those fields, the threshold policies such as
The above state-dependent feedback control strategies can be defined in broad terms in real biological problems, which are usually modeled by the impulsive semi-dynamical systems. The continuity of the function
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