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Introduction
Despite the global economic recession, the luxury goods
market has been booming in the past decades. Even aer
the economic contraction in 2020 due to the COVID-19
pandemic, the market was expected to grow by 13% to 15%
in 2021 to EUR 1.14 trillion (Bain & Company, 2021)1.
Some wealthy consumers are motivated to consume highly
conspicuous goods and services to aunt their wealth and
thereby achieve their expected social status (Veblen, 1899).
Conspicuous consumption also applies to the housing mar-
ket. Zahirovic-Herbert and Chatterjee (2011) found that
wealthier buyers tend to pay an extra premium for the dier-
ent names of the housing even though some buyers are less
willing to pay during recession times. According to Leguiza-
mon (2010), “housing lends itself very neatly to spatially de-
termined reference groups and is also a highly visible form of
1 Source: Bain & Company, 2021. https://www.bain.com/in-
sights/from-surging-recovery-to-elegant-advance-the-evolv-
ing-future-of-luxury/
International Journal of Strategic Property Management
ISSN: 1648-715X / eISSN: 1648-9179
2023 Volume 27 Issue 4: 246–260
https://doi.org/10.3846/ijspm.2023.20257
*Corresponding author. E-mail: swtzang@gmail.com
DOES HIGHEND HOUSING ALWAYS HAVE A PREMIUM LUXURY VALUE?
A THEORETICAL AND NUMERICAL STUDY
Chih-Hsing HUNG1, Ming-Chi CHEN2, Shyh-Weir TZANG 3,*, Chung-Chieh CHENG4
1 Department of Money and Banking, National Kaohsiung University of Science and Technology,
Kaohsiung, Taiwan,R.O.C.
2 Department of Finance, National Chengchi University, Taipei, Taiwan,R.O.C.
3 Department of Finance, Asia University, Taichung, Taiwan,R.O.C.
4 Department of Information Management and Finance, National Yang Ming Chiao Tung University,
Hsinchu, Taiwan,R.O.C.
Received 14 May 2023; accepted 25 October 2023
Abstract. Using the real options approach, we try to evaluate the luxury value inherent in high-end housing and estimate
its premium returns based on the simulation of the model. e key nding of the paper is that the luxury premium from
the value of the high-end housing can be identied by the real options model, which is rarely documented in the literature.
In addition, the luxury value per unit size of high-end housing can be imputed through the model simulation. Based on
the results, we nd that the changes of the estimated value per unit size can explain the dynamic housing market behaviour
in the recessions and expansions over the business cycle. e luxury value will even become negative during the recession
period. In summary, the luxury premiums of high-end housing are higher than those of general housing, but not all high-
end housing has positive luxury premiums. If sellers and/or builders of high-end housing cannot meet the conditions that
maximize the utility of high-end housing buyers, negative returns will accrue from selling high-end housing.
Keywords: luxury value, high-end housing, luxury premium, high-end housing value, real options.
consumption”. As conspicuous consumption behaviors tend
to cause price deviations in goods from their fundamental
values (Bagwell & Bernheim, 1996), luxury houses are also
likely to command higher premiums than standard residen-
tial houses. In other words, conspicuous high-end housing
buyers will have to pay positive housing premiums in some
cases. Lee and Mori (2016) provided empirical evidence to
show that conspicuous demand has a stronger relationship
with high-end housing price increases in the U.S. metropoli-
tan statistical areas (MSAs) with a steady, higher housing
premium than in MSAs with volatile and lower premiums
during the boom period. erefore, high-end housing seems
capable of generating higher prots for housing builders in
comparison to general residential housing.
Luxury premiums on the high-end housing price
may not just come from the intrinsic value of high-end
housing but can also be derived from the buyers’ moti-
vation to signal their wealth and social status. Turnbull
etal. (2006) proposed that a larger house can sell at a pre-
mium when compared with otherwise identical houses
in a homogenous neighborhood. Besides, luxury homes
International Journal of Strategic Property Management, 2023, 27(4): 246–260 247
may imply higher quality of neighboring public goods
and services (Downes & Zabel, 2002; Myers, 2004; Chay
& Greenstone, 2005). Zahirovic-Herbert and Chatterjee
(2011) analyzed the values implied by the property name
like “country” and “country club” within a neighborhood.
Based on the data sampled from a local housing market
in U.S.A., they found that wealthier buyers tend to pay
higher price premiums for a property name with “country
club” than other buyers. Lee and Mori (2016) also pro-
posed that certain types of housing gain visibility in terms
of size, luxurious design, and high-quality locations with
excellent neighborhood amenities. Additionally, by us-
ing the sampled data from the housing market in Israel,
Levy and Snir (2018) found that, luxury housing prices
are stickier and less exible than the middle-class housing
prices as the homebuyers in search of luxury will lead to
price rigidities in some market segments and may aect
the propagation of economic cycles.
Instead of relying on the characteristics of high-end
housing such as quality, size and social-economic status of
homeowners, researchers tried to examine the investment
and consumption implied by the housing behavior, which
are the dual motives of the general and high-end housing
buyers in their decision making. Henderson and Ioannides
(1983) distinguished between investment and consumption
demands by maximizing housing utility with the given fam-
ily budget constraints. In view of their model’s assumptions
and parameter setups, Bourassa (1995) and Arrondel and
Lefebvre (2001) modied their model and applied it to
countries such as Australia and France, with mixed results.
Furthermore, Brueckner (1997) introduced a portfolio ap-
proach to analyze the optimal allocation of consumption
and investment by homeowners. His approach was further
expanded by Yao and Zhang (2005) to measure the eect of
investment constraints on homeowners’ consumption and
choice of housing tenure. eir ndings show that buyers
and/or renters will place dierent weightings on liquid as-
sets (bonds and stocks) and housing to maximize their util-
ity from their suboptimal decision making.
As an alternative to the traditional approach in the
aforementioned literature, the real options approach was
applied to evaluate the option value of waiting while ac-
counting for the uncertainty regarding the future value
of investments by rms, such as investment projects un-
der uncertainty (Bloom etal., 2007; Bloom, 2009; Dixit
& Pindyck, 1994; Childs etal., 1998), land development
(Titman, 1985), lease contracts (Grenadier, 1995), and the
decision for homeowners to sell (Qian, 2013). For exam-
ple, Qian (2013) found that the supply is constrained by
the homeowners with embedded call options who will de-
lay their trading decision in expectation of higher prices
in the future. In addition, Wang etal. (2020) applied the
real options to rental market to derive the supply and de-
mand of renting houses in Hong Kong and cities in main-
land China. ey found that in a highly volatile housing
market, the decision made by renters to buy houses and
landlords to sell will aect the equilibrium rental rate
through the size of shis in supply and demand. Hung
and Tzang (2021) also used the real options model to de-
compose housing value into consumption and investment
by evaluating the put options owned by houseowners with
a given set of parameters. ey proposed that the comfort
and utility provided by housing are critical for homeown-
ers in deciding whether to sell their houses.
In this study, we extend the model of Hung and Tzang
(2021) to derive the value of high-end housing premi-
ums and obtain an analytical solution to the luxury value.
To the best of our knowledge, our model is the rst to
theoretically evaluate high-end housing premiums. It
also complements the deciency in the current literature
with which focuses mainly on the empirical analysis of
conspicuous consumption behavior inuencing high-end
housing purchases. In addition, we assume that dier-
ent utility rental benets exist for high-end and general
housing buyers, which helps us dierentiate the premium
values attributed to the housing type. Based on this as-
sumption, we can decompose high-end housing values
into consumption, investment, and luxury values, which
can be derived from our proposed real-options model.
Finally, based on the simulated results from the model,
we nd that high-end housing cannot always command
higher premiums if its luxury value does not meet the de-
mands of homebuyers.
We believe Taiwan’s real estate market is ideal for
lending support to our simulated results. As Taiwan is a
small open economy germinated from Chinese culture,
people tend to treat housing as one of the most impor-
tant assets in their portfolios. Furthermore, housing in
Taiwan is widely considered an investment in the family
assets which can be inherited by descendants. e Taiwan
Household and Population Census showed a home owner-
ship rate of 79% in 2020. According to the Hsinyi Hous-
ing Index, 2021, housing prices have more than tripled in
Taichung and Kaohsiung since 20082. With the increasing
popularity of high-end housing trends since 2010, many
people in Taiwan have also preferred high-end housing to
replace their current residential houses in order to satisfy
their specic tastes for residential comfort as well as to
gain possible value-addition from owning the properties.
erefore, we focus on high-end housing buyers who also
decide to reside in houses so that they can maximize their
utility from both owning the house and living in it3.
2 Taichung and Kaohsiung are the second and third largest cities
in Taiwan, respectively.
3 is is a strong assumption as some of the buyers of high-end
housing may consider high-end housing just for renting or
as long-term investments according to their assetal.ocation
purpose. However, the number of this kind of buyers should
be limited and accounts for a small group belonging to certain
economic elites or people in the top ranks of the society. In
this study, we focus on the larger number of housing buyers
who, within their nancial capacity, have the option to ex-
change their currently resided housing for high-end housing
for residential purposes.
248 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
Section 1 presents our model and theory. Section 2
describes the simulation and numerical analysis of the
model. Section 3 provides an empirical analysis of trans-
action data in the Taiwan luxury housing market based on
the model. e last section concludes the study.
1. Model
According to Hung and So (2012), when housing buy-
ers decide to invest in real estate, they consider prices
of housing and their ability to pay for them. Essentially,
there are two values provided by general housing prop-
erties: consumption and investment. erefore, FH, the
value of general housing properties, can be separated into
consumption value (HC) and investment value (FIG). HC
is the housing utility oered to residents in their houses.
Investment value (FIG) is a real option for selling housing
and realizing capital gains. Whereas, FQ, the value of high-
end housing, has one additional value, which is, luxury
value (HL), when compared with the general housing val-
ue (FH). Demanders of high-end housing normally have
higher requirements for houses that are dierent from the
general ones. Richer housing buyers pay more for HL to
buy high-end housing (Lee & Mori, 2016).
We used the real options model (Dixit & Pindyck,
1994) to derive the consumption, investment, and luxury
values of high-end housing. As general housing value is
composed of consumption value and investment value,
the dierence between the value of high-end housing and
general housing is the luxury value. Consequently, the
consumption and luxury values can be as follows:
= −
H IG
HC F F
; (1)
= −
QH
HL F F
. (2)
Housing prices are also determined by housing loca-
tion and region. erefore, the average housing price in-
dex can be obtained for each region according to its popu-
lation and commercialization level, and we can use this
index as a proxy for housing prices4. e housing price
index used in this study represents the mean housing price
in a city. Following Dixit and Pindyck (1994), we assume
that the current regional housing price index H follows a
random geometric Brownian motion:
( )
= µ −δ +σ
H H Ht
dH dt dZ
H
, (3)
where mH is the housing price index return, dH is the de-
preciation rate of the housing price, sH is the return vari-
ation of the housing price index, and Zt is the standard
Brownian motion. Following Leland (1994), Dixit and
Pindyck (1994), and Uhrig-Homburg (2005), we make
three assumptions. First, we assume the existence of a
risk-free asset with a constant rate of interest r. Second,
4 Housing price index, FAFH, is composed by Federal Housing
Finance Agency every month based on the data of Freddie
Mac and Fannie Mae to show the changes of housing prices
in the recent two months.
as H is the housing price index, we assume that holding
housing assets is similar to holding a housing portfolio
with price proxied by H. Fi is dened as the derivative
of the housing price index, which can be regarded as the
portfolio cash-ow yield5, Citdt, where i denotes dierent
types of housing buyers. When H is not high enough to
attract owners to sell their houses, the housing portfolio
continuously generates cash ow yields. ird, we exclude
the explicit time dependence of H.
As Fi is the housing price index derivative,
( )
σ + −δ + − + =
22
0.5 0
i iii
H HH H H t t
H F r HF FrFC
. (4)
Equation (4) has the general solution:
λλ
=++
12
01 2
i
F X XH XH
, (5)
where6
−δ −δ
λ= − + − +
σσ σ
2
122 2
2
0.5 0.5
HH
HH H
rr r
(5.1)
and
−δ −δ
λ= − − − +
σσ σ
2
2
22 2
2
0.5 0.5
HH
HH H
rr r. (5.2)
X0, X1 and X2 are constants determined by the boundary
conditions. Any time-independent claim with Fi whose
payout Ct is greater than zero, we can further examine
derivative securities.
1.1. General housing value (FH)
is study assumes that house buyers are real house de-
manders. We also assume that, except for the wealthiest,
the high-end housing demanders are the people who will
be the residents in their purchased houses. is assump-
tion also applies to the general housing demanders. Con-
sequently, the owner (dweller) of the house incurs implied
rental income7 and related maintenance expenses in each
period. According to Equation (4), Ct can be dened as
( )
00 0
1
H HH H c
Hw Hw w Hz H t+ ∆ − −δ −
, of which the
rst two terms,
+∆
00H HH
Hw Hw w
, are proxies for pe-
riodic rent and rent variants and can also be regarded as
the utility rental benet for the general housing of house
5 For housing residents, owner-occupied houses can generate
rental cost savings which can be treated as the cash-ow yields.
is also applies to investors’ housing which can generate rent-
al cash ow.
6 As Equation (5) is the solution to the dierential Equation (4),
l is assumed to be the root of the fundamental quadratic equa-
tion:
( ) ( )
2
0.5 1
HH
rr≡ σ λ λ− + −δ λ−
, where l1 > 1 and l2 < 0
(see p. 180–181 of Dixit and Pindyck, 1994).
7 We adopted real options model to evaluate the option value
held by homeowners to decide whether to live in or sell their
houses in the future. erefore, homeowners who reside in the
houses will incur implied rental income, which can be treated
as an opportunity cost of living in the houses.
International Journal of Strategic Property Management, 2023, 27(4): 246–260 249
Let HL denote the housing price level at which housing
owners are willing to sell and realize their capital gains.
According to the real options model, when H approaches
targeted HL, a homeowner sells their houses and receives
aer-tax capital gains, as shown by the boundary condi-
tion in Equation (6.1). However, as H decreases, home-
owners would continue to live in their homes. Condition
(6.2) holds that the decision to sell becomes irrelevant as
H decreases, and the value of general housing approaches
the value of the net rental house. e values and boundary
conditions of FH are as follows:
=
L
HH
,
( )
=− −×
0
HLL c
F H HH t
; (6.1)
→0H
,
( )
= − −−
−∆
0
1
H
Hc
H
wz
F HH t
rw r
. (6.2)
According to Equation (5), it is apparent that X2 should
be equal to 0 when H approaches zero with negative l2.
As
λ
→
1
0 H
as H → 0, together with Equation (6.2), this
implies that
( )
= − −−
−∆
00
1
Hc
H
wz
X HH t
rw r
. Finally,
using Equation (6.1),
( ) ( )
λ
= − − × − − − ×− ×
−∆
1
20 0
1
1
H
LL c c
HL
wz
X H H H t HH t
rw r H
( ) ( )
λ
= − − × − − − ×− ×
−∆
1
20 0
1
1
H
LL c c
HL
wz
X H H H t HH t
rw r H
. In this case,
Equation (5) and the boundary conditions of the subjec-
tive value of the general house price FH are as follows:
( ) ( )
λλ
= − − ×− ×− + − − × ×
−∆
11
00
11
H
Hc LL c
HL L
wzH H
F HH t H HH t
rw r H H
( ) ( )
λλ
= − − ×− ×− + − − × ×
−∆
11
00
11
H
Hc LL c
HL L
wzH H
F HH t H HH t
rw r H H
.
(7)
Equation (7) can also be written as FH =
( )
( )
( )
= − − ×− ×− + − − × ×
−∆
00
11
H
H HH
c L L L cL
H
wz
F HH t P H HH t P
rw r
,
where
λ
≡
1
H
L
L
H
PH
represents the probability that high-
end housing buyers sell their houses at
L
H
.
Interest tax shield and mortgage value: Fint and FD
Most homebuyers use mortgage loans to buy houses,
which generate interest expenses and tax shields. ere-
fore, we can calculate the sum of the present value of in-
terest payments in the entire loan period as the dierence
between the sum of the present value of the mortgage
payments in each period and the original loan balance,
as represented in Equation(8.1). e mortgage payment
PMT given by the standard annuity formula is represented
in Equation (8.2) as follows:
−
× −×
∫
0
0
Trt c
PMT e dt M t
; (8.1)
( )
−−
×− ×
×
= =
−−
0
0
1
11
yT yT
H dy
My
PMT ee
, (8.2)
demanders8. e utility rental benet rate of the general
housing and the rental growth rate are represented by wH
and DwH, respectively. H0z is the housing maintenance
expense,
( )
1
Hc
Htδ−
is the after-tax depreciation
expense. e house owner also must pay management
costs H0z and tax depreciation costs
( )
1
Hc
Htδ−
; tc and z
are the income tax rate of the buyer and the house main-
tenance expense rate, respectively. e sum of the rent and
future rent growth is
−
−∆
0
H
H
wzH
rw r
. We assume that
housing maintenance costs are proportional to H, because
maintenance costs are aected by ination and housing
market prices (Gallin, 2008; Mikhed & Zemčík, 2009;
Kishor & Morley, 2015). In contrast to general housing
buyers, high-end housing buyers attach more luxury value
since they show o high-end housing as a luxury. ere-
fore, we denote the utility rental benet as wj, where j= H
or Q based on the type of housing buyer:
1. Rental expenses: If house demanders do not own
any housing, they would live in a rental house and
incur rental expenses. Consequently, wj is equal to
wH which is the expense rate that homeowners can
save by buying their own houses instead of renting
houses. is rental expense (or rental revenue) ap-
plies to both general and high-end housing buyers.
2. Satisfaction with high-end housing buyers: ere
are many types of high-end housing in the hous-
ing market, each of which has unique features that
are attractive to high-end housing buyers. erefore,
they are more concerned about the satisfaction de-
rived from conspicuous housing expenditure. Sat-
isfaction, that is, the utility rental benet, can be
represented as wQ.
In addition, we also assume wQ to be dependent on
the economic condition. Homebuyers are more willing to
pay more to gain higher satisfaction (higher wQ) from the
luxury investment on housing in the booming period than
they are in the recession period. is is also consistent
with the rationality of consumption behaviour sensitive to
the economic cycle. In other words, during the economic
recession, the price of housing with high luxury invest-
ment may show some rigidity that makes it undervalued
by homebuyers (Levy & Snir, 2018).
For general housing buyers, wH is the utility of gen-
eral housing rental costs which does not satisfy the util-
ity condition of conspicuous consumption. However, for
high-end buyers, wQ is the utility rental benet for high-
end housing buyers and wQ includes more conspicuous
utility rental benets than wH. By not complicating the
quantitative analysis of utility costs, we assume that wj is
an exogenous variable9 applied to the utility rental benet
rate for housing.
8 Here wH is the same as w denoted in Hung and Tzang (2021).
9 e rental utility can be estimated according to Campbell and
Cocco (2015)’s model. As it is not the main concern of this
study, we assume that wj is an exogenously set variable.
250 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
where d is the required down payment, y is the interest
rate the household pays on a xed-rate mortgage with ma-
turity T, M0 is the original loan balance, tc is the income
tax rate of the buyer.
When H increases to HL, homeowners would sell their
house and prepay the mortgage so that they do not have to
pay any interest on the mortgage. When H decreases, the
homeowner will continue to pay the interest and mortgage
principal. Unlike investments in the security market, which
may induce a stop-loss strategy, homeowners will not sell
their houses even though the housing prices take a hit be-
cause we assume in the model that homeowners are also
residents of the house. Fint is dened as the tax-sheltering
value of the interest payments carried by mortgage loans.
According to Equation(4), C represents all payments of
mortgage-deducted principal
−
× −×
∫
0
0
Trt c
PMT e dt M t
and the boundary conditions are as follows:
= =, 0
int
L
HHF
; (9.1)
−
→ = × −×
∫0
0
0, T
int rt c
H F PMT e dt M t
. (9.2)
Equation (9.1) reects the loss of tax-shelter benets
if the homeowner sells the home. Using Equation(5), the
boundary conditions above can be reformulated as
( )
λ
−
= − − ×× −
1
0
11
int rT c
L
PMT H
F e Mt
rH
. (10)
Fint is a decreasing, strictly convex function of H. FD
is dened as the mortgage value, which is, the payments
of the mortgage. According to Equation(4), where Ct is
−
×
∫
0
Trt
PMT e dt
the boundary conditions are as follows:
= = 0
, D
L
HH F M
; (11.1)
−
→= ×
∫0
0, T
D rt
H F PMT e dt
. (11.2)
By the boundary conditions, Equation(5) has a solu-
tion:
( )
λλ
−
= − ×− + ×
11
0
11
D rT
LL
PMT H H
Fe M
r HH
. (12)
Transfer costs Fk
We assume that when high-end house owners want to sell
in their houses and move to another house, they incur a
transfer cost Fk which is assumed to be a proportion b
of the house selling price HL. According to Equation(4),
where Ct is 0, the boundary conditions apply:
= = β, k
LL
HHF H
; (13.1)
→=0, 0
k
HF
. (13.2)
In this case, Equation(4) and boundary conditions
have a solution:
λ
= β
1
kL
L
H
FH
H
. (14)
e transfer cost is an increasing, strictly concave
function of H. Equation(14) can also be represented as
= β
kH
LL
F HP
, implying that the current value of the trans-
fer cost is proportional to the selling price multiplied by
the selling probability.
Optimal decision for general housing owners
e general housing owner chooses a level of H to maxi-
mize the current value of home equity. According to Equa-
tion(15), the home equity for general house owners is the
housing value plus interest tax shield value less transfer
costs and mortgage value:
( )
( ) ( )
( )
−−
λλ
= + −− =
− − ×− +
−∆
×
− − ×− −
− + − − × − −β ×
11
0
0
00
1
11
1 .
H int k D
Hc
H
rT rT
c
LL c L
LL
EF F F F
wzHH t
rw r
PMT PMT
e Mt e
rr
HH
H HH tM H
HH
(15)
when H approaches HL, general housing owners are more
likely to sell their houses and earn a prot. us, the
higher possible value HL for consistent, positive home eq-
uity value for all H < HL is such that
=
∂∂ = /| 0
L
LHH
EH
:
a “smooth-pasting” condition (Leland, 1994) at H= HL.
Dierentiating Equation(15) with respect to HL and set-
ting the expression equal to zero with H= HL, we can
solve for the optimal selling price for
#
L
H
:
( )
( ) ( ) ( )
−
− λ− − − ×
−∆
− λ −λ ×
=× − λ −βλ − − −β
01 0
1 10
#
11
() 1
1.
21 1
HrT
H
cc
L
cc
wz PMT
H eM
rw r r
t Ht
Htt
(16)
Proof: See Appendix A.
According to Equations (16) and (7), we can solve for
the optimal ordinary housing value:
( ) ( )
( )
λλ
−∆
= + − ×− ×
−∆
− + − − ××
11
#
0
##
0
##
.
1
1
HHH
H
Lc
H
LL c
LL
wz
ww
F HH t
r rw
HH
H HH t
HH
(17)
Equation (17) can also be written as
( )
( ) ( )
= − − ×− ×
−∆
− + − − ××
#
0
##
0
,
1
1
H
HLc
H
HH
L L L cL
wz
F HH t
rw r
P H HH t P
where
λ
≡
1
#
H
L
L
H
PH
represents the probability that general
housing owners would sell their houses as H increases.
International Journal of Strategic Property Management, 2023, 27(4): 246–260 251
1.2. High-end housing value (FQ)
As we assume that high-end housing buyers are also resi-
dents of the house, utility rental benet wQ can be meas-
ured in our model. In general, the utility rental benet
wQ can be aected by many features of the houses, such
as location, luxury status of the building, structural safety,
high security, luxury private facilities, and luxury public
facilities for the building. Because high-end housing buy-
ers are willing to pay a higher price for high-end housing
than for general housing, builders invest aH0 in high-end
housing than in general housing. When a builder has
constructed featured and stylish high-end housing that is
dierent from general housing, the utility rental benet
wQ could be higher if high-end housing buyers favor the
builder’s high-end housing.
According to Equation (4),
+∆
00Q QQ
Hw Hw w
re-
fers to the utility rental benet of high-end housing for
buyers. e utility rental benet rate of high-end housing
and its growth rate are denoted as wQ and DwQ, respec-
tively. e sum of the rent and future rent change pre-
sent value can be represented as
−
−∆
0
Q
Q
wzH
rw r
. We
assume that maintenance costs are relative to H because
they are aected by ination and housing market prices.
Furthermore, the homeowner must pay management
costs H0z and tax depreciation costs or maintenance costs
( )( )
δ +α − 11
Hc
Ht
, where tc and z are the income tax
rate of the buyer and the maintenance expense rate of the
house, respectively.
When H increases to the targeted
L
H, homeowners
would sell their houses and realize capital gains, but when
H decreases, homeowners would continue to reside in the
houses, and the value and boundary conditions of FQ are
as follows:
=
L
HH
,
( ) ( ) ( )
( )
= × +α − +α − +α
0
1 11
QLL c
FH H H t
;
(18.1)
( )( )
→ = − − +α −
−∆
0
0, 1 1
Q
Qc
Q
wz
H F HH t
rw r
. (18.2)
In this case, Equation (5) and the boundary conditions
of the subjective value of the high-end house price FQ are
given as follows:
( )( )
( ) ( ) ( )
( )
λ
λ
= − − +α − × − +
−∆
+α − +α − +α ×
1
1
0
0
.
11 1
1 11
Q
Qc
QL
LL c
L
wzH
F HH t
rw r H
H
H H Ht
H
(19)
Conspicuous consumption value (FUR)
As we assume that high-end housing buyers are conspicu-
ous consumers, their demands dier from those of general
housing buyers. High-end housing buyers prefer to aunt
their wealth (Lee & Mori, 2016). We assumed that high-
end housing owners would require an extra conspicuous
consumption value, FUR, included in their selling thresh-
old. is selling threshold also guarantees that high-end
housing owners achieve the minimum required rate of re-
turn R based on the selling threshold. Because high-end
housing owners have a special taste and preference for
high-end housing, they are very likely to hold and reside
in their houses unless they can realize the minimum re-
quired return R for their high-end housing.
When high-end housing demanders purchase high-
end houses, they oen invest large expenses in furnishing
and decorating. We assume housing prices have a g ratio.
When H approaches
L
H, homeowners are more likely to
sell their houses and realize capital gains. When H de-
creases, however, homeowners would continue to reside
in their houses, and the boundary conditions of FUR are
as follows:
( )
= = × +γ ×
0
, 1
UR
L
HH F H R
; (20.1)
→0H
,
=0
UR
F
. (20.2)
Using Equation (4), where Ct is zero, the boundary
conditions above yield the following:
( )
λ
= × +γ × ×
1
0
1
UR
L
H
FH R
H
. (21)
High-end housing optimum decision
To maximize the current value of home equity E,
high-end housing owners sell their houses at price
L
H. e home equity value of high-end housing is de-
ned as the high-end housing value plus the interest tax
shield value less the transfer costs and mortgage value
(
= + −−
Q int k D
EF F F F
). High-end housing owners de-
cide to sell their houses at
L
H which is dierent from
the asking price HL of general housing owners. e key
dierence was FUR. As mentioned above, we assume that
the utility from home equity is Eu= E – FUR, and Eu can
be derived as follows:
( )( )
( ) ( ) ( )
( )
( ) ( )
λ
λλ
−−
λ
= + −− − =
− − +α − ×
−∆
− + +α − +α − +α ×
+ − − ××− − − ×
− −×
1
11
1
0
0
0
0
11
1 1 11
1 11
1
u Q int k D UR
Q
c
Q
LL c
L
rT rT
c
LL
L
EF F FF F
wzHH t
rw r
HH H Ht
H
H PMT H PMT
e Mt e
Hr Hr
HH
M
HH
( )
λλ λ
−β − × +γ × ×
11 1
0
,1
L
LL L
HH
H HR
HH
(22)
when H increases to
L
H, high-end housing buyers may
consider selling the house to realize capital gains. us,
the higher possible value
L
H for consistent and positive
home equity values of the high-end housing owners for
all
<
L
HH
are such that
=
∂∂ =/0
L
u
HH
EH
, a “smooth-
252 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
pasting” condition (Leland, 1994) at
=
L
HH
. Dierenti-
ating Equation(22) with respect to
L
H, we set the expres-
sion equal to zero with
=
L
HH
to solve for
L
H:
( )
==
∂ + −− −
∂= =
∂∂
0
LL
H int k D UR
u
HH HH
F F FF F
E
HH
. (23)
We can solve for the optimal selling house price
*
L
H
that maximizes the home equity value of high-end hous-
ing buyers as follows:
( )
( )
( ) ( )
( )( ) ( )( ) ( )
−
− − − − −−
−∆ λ
+α + × +γ ×
=
+α − λ + +α − −β λ −
00
1
00
*
11
11
11 .
11 11 1
QrT c
Q
c
L
cc
wz PMT
H eMt
rw r r
H tH R
Htt
(24)
Proof: See Appendix B.
Using Equation(24),
*
L
H
is aected by factors such
as w, tc, r, z, dH, sH, H0, T, PMT and M0. We also note
that the regional housing price index,
*
L
H
, at which sell-
ing occurs,
1. increases with sH, wQ, DwQ, H0, y, tc, b, g, R and M0;
2. decreases with z, r, T and dH.
According to Equations (19) and (24), we can solve for
the optimal high-end housing value:
( )( )
( ) ( ) ( )
( )
λλ
= − − +α − ×
−∆
− + +α − +α − +α ×
11
0
**
0
**
.
11
1 1 11
Q
Qc
Q
LL c
LL
wz
F HH t
rw r
HH
H H Ht
HH
(25)
Equation (25) can also be written as
( )( )
( )
( ) ( ) ( )
( )
= − − +α − ×
−∆
− + +α − +α − +α ×
0
**
0
11
1 1 11
Q
Qc
Q
QQ
LL c
LL
wz
F HH t
rw r
P H H H tP
,
where
λ
≡
1
*
Q
L
L
H
PH
represents the probability that
high-end housing owners would sell their houses as H
approaches
L
H.
2. Numerical analysis
In this section, we provide simulated results to ensure
the consistency of the luxury behavior of high-end hous-
ing buyers that is commonly observed in the real world.
Table 1 shows the initial values of all parameters assumed
for the baseline case. Furthermore, by referencing Camp-
bell and Cocco (2015), we adjusted the values of some of
the parameters according to Taiwan’s real estate market
condition to measure the degree to which the simulated
results of the models are aected by the parameter values
in the model. Part of the initial values of parameters are
based on the regulations of Ministry of the Interior of Tai-
wan (MIT) and the report of ROC Real Estate Appraisers
Association (ROCREAA)10.
In Panel A of Table 1, we assume the housing price
depreciation rate to be 0.02 per year because the service
life of Taiwan’s housing is estimated to be 50 years11. e
house price index return variation (0.162) is computed
using historical data from the Taiwan housing price in-
dex. For calculation, the housing price index is initialized
at 100. In Panel B, the utility rental benet rate of general
housing (wH) is assumed to be 2.5% of the housing price,
which represents the widely accepted annual rental yield
in the Taiwanese housing market. However, we assumed
a slightly higher rate of 3.5% for the utility rental ben-
et of high-end housing (wQ). In Panel C, the original
loan balance (M0) is assumed to be 70, as we initialize
the housing price to 100 (H0). Relocation fee (b) also
includes refurnishing fees. In proportion to the housing
price, a is the additional investment by builders in high-
end housing to satisfy buyers’ conspicuous consumption
demands.
By Equation (2), luxury values dier between high-
end and general housing prices. We grouped the values
in Table2 into four regions with gray shading on the
table corners, dened as A, B, C, and D, as shown in
Table3, to summarize the subjective values of high-end
housing in dierent levels of a and wQ. Lee and Mori
(2016) mentioned that when luxury values are high, a
builder gains more benets. ey also proposed that
conspicuous consumption behavior has a much more
signicant, positive relationship with high-end housing
premiums among MSAs, including the top 30% of the
high-end housing premiums, when compared to MSAs,
including the bottom 30% high-end housing premium
group. As a result, not all high-end housing has the same
premium. However, as Lee and Mori did not clearly dis-
tinguish the values among dierent types of high-end
housing, we analyzed the values of four types of high-
end housing for further analysis.
Table 2 summarizes the changes in the subjective val-
ues of high-end housing with a according to the various
levels of buyers’ utility rental benet wQ. We nd that for
a given wQ, a higher a will lead to lower subjective values
of high-end housing. In other words, the more the builder
invests in the construction of the housing, the more high-
end housing buyers would have to pay for that “particular”
10 ROCREAA is a non-prot organization to provide fair and
trustworthy land and real estate valuation information in the
Taiwan real estate market. ROCREAA publishes monthly eco-
nomic report and rules of evaluation based on the most cur-
rent economic data. Technical issues in real estate evaluation
like service tenure of building, residual values, land develop-
ment fees, cost of management and sales are also articulated
in its report for appraisers’ reference.
11 Directorate General of Budget, Accounting and Statistics, Ex-
ecutive Yuan of Taiwan decreed that the service life of Taiwan
residential houses is 55 years. We use 50 years for simulation
purposes only.
International Journal of Strategic Property Management, 2023, 27(4): 246–260 253
Table 1. Baseline parameters*
Description Parameter Val u e
Panel A: Housing price
Housing price depreciation rate dH0.02
Housing price index return variation sH0.162
Initial housing price index H0100**
Panel B: High-end housing buyer utility value
Utility rental benet rate of general housing wH0.025
Utility rental benet rate of general housing growth rate DwH0
Utility rental benet rate of high-end housing wQ0.035
Utility rental benet of high-end housing growth rate DwQ0
Panel C: Housing expense and tax
Income tax rate of buyer tc0.2
Maintain expense rate z0.005
Rate of interest r0.01
Required down payment d0.3
Interest rate that household pays on the xed-rate mortgage y0.02
Maturity of mortgage (in year) T20
Original loan balance M070
Relocation fee rate b0.1
Additional investment on housing (proportion of H0) a0.2
Luxuriously furnished expense ratio g0.3
Note: *Part of the initial values of parameters are based on the regulations of Ministry of the Interior of Taiwan (MIT) and the report of ROC Real Estate
Appraisers Association (ROCREAA). ROCREAA is a non-prot organization to provide fair and trustworthy land and real estate valuation information
in the Taiwan real estate market. ROCREAA publishes monthly economic report and rules of evaluation based on the most current economic data
such as business indicators, interest rate, Taiwan Manufacturing PMI, Consumer Condence Index, etc. Technical issues in real estate evaluation like
service tenure of building, residual values, land development fees, cost of management and sales are also articulated in its monthly report for appraisers’
reference. **For comparison purpose, we set the housing price index to 100.
Table 2. Value of high-end housing*
a= 0.1 a= 0.2 a= 0.3 a= 0.4 a= 0.5 a= 0.6 a= 0.7
wQ= 2.5% 112.05 104.06 96.07 88.09 80.10 72.12 64.14
wQ= 3.0% 162.05 154.06 146.07 138.09 130.10 122.12 114.14
wQ= 3.5% 212.05 204.06 196.07 188.08 180.10 172.12 164.14
wQ= 4.0% 262.05 254.06 246.07 238.08 230.10 222.12 214.14
wQ= 4.5% 312.05 304.06 296.07 288.08 280.10 272.12 264.14
wQ= 5.0% 362.05 354.06 346.07 338.08 330.10 322.12 314.14
wQ= 5.5% 412.04 404.06 396.07 388.08 380.10 372.12 364.13
wQ= 6.0% 462.04 454.06 446.07 438.08 430.10 422.11 414.13
Note: *is table reports how the subjective values of high-end housing will change with a according to dierent levels of buyers’ utility rental benet wQ .
a is the builder’s additional investment in proportion to H0.
housing, which may not fully satisfy the utility of high-end
housing buyers and thus cause a fall in their subjective
values for high-end housing. If the builder’s additional in-
vestment can also increase the utility of the rental benet
of high-end housing buyers (wQ), the subjective value of
such high-end housing will rise. For example, when a=
0.1 and wQ= 2.5%, the subjective value of high-end hous-
ing is 112.05. When a increased to 0.2, and wQ increased
to 3.0%, the subjective value of high-end housing rises to
154.06.
Alternately, even a minimal investment in high-end
housing (a= 0.1) can deliver higher subjective values of
the housing to buyers (from 112.05 to 462.04), when the
investment not only satises the utility rental benet of
the high-end housing buyers but also raises their benet
level (from 2.5% to 6%). More interesting observations
can be made from the boom-bust cycle of the economy.
For example, top-le block in Table 2, which can be
regarded as the economic recession period, shows that
developers tend to make less investment in high luxury
254 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
housing. Meanwhile, homebuyers with low utility rental
benet will be more easily satised with minimal invest-
ment in luxury housing. When the economy is gradually
recovering, homebuyers will move into bottom-le block
in Table2. ey will demand higher utility rental benet
derived from luxury housing, thus raising the housing
value in the market. In this period, however, developers
are not able to increase the supply in time for homebuy-
ers of high-end housing and, therefore, homebuyers will
only have to consume the inventories of luxury housing
accumulated in the recession period.
According to Table 3, TypesA and B are the hous-
ing with more luxury investments, whereas TypesC and
D are the housing with less luxury investments12. From
the perspectives of high-end housing buyers in the boom-
bust economic cycle, they will demand higher wQ from
TypesA and C than from Types ofB and D. Housing lux-
ury values and luxury-premium returns can also be com-
puted for these four types of housing (see Tables4 and 5).
High-end housing of TypeA is housing in which builders
make the highest amount of investment and can fully sat-
isfy the buyer’s utility rental benet. TypeB is not worthy
of the name high-end housing because the builder’s in-
vestment seems incapable of receiving appreciation from
high-end housing buyers. In other words, they did not like
this type of housing. TypeC is dened as the quality lev-
el, which has attractive features such as location, pleasant
12 As we have shown in Table 2, types A, B, C and D correspond
to the economic boom-bust cycle. Types A and B, located in
the bottom- and top-right blocks in Table 2, can be regarded
as the economic boom period. However, type A is in the eco-
nomic boom period whereas type B is in the economic rever-
sal period. Type D is in the economic recession. Type C is in
the economy recovering from the recession.
environment, and/or transportation convenience to meet
the demands of high-end housing buyers, and the build-
ers do not have to invest a lot in the construction of the
building (Kiel & Zabel, 2008). TypeD has the lowest level;
the builder’s investment is low, and the high-end housing
buyer can accept the quality of this building but will not
pay much money to buy the housing.
To realize the dream of owning a luxury home, high-
end housing buyers allocate an excess amount of wealth
to their high-end housing. ey will pay higher premiums
to buy houses that satisfy their utility from conspicuous
housing. Type A high-end housing can create more luxury
value, and buyers would be more willing to pay higher
prices to buy such high-end housing, especially in the
economic booming period. However, Table4 shows that
TypeC high-end housing can create the highest luxury
value compared with TypeA. We propose that because in
TypeC, high-end housing buyers will gain higher utility
rental benet with from small a when the economy condi-
tion is recovering from the recession. By contrast, TypesB
and D can only create low or negative luxury values as
the economy is reversing from top or trapped in a deep
recession. In summary, not all high-end housing can cre-
ate high and positive luxury values.
Although Type D can deliver a positive luxury value
when investment a is minimal (a= 0.1), the builder may
also receive negative premium returns on that investment
in high-end housing (–35.57% when wQ= 2.5% in Table5).
When a rises to 0.7, the premium return (loss) can be as
low as–159.23%. erefore, it is important that builders
analyze high-end housing buyers’ preferences. If investment
in high-end housing can evoke interest, the builder can in-
crease the value of wQ for high-end housing buyers.
According to Table 5, Type C high-end housing cre-
ates the highest premium returns. When wQ= 6.0% and
Table 3. Dierent types of high-end housing*
Small a (small investment) Large a (large investment)
Low wQType D: Lowest level Type B: Not worthy of the name
High wQType C: Quality level Type A: Highest level
Note: *a is the builder’s additional investment in proportion to H0. wQ is the buyers’ utility rental benet.
Table 4. Luxury value of high-end housing*
a= 0.1 a= 0.2 a= 0.3 a= 0.4 a= 0.5 a= 0.6 a= 0.7
wQ= 2.5% 6.44 –1.55 –9.53 –17.52 –25.50 –33.48 –41.46
wQ= 3.0% 56.44 48.45 40.47 32.48 24.50 16.52 8.54
wQ= 3.5% 106.44 98.45 90.47 82.48 74.50 66.52 58.53
wQ= 4.0% 156.44 148.45 140.47 132.48 124.50 116.51 108.53
wQ= 4.5% 206.44 198.45 190.47 182.48 174.50 166.51 158.53
wQ= 5.0% 256.44 248.45 240.47 232.48 224.50 216.51 208.53
wQ= 5.5% 306.44 298.45 290.47 282.48 274.49 266.51 258.53
wQ= 6.0% 356.44 348.45 340.46 332.48 324.49 316.51 308.53
Note: *is table reports how the luxury values of high-end housing will change with a according to dierent levels of buyers’ utility rental benet
wQ. a is the builder’s additional investment in proportion to H0.
International Journal of Strategic Property Management, 2023, 27(4): 246–260 255
a= 0.1, the premium return is approximately 3464.41%.
Even with a low a, Type C has the highest value wQ be-
cause of some specic features, such as excellent location
(Kiel & Zabel, 2008). Type A can also create higher pre-
mium returns but is not as high as that of TypeC. When
wQ= 6.0% and a= 0.7, the premium return for TypeA is
approximately 340.76%. Type D can improve its premium
return from negative to positive when wQ increases from
2.5% to 3.5%, and a increases from 0.1 0.3. e premium
returns generated within this region can be improved
from the lowest level of–131.77% (a=0.3, wQ=2.5%) to
964.43% (a=0.1, wQ=3.5%). In view of Type D high-end
housing, which has the lowest values of wQ and a, builders
should focus on how to increase wQ with a slight increase
in investment to obtain higher rewards.
Table 6 lists the values of FQ–
FH. Generally, FQ is
higher than FH. However, when wQ and wH are very low,
FQ is less than FH. It is possible that high-end housing
buyers do not pay more to buy high-end housing with low
wQ. When wH remains unchanged, the price dierence in-
creases by 50 for every 0.5% increase in wQ. When wQ
is unchanged, the price dierence decreases by approxi-
mately 15 for every 0.5% increase in wH. According to the
analysis above, the marginal contribution of the utility of
high-end housing buyers is higher than that of ordinary
housing buyers.
Figure 1 summarizes these ndings. e subjective
values of luxury premium returns for high-end housing
increase with wQ but decrease with a. For luxury premi-
um returns on high-end housing, wQ is a crucial factor.
Before builders decide to build high-end housing, they
must investigate the preferences and demands of buyers.
When builders want to invest in high-end housing, they
can increase wQ by a. If they cannot fully understand
high-end housing buyers’ demand for high-end housing,
they could suer from investment losses, and the cost of
the losses is much higher than the value of the house.
Table 5. Luxury premium returns of high-end housing based on the initialized parameter values in Table 1*
a= 0.1 a= 0.2 a= 0.3 a= 0.4 a= 0.5 a= 0.6 a= 0.7
wQ= 2.5% –35.57% –107.73% –131.77% –143.79% –151.00% –155.81% –159.23%
wQ= 3.0% 464.43% 142.27% 34.89% –18.80% –51.00% –72.47% –87.81%
wQ= 3.5% 964.43% 392.27% 201.56% 106.20% 48.99% 10.86% –16.38%
wQ= 4.0% 1464.43% 642.27% 368.22% 231.20% 148.99% 94.19% 55.05%
wQ= 4.5% 1964.42% 892.27% 534.89% 356.20% 248.99% 177.52% 126.48%
wQ= 5.0% 2464.42% 1142.27% 701.55% 481.20% 348.99% 260.85% 197.90%
wQ= 5.5% 2964.42% 1392.26% 868.22% 606.20% 448.99% 344.19% 269.33%
wQ= 6.0% 3464.41% 1642.26% 1034.88% 731.20% 548.99% 427.52% 340.76%
Note: *e luxury premium of high-end housing is
− +α
+α
*0
0
(1 )
(1 )
L
HH
H
.
Table 6. Subjective value dierence between high-end housing and general housing*
wH= 2.5% wH= 3.0% wH= 3.5% wH= 4.0% wH= 4.5% wH= 5.0% wH= 5.5% wH= 6.0%
wQ= 2.5% –1.55 –12.69 –26.24 –41.02 –56.50 –72.42 –88.61 –105.01
wQ= 3.0% 48.45 37.31 23.76 8.98 –6.50 –22.42 –38.61 –55.01
wQ= 3.5% 98.45 87.31 73.76 58.98 43.50 27.58 11.39 –5.01
wQ= 4.0% 148.45 137.31 123.76 108.98 93.50 77.58 61.38 44.99
wQ= 4.5% 198.45 187.31 173.76 158.98 143.50 127.58 111.38 94.99
wQ= 5.0% 248.45 237.31 223.76 208.98 193.50 177.58 161.38 144.99
wQ= 5.5% 298.45 287.31 273.76 258.98 243.50 227.58 211.38 194.99
wQ= 6.0% 348.45 337.31 323.76 308.98 293.50 277.58 261.38 244.99
Note: *is table displays the subjective value dierence between high-end (FQ) and general housing (FH) based on utility rental benet wQ and wH.
Figure 1. e changes of luxury premium returns across utility
rental benet wQ and investment on high-end housing a
Luxury premium returns
256 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
3. Empirical results
Table 7 is the summary statistics of the housing transac-
tion data from 2016/01 to 2018/08 in the three biggest
cities in Taiwan: Taipei, Taichung, and Kaohsiung, of
which the number of the population is around 2.7 million
equally for each city as of 2022. e datasets are collected
from the Ministry of the Interior of Taiwan (MIT) and the
ROCREAA. e transaction data is limited to residential
homes in high-rise buildings sold in contiguous regions
within the urban elite area. is study uses a sample con-
sisting of broker-assisted high-end housing transactions
within this sampled period.
We divide the high-end housing transaction data into
high- and middle-to-low oors13. High-end housing buy-
ers prefer high-oor homes to middle-to-low-oor ones14,
but the construction costs for high oors are higher than
those for middle-to-low oors. We assume that high-end
housing demanders have a higher utility rental benet wQ
for high-oor housing owing to better view and light. Ta-
ble7 presents a summary of the sample data. e mean
value is the average trading price per square meter (m2)
in New Taiwan Dollar (NTD) for Taipei, Taichung and
Kaohsiung, and the prices of higher oors are higher
than middle-to-low oors. We noted that the mean price
of high oors in Taipei is NTD 401,127, which is signi-
cantly higher than the building cost (NTD 244,511). e
price and cost spread in Taipei is also the highest (156,617
and 114,697, respectively). e cost of building includes
land, construction, management, and sales costs, and we
appraise it according to ROCREAA rules.
13 In Taiwan, low oors of the housing are the oor from the 1st
to the 5th and middle oors from the 6th to the 10th.
14 In Taiwan, housing on higher oors symbolizes the level of
luxury for housing. Housing price increases as the height of
the oor increases. However, high oors also suer from the
risks of re escape and earthquakes in Taiwan.
Table 7 also shows that the cost of building high oors
is greater than the cost of building middle-to-low oors;
however, there is a slight dierence in Taichung city where
the cost of buildings with middle-to-low oors is higher
than that of buildings with high oors. We think that this
is due to the buyers’ preference for middle-to-low oors,
as Taichung City experienced a severe earthquake on Sep-
tember 21, 1999. Another reason is the limited number
of transaction data (36 and 27) from Taichung city when
compared with the other two cities (126 and 75 in Taipei;
609 and 528 in Kaohsiung). During the sampling period,
many high-rise buildings were still under construction
with luxury housing units in the central areas of Taichung
such as the 7th land readjustment zone. e land and con-
struction costs of high oors are much higher than the
costs of middle-to-low oors. erefore, the sampled data
of the construction cost in Taichung may not be repre-
sentative of the Taichung market.
Table 8 lists the luxury premium returns of high-end
housing of Taipei, Taichung, and Kaohsiung. By Table8,
the luxury premium returns of the high oors of Taipei
and Taichung are higher than those of the middle-to-low
oors, and luxury premium returns decrease as a increas-
es. is nding is consistent with the results presented
in Table5. When a = 0.6, luxury premium returns for
high-end housing for both Taichung and Kaohsiung are
negative. In Kaohsiung, the housing prices for high oors
were higher than those of middle to low oors. However,
the fact that the construction cost of high oors is higher
than that of middle-to-low oors does not warrant a pro-
portional increase in the luxury premium returns of high
Table 7. Summary statistics of the housing transaction data from Jan 2016 to August 2018 in three biggest cities in Taiwan
City Description Quantity Cost of building (NTD) Price/m2 (NTD) Di. in means
(p-value)
Mean Std. dev. Mean Std. dev.
Tai p ei High oors 126 244,511 20,761 401,127 59,693 156,617***
(7.9E-21)
Middle-to-low
oors
75 209,379 36,456 324,076 88,476 114,697***
(2.0E-06)
Taichung High oors 36 130,373 20,096 188,159 28,217 57,786***
(0.001211)
Middle-to-low
oors
27 140,280 17,625 145,925 26,021 5,646
(0.70084)
Kaohsiung High oors 609 53,600 4,444 82,586 15,975 28,986***
(3.124E-67)
Middle-to-low
oors
528 48,728 5,189 82,287 23,492 33,559***
(2.179E-43)
Note: ***, **, and * indicate signicance at the 1%, 5%, and 10% levels, respectively.
International Journal of Strategic Property Management, 2023, 27(4): 246–260 257
oors in Kaohsiung. is may be due to the high-end
housing buyers in Kaohsiung, who are not willing to pay
more for the luxury premium. In addition to the measure-
ment of high-end housing buyers’ utility rental benet wQ,
we believe that builders may also have to consider possi-
ble factors aecting residents’ preferences, such as income,
spatial location, and scarcity of green environments across
dierent cities.
Since the average income in Taipei and Taichung is
higher than that in other cities, residents are willing to pay
for the luxury premium. e most important decision of
high-oor housing suppliers is to measure high-end hous-
ing buyers’ utility rental benets, wQ. We note that high-
oor high-end housing has luxury premium returns in
three cities, and the luxury premium returns of high-end
housing in Taipei and Kaohsiung are higher than those of
Taichung. If builders want to invest in high-end housing,
they can invest in Taipei and Kaohsiung, but they must
carefully consider the middle-to-low oor buildings in
Taichung, as their luxury premium returns are negative.
According to the above analysis, builders must consider
three important points: 1)the high-end housing buyers’
utility rental benet wQ, 2)the income of the local resi-
dents, and 3)the cost of building.
Conclusions
Buyers of high-end, owner-occupied homes, oen pay
higher prices to buy high-end housing. ey are moti-
vated to consume highly conspicuous high-end housing
and aunt their wealth, thereby achieving better social sta-
tus (Veblen 1899). High-end housing buyers are wealthy
individuals who consume luxury high-end housing at a
price higher than their intrinsic value. Builders can earn
strictly positive prots when high-end housing is of Types
A and C. Because certain types of homes are more visible
in terms of size, location, and design, high-end housing
buyers would purchase high-end housing not only for the
pleasure of their intrinsic value but also for additional so-
cial esteem because such housing signals their own wealth,
and the value of wQ will increase. If high-end housing can
create a high-value wQ, the buyer will earn higher luxury
premium returns.
According to our results, high-end housing can create
higher luxury premium returns, but not all builders can
earn higher luxury premium returns. Our results show
that Types B and D are not sound investment projects,
especially TypeB. Builders who have little experience with
high-end housing investment must prepare to investigate
what high-end housing buyers enjoy.
Our results show that location, one of the features of
housing, may be the most crucial factor. TypeC can gain
the highest prots with investment a at a low level because
of homes with excellent neighbourhood amenities, the
same race of neighbourhoods, and good transport facili-
ties (Cutler etal., 1999; Crowder, 2000; Lee & Mori, 2016).
If builders have an excellent location, they can construct
high-end housing without investing too much a to gain
higher luxury premium returns, as in Type A. Owing to
the scarcity of land properties and the high costs of well-
located land, builders with well-located land can construct
high-end housing that is not easy to construct. If builders
want to earn more prots, they can invest in luxury build-
ings to raise wQ (e.g., they can build pleasant and spacious
homes with excellent public amenities and designs that
signal the wealth of buyers who want to display their own
wealth and achieve greater social status), as in TypeA.
Our model can appraise luxury valuations and premi-
um returns in high-end housing. In contrast, Lee and Mori
(2016) discovered through empirical research that conspic-
uous behaviour has a positive relationship with high-end
housing premiums. Our results show that not all high-end
housing units have positive premiums. If builders do not
attract high-end housing buyers to invest in high-end hous-
ing, they will experience negative premium returns.
Acknowledgements
e authors would like to thank the editor and two anony-
mous reviewers for their valuable suggestions and con-
structive comments. Our gratitude also goes to Michael
Burton, Asia University.
Table 8. Luxury premium returns of high-end housing of Taipei, Taichung, and Kaohsiung
a= 0 a= 0.1 a= 0.2 a= 0.3 a= 0.4 a= 0.5 a= 0.6
Tai p ei
Middle-to- low oors 60.22%*** 45.66%*** 33.52%*** 23.25%*** 14.44%** 6.81% 0.14%
High oors 61.86%*** 47.15%*** 34.88%*** 24.51%*** 15.62%*** 7.91%** 1.16%
Taichung
Middle-to-low oors –29.12%*** –29.94%*** –30.62%*** –31.19%*** –31.68%*** –32.11%*** –32.49%***
High oors 49.63%*** 36.02%*** 24.69%*** 15.1%** 6.88%*** –0.25%** –6.48%
Kaohsiung
Middle-to- low oors 59.22%*** 44.74%*** 32.68%*** 22.48%*** 13.73%*** 6.15%*** -0.49%
High oors 54.61%*** 40.56%*** 28.84%*** 18.93%** 10.44%*** 3.07%*** –3.37%***
Note: ***, **, and * indicate signicance at the 1%, 5%, and 10% levels, respectively. is table displays the subjective values of high-end housing clas-
sied by two types of housing, and a is the builder’s initial investment compared to the proportion of H0. e luxury premium of high-end housing
computed is
( ) ( )
− +α +α
*00
( 1) /(1)
L
HH H
.
258 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
Funding
is work is supported by the Ministry of Science and
Technology of Taiwan under Grant (MOST 111-2410-H-
992-036).
Author contributions
Chih-Hsing Hung conceived the study and is responsi-
ble for the theoretical work. Shyh-Weir Tzang, the cor-
responding author, and the other two coauthors are re-
sponsible for the data analysis, numerical simulation and
interpretation.
Disclosure statement
Authors do not have any competing nancial, profession-
al, or personal interests from other parties.
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Appendix A
Proof: By optimal selling price for
#
L
H
, we obtain
( )
( )
( ) ( ) ( )
01 0
1 10
#
11
( )1
1
21 1
HHH rT
H
cc
L
cc
wz
ww PMT
H eM
r rw r
t Ht
Htt
−
−∆
+ λ− − − ×
−∆
− λ −λ ×
=× − λ −βλ − − −β
Home equity is as follows:
= + −−
H int k D
EF F F F
(A.1)
Substituting Equations (7), (10), (12), and (14) into
Equation (A.1) yields
( )
( )
( )
( )
λλ
λ
−
λλ
−
= + − − = − − ×− ×
−∆
− + − − ×× +
− − ××− −
− × − − × −β
11
1
11
0
0
0
0
1
1
11
11
H
H int k D c
H
LL c
LL
rT c
L
rT L
L LL
wz
EF F F F H H t
rw r
HH
H HH t
HH
PMT H
e Mt
rH
PMT H H H
e MH
r H HH
λ
1
.
(A.2)
We can arrange Equation (A.2) as:
( )
( ) ( )
( )
λ
−−
λ
− −×− +
−∆
= ×− +
− − ×− −
− − × − −β ×
1
1
0
0
00
.
1
1
11
Hc
H
L
rT rT
c
LL c L
L
wzHH t
rw r H
EH
PMT PMT
e Mt e
rr
H
H HH tM H H
(A.3)
Dierentiating Equation (A.3) with respect to HL, a
“smooth-pasting” condition (Leland, 1994) at H= HL, and
solving for optimal selling price for
#
L
H
:
=
∂=
∂0
L
LHH
E
H
( )
( ) ( )
( )
( )
=−−
λλ
λ
− − ×− +
−∆
∂
= λ×
∂
− − ×− −
− − − × − −β λ +
− −β × =
11
1
0
1
0
00 1
11
11
1
1 0.
L
Hc
H
LL
HH rT rT
c
LL
LL c L
L LL
L
c
L
wzHH t
rw r
E
HH
PMT PMT
e Mt e
rr
HH
H H H tM H
H HH
H
tH
(A.4)
We can arrange Equation (A.4) as follows:
( )
( ) ( ) ( )
−
− λ− − − ×
−∆
− λ−λ × = × − λ−βλ− − −β
01 0
1 10 1 1
(
;
)1
1 21 1
HrT
H
c c c cL
wz PMT
H eM
rw r r
t Ht t t H
(A.5)
( )
( ) ( ) ( )
−
− λ− − − ×
−∆
− λ −λ ×
=× − λ −βλ − − −β
01 0
1 10
#
11
() 1
1
21 1
HrT
H
cc
L
cc
wz PMT
H eM
rw r r
t Ht
Htt
. (A.6)
Appendix B
Proof: By optimal selling price for
*
L
H
, we obtain
( )
( )
( ) ( )
( )( ) ( )( ) ( )
−
− − − − −−
−∆ λ
+α + × +γ ×
=
+α − λ + +α − −β λ −
00
1
00
*
11
11
11
11 11 1
QrT c
Q
c
L
cc
wz PMT
H eMt
rw r r
H tH R
Htt
By the home equity equation:
= + −−
Q int k D
EF F F F
. (B.1)
We can substitute Equations (19), (10), (12), and (14) into
Equation (B.1) to obtain the following:
260 C.-H. Hung et al. Does high-end housing always have a premium luxury value? A theoretical and...
( )( )
( ) ( )
( )
( )
( )
λ
λλ
−
λλ
−
= − − +α − ×
−∆
− + +α − +α − ×
+ − − ××− −
− × − − × −β
1
11
11
0
0
0
0
11
1 11
11
11
Q
c
Q
LL c
L
rT c
LL
rT L
L LL
wz
E HH t
rw r
HH H Ht
H
H PMT H
e Mt
Hr H
PMT H H H
e MH
r H HH
λ
1
.
(B.2)
By setting
= −
u
E E CT
, we can get the following:
( )( )
( ) ( ) ( )
( )
( ) ( )
λ
λ
λ
−−
λ
= + −− −
− − +α − × − +
−∆
+α − +α − +α ×
− − ×× − − − ×
− −×
=
+
1
1
1
1
0
0
0
0
11 1
1 11
1 11
1
u Q int k D UR
Q
c
QL
LL c
L
rT rT
c
L
L
EF F FF F
wzH
HH t
rw r H
H
H H Ht
H
PMT H PMT
e Mt e
r Hr
HH
M
HH
( )
λλ
λ
−β
× +γ × ×
−
11
1
0
.1
L
LL
L
H
HH
H
HR
H
(B.3)
We can rearrange Equation (B.3) as follows:
( )( )
( ) ( )
( ) ( ) ( )
( )
( )
1
1
0
0
0
00
.
11
1
11
1 11
1
Q
c
Q
u
L
rT rT
c
LL c
L
L
wzHH t
rw r H
EH
PMT PMT
e Mt e
rr
H H Ht
H
H
M HH R
λ
−−
λ
− − +α − +
−∆
= ×− +
− − ×− −
+α − +α − +α −
×
−β − × +γ ×
(B.4)
Dierentiating Equation (B.4) with respect to HL, a
“smooth-pasting” condition (Leland, 1994) at H= HL, we
can derive the optimal sell price for
*
L
H
:
( )( )
( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )
0
0
0
1
00
1
11
11
1 11
1
1 1 0.
L
Q
c
uQ
LHH rT rT
c
LL c
LL
c
L
wzHH t
rw r
E
HPMT PMT
e Mt e
rr
H H Ht
HM HH R
t
H
=−−
− − +α − +
−∆
∂
= ×
∂
− − ×− −
+α − +α − +α −
λ
−×
−β − × +γ ×
λ
+ +α − +α −β =
(B.5)
We can further rearrange Equation (B.5) to obtain the
following:
( )( )
( ) ( )
( ) ( ) ( )
( )
( )
( ) ( )
0
1
0
0
1
00
11
11
1 11
1
11 0
Q
Lc
Q
rT rT
c
LL c
L
cL
wzHH t
rw r
PMT PMT
e Mt e
rr
H H Ht
M HH R
tH
−−
− − +α − +
−∆
λ−
− − ×− −
+α − +α − +α −
λ+
−β − × + γ ×
+α − +α −β =
(B.6)
and
( )( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
−−
+α − λ+ +αλ− +α λ−β λ−
+α − +α −β = − λ +
−∆
− − λ× − − λ−
+αλ+ λ+ × +γλ×
1 1 11
01
01 1
0 1 01 0 1
11 1 1
11
11
1 1.
L cL Lc L
Q
cL
Q
rT rT
c
c
H tH H tH
wz
tH H
rw r
PMT PMT
eMt e
rr
Ht M H R
(B.7)
erefore, we have:
( )
( )
( ) ( )
( )( ) ( )( ) ( )
00
1
00
*
11
11
11 .
11 11 1
QrT c
Q
c
L
cc
wz PMT
H eMt
rw r r
H tH R
Htt
−
− − − − −−
−∆ λ
+α + × +γ ×
=
+α − λ + +α − −β λ −
(B.8)
