Rental and sale prices of agricultural lands under spatial competition

G aubne , Ma en; Hü el, Silke
A icle — Published Ve sion
Ren al and sale p ices o ag icul u al lands unde spa ial
compe i ion
Le e s in Spa ial and Resou ce Sciences
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Sugges ed Ci a ion: G aubne , Ma en; Hü el, Silke (2024) : Ren al and sale p ices o ag icul u al
lands unde spa ial compe i ion, Le e s in Spa ial and Resou ce Sciences, ISSN 1864-404X, Sp inge ,
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ORIGINAL PAPER
Ren al andsale p ices o ag icul u al lands unde spa ial
compe i ion
Ma enG aubne 1 · SilkeHü el2
Recei ed: 16 May 2024 / Accep ed: 6 No embe 2024 / Published online: 28 No embe 2024
© The Au ho (s) 2024
Abs ac
Much o he land economics li e a u e has la gely igno ed he spa ial na u e o com-
pe i ion and ela ed di e ences be ween a mland en al and sales ma ke s when
assessing e u n a es om a ming, he capi aliza ion o ag icul u al, en i onmen-
al and ene gy policy in o land alues, and clima e change impac s. We p opose a
model o p ice o ma ion in bo h ma ke s unde a spa ial compe i ion amewo k.
We demons a e ha p ice o ma ion di e s, pa icula ly unde policy-induced ou -
pu p ice shocks.We sugges ha using he en -p ice a io as an app oxima ion o
expec a ions in he ne e u ns o a ming, based on he ne p esen alue model,
may p oduce biased esul s. In consequence, s udies elying on land p ices need o
con ol o local land compe i ion, a ming s uc u e, and policies.
Keywo ds Land ma ke s· Ren -p ice Ra io· Spa ial compe i ion· Policy
capi aliza ion· P ice o ma ion
JEL Classi ica ion L13· Q12· Q18
1 In oduc ion
In his no e, we in es iga e he land ma ke om an indus ial o ganiza ion pe spec-
i e. Land is a sca ce esou ce wi h declining o e all supply, ixed loca ion and o he
he e ogeneous a ibu es. As a consequence, e e y ansac ion is speci ic, loca ion
ma e s and in a ypical cons ella ion a single selle mee s se e al po en ial buye s.
* Ma en G aubne
ma en.g aubne @landw.uni-halle.de
1 Ins i u e o Ag icul u al andNu i ional Sciences, Chai o Fa m Managemen , Ma in-Lu he -
Uni e si y Halle-Wi enbe g, Ka l-F eihe - on-F i sch-S . 4, 06120Halle, Ge many
2 Depa men o Ag icul u al Economics andRu al De elopmen , Ag icul u e andFood Business
Managemen G oup, Geo g-Augus -Uni e si y Gö ingen, Pla z de Gö inge Sieben 5,
37073Gö ingen, Ge many
M.G aubne , S.Hü el
32 Page 2 o 12
In he ollowing, we elabo a e he di e ence be ween he sho - un leasing ma ke
and he long- un sales ma ke .1
The spa ial aspec s o compe i ion and associa ed dis inc ions be ween he en al
and sales ma ke s o ag icul u al lands a e as impo an as loca ion speci ic cha ac-
e is ics and spa ial dependencies (c . Nicke son e al. 2012). Fo ins ance, en s may
be he esul s o less compe i i e ma ke se ings compa ed o sales ma ke s, since
local a ms compe e p ima ily in he en al ma ke , while non-local ag icul u al and
non-ag icul u al in es o s compe e p ima ily in he sales ma ke . Igno ing he spa ial
na u e o compe i ion may challenge he esul s gi en by he ne p esen alue model
o a mland p ices (c . Dea on and Lawley 2022), i.e. elying on he land-p ice a io
o app oxima e he e u ns om a ming (e.g. Bo che s e al. 2014; Plogmann e al.
2020; Schaak and Mußho 2022). This may o ins ance explain he no ed di e -
gence in policy capi aliza ion a es in en al and sales ma ke s (e.g. Salho e and
Feich inge 2020; Ciaian e al. 2021 ). Assessmen s o clima e change on ag icul u e
which use Rica dian app oaches based on en al a es o land alues igno ing spa ial
aspec s o he ma ke s may also gi e biased esul s (e.g. O iz-Bobea 2020; Ba eille
and Chaki 2023 ).
To demons a e how changes in ma ginal e enues may a ec equilib ium en al
and sales p ices, we de elop a model o p ice o ma ion in a mland ma ke s unde a
spa ial compe i ion amewo k. Unlike exis ing models o spa ial compe i ion unde
a m policies (G aubne 2018) and app oaches a emp ing o explain he beha iou al
di e ences o ag icul u al and non-ag icul u al bidde s in a mland ma ke s (Cu -
iss e al. 2021; Sei e e al. 2021; Balmann e al. 2021; Deininge e al. 2023), ou
model is be e able o accoun o p e ious empi ical indings o he di e ences in
policy capi aliza ion a es on land p ices and en al a es, espec i ely, and he bid-
ding beha iou s o owne s, buye s and en e s. This leads us o p opose he ollow-
ing hypo hesis: gi en he spa ial na u e o compe i ion in en al and sales ma ke s
o ag icul u al lands, compounded en s di e sys ema ically om sales p ices, bu
pa icula ly unde an ou pu p ice shock and al e na i e u u e use o land.
This no e is o ganized as ollows. Sec ion2 desc ibes ou heo e ical amewo k,
in oduces he g aphical models o spa ial compe i ion in he en al and sales a m-
land ma ke s as well as ou hypo hesis. In Sec s.3 and 4 we demons a e he e ec s
o shocks in downs eam ma ke s and al e na i e uses o land on en al and sales
p ices, espec i ely. Sec ion5 discusses he esul s, and Sec .6 concludes wi h sug-
ges ions o u u e esea ch.
1 While he pape ocuses on ag icul u al land ma ke s, he model and i s esul s can be ele an o ma -
ke s wi h simila cha ac e is ics, e.g., he o es land, housing, and u ban land ma ke in pa icula o o he
ma ke s o ho izon al p oduc di e en ia ion and he possibili y o p ice disc imina ion in gene al.
Ren al andsale p ices o ag icul u al lands unde spa ial… Page 3 o 12 32
2 A spa ial compe i ion amewo k o land ma ke s
2.1 Land en al ma ke
Following G aubne  (2018), we assume wo a ms, A and B, loca ed a he end-
poin s o a line ma ke wi h uni leng h and uni o mly dis ibu ed land along his
segmen . Bo h a ms ope a e unde dis ance cos e lec ing hei dec easing will-
ingness o pay (WTP) o land wi h inc easing dis ance o he a ms ead.2 Unde
pe ec compe i ion in he ag icul u al ou pu ma ke , hey ecei e a ne ma ginal
e enue om land MR, i.e. he ma ginal e enue o land ne o p oduc ion cos s bu
he en al p ice o land.
A each loca ion
x=[0, 1]
, a landowne supplies one uni o land o he a m-
land en al ma ke , gi en he en al p ice (x) exceeds he landowne ’s ese a ion
p ice . Fa ms can se he en al p ice o land a each loca ion, i.e. o each indi-
idual plo . This decision is in luenced by hei linea dis ance cos s and gi es:
WTPA(x)=MRA− x
and
WTPB=MRB− (1−x)
. Depending on hei cos and
p oduc ion s uc u e, hei ne ma ginal e enue migh di e , i.e.
MRA≠MRB
. We
ind he loca ion
x
whe e A and B ha e he same willingness o pay o land in he
en al ma ke by:
Fig. 1 A spa ial model o he land en al ma ke
2 Dis ances depic ed in ou model do no necessa ily measu e he dis ance be ween a ms ead and ield
bu , mo e b oadly, include any e e ence loca ion ele an o a m ope a ions such as s aples o p oduce
magazines as well as he dis ance o simila ly a med land owned o en ed by he same a m.
M.G aubne , S.Hü el
32 Page 4 o 12
Wi h su icien ly low , he ma ke is co e ed and A and B can p o i ably en
land neighbou ing he a ms ead o hei compe i o as shown in Fig.1, o mally
+ ≤min[MRA,MRB]
.
Gi en he dis ance cos , a m A (B) on he le ( igh ) o
x
has a highe WTP, e.g.
i
MRA=MRB=MR
,
x=1∕2
and he maximum WTP o land is
WTPA(x1)
a loca-
ion
x1
o a m A, bu B is only able o pay
WTPB(x1)
and he landowne s’ willing-
ness o accep (WTA) a
x1
is (see Fig.1).
Because o he (pe ec ly) p ice-inelas ic local land supply, uni o m p icing is he
p o i maximizing p ice s a egy o a ms (Espinosa 1992; G aubne e al. 2011).
Unde uni o m p icing, a a me o e s he landowne an iden ical en al p ice i e-
spec i e o he dis ance om he landowne ’s plo o he a ms ead as long as i gen-
e a es (local) su plus o he a m. In a non-coope a i e se ing, no Nash equilib ium
unde uni o m p icing exis s (Schule and Hobbs 1982; Zhang and Sex on 2001).3
I a ms A and B decide hei en al p ices acco ding o an a e age o he p ices
o neighbou ing a ms (Balmann e al. 2021), spa ially-coope a i e p ice ma ching
compe i ion eme ges (G onbe g and Meye 1981; G aubne e al. 2011). In equilib-
ium, a ms se en al p ices a he landowne s ese a ion p ice (G aubne 2018)
o cap u e all o he supplie s’ (landowne s’) su plus (Zhang and Sex on 2001). Fo
ins ance, a loca ion
x1
he owne ’s su plus is ze o because
u
=
, bu bo h a ms
could yield non-ze o p o i s i hey o e
u
=
and en ha land (see Fig. 1).
The po en ial su plus o a m A is
MR − x1−
and la ge compa ed o a m B:
MR − + x1−
. Tie-b eaking ules de e mine which a m en s land a loca ion
x1
(G onbe g and Meye 1981; Iozzi 2004). Since bo h a ms o e he same p ice
u
, one could assume ha landowne s andomly selec he enan , bu a me s (e.g.
in Eas e n Ge many) o en exchange en ed land o ound o hei a mland a ea
(Ma ga ian 2008). The p ac ice co esponds o he e icien ie-b eaking ule (Iozzi
2004), i.e. he a m wi h he lowes dis ance cos s en s he plo . Hence, a m A
ob ains he su plus om he plo a
x1
.
I all land in he ma ke is en ed so ha no a m owns (a leas pa o ) i s ope -
a ed land, he equilib ium en al p ice
u
=
yields landowne s su plus in he ma -
ke o
while he su plus o he a me s is
(1)
x
=
MR
A
−MR
B
+
2
.
(2)
∫1
0
( u− )dx =
0
3 Fo ins ance, Fa m A could o e
A
(see Fig.1) and en all land le o
x1
. Fa m B’s maximum WTP a
x1
is
B
, which acili a es o en all land igh o
x1
. Nei he p ice is an op imal esponse o he compe i-
o ’s p ice hough. Fa m B is be e o wi h
B
=
, which incen i es Fa m A o lowe i s p ice as well
and o ma ginally o e bid B.

Ren al andsale p ices o ag icul u al lands unde spa ial… Page 5 o 12 32
wi h
xi=[0, 1]
.
2.2 Land sales ma ke
Ins ead o en ing land, a me s may p e e buying i due o he ansac ion cos s o
nego ia ing en al con ac s, he sea ch cos s associa ed wi h losing con ac s and
ela ed isks. Seeking hedges agains in la ion, s o ing weal h, s abilizing po olios,
e c., may mo i a e also non- a me buye s o acqui e a mland. Liquidi y easons o
o he in es men op ions a e incen i es o landowne s o sell land.
The common app oach o model land alues R is he ne p esen alue (NPV)
model, which discoun s a s eam o expec ed e u ns o e an in ini e ime ho izon
(Goodwin e al. 2003); cash en s a e an obse able op ion o such e u ns (Bo ch-
e s e al. 2014). Acco dingly, any en al p ice (x) in Fig.1 ep esen s he po en ial
annual e u ns om owning land. Using he NPV model yields a local sales p ice:
whe e d is a cons an discoun ac o .
Lands immobili y, local speci ici y, spa ial dis ibu ion and low ma ke liquidi y
(Bigelow e al. 2020; Kionka e al. 2022) cha ac e ize a mland sales ma ke s as a
(3)
∫1
0
(max[WTPA(x),WTPB(x)] − )dx =MR −
4−
(4)
p
(x)=
∞
∑
n=1
(x)
(1+d)n
Fig. 2 A spa ial model o he land sales ma ke
M.G aubne , S.Hü el
32 Page 6 o 12
s a ic, one-sho game. In his se ing, a ms ha e less incen i es o collabo a ion
(Espinosa 1992). In e ms o local e u ns, he lowes WTP a any loca ion de e -
mines he non-coope a i e, Nash-equilib ium sales p ice
p∗(x)
(G aubne e al. 2021;
Lede e and Hu e 1986; Thisse and Vi es 1988). The ed lines in Fig.2 show he
esul ing local land p ice schedule.
Fa m A (B) can p o i ably pu chase land le ( igh ) o
x
. A loca ion
x1
he su -
plus o a m A, p icing ma ginally abo e
WTPB(x1)
, is
WTPA(x1)−p∗(x1)
and he
landowne ’s su plus is
p∗(x1)−
. Unde pe ec in o ma ion, all landowne s and
po en ial buye s can obse e he local p ices. The cos o sea ch and in o ma ion
ga he ing, howe e , may be asymme ically dis ibu ed among ma ke pa icipan s;
selle s and buye s migh no be able o acqui e all he in o ma ion abou ma ke con-
di ions and speci ic a ibu es o he espec i e land plo (Meissne and Mussho
2022). Fo ins ance, local a me s can be be e in o med han non-local a me s and
o he buye s (Sei e e al. 2021). Acco dingly, hese g oups only obse e he a e -
age sales p ice
p
in a egion shown as he do ed line in Fig.2 gi en by:
We obse e ha
p
inc eases wi h inc easing ma ginal e enue om he land bu
dec eases wi h dis ance cos s. We can make quali a i ely simila obse a ions o
he a me ’s WTP and hus he equilib ium sales p ices, bu no o he equilib ium
en al p ices ha a e independen o MR o (2). The landowne su plus in he sales
ma ke is
whe e
p(x)=min{WTPA(x),WTPB(x)}
. The su plus o he a me s is
which is always smalle compa ed o he (discoun ed) su plus o a ms in he en al
ma ke (3). In o he wo ds, en ing is p e e able o buying in an a omis ic landown-
e ship s uc u e and unde he assump ion ha he en al ma ke is less compe i i e
han he sales ma ke .
3 Shocks in a m ou pu ma ke s
Many empi ical s udies iden i y subs an ial capi aliza ion o p ice shocks in a m
ou pu ma ke s caused by a ming policies o o he ac o s on land en als. How-
e e , capi aliza ion is lowe han heo e ically expec ed (Ciaian e al. 2021; La u e
and Le Mouël 2009). This has been a ibu ed o impe ec compe i ion in local
land en al ma ke s (Ki wan and Robe s 2016): i he ma ginal e enue o land
MR changes due o ex e nal p ice shocks, a ms’ WTP changes as well. Bu i he
(5)
p=
MR(0)+MR(x)
2
x+
MR(x)+MR(1)
2
(1−x)=MR −3
4
.
(6)
∫1
0
[p(x)− ]dx =1
4(4MR −3 −4 )>
0,
(7)
∫1
0
|
WTPA−WTPB
|
dx =
2
,
Ren al andsale p ices o ag icul u al lands unde spa ial… Page 7 o 12 32
landowne s’ ese a ion p ice is independen o a plo ’s ma ginal e enue, he
equilib ium en al p ice does no change, and no p ice ansmission om he a m
ou pu ma ke shock o he en al ma ke occu s (G aubne 2018). I , howe e , land-
owne s belie e ha an ex e nal shock o policy may a ec a plo ’s u u e use and i s
e u n he ese a ion p ice does change.4
The esul ing e ec s on he land sales p ices p will depend on whe he all o only
a pa o he a m popula ion bene i s o loses by he ex e nal shock.5 Figu e3 shows
ha when a m B bene i s by a highe ne ma ginal e enue o land, i s WTP shi s
by s o each loca ion.
No ecei ing a highe e u n, a m A’s WTP does no change, bu does al e he
local p ice p(x) i has o pay o ob ain land ( o
x=[

x�
,

x]
) and also inc eases he
a ea whe e a m B has a cos ad an age o e a m A o
1−x�
. The co esponding
Fig. 3 E ec o shocks in he ou pu ma ke on en al and sales p ices
4 The ese a ion p ice e lec s al e na i e uses (oppo uni y cos s) o ag icul u al land, e.g. o es a ion,
subsis ence o hobby ag icul u e, building land o enewable ene gy p oduc ion. In he sho un and
depending on a plo ’s loca ion, some al e na i e uses may be limi ed, and he ese a ion p ice may no
accoun o changes in ex e nal condi ions o a ming (G aubne 2018). In he long un, howe e , land-
owne s may adjus hei ese a ion p ice by inco po a ing go e nmen paymen s, po en ial al e na i e
land designa ions, and he like, in expec a ions o u u e ea nings (Hend icks e al. 2012; Ki wan and
Robe s 2016; Hü el e al. 2016).
5 Fo ins ance, p ice shocks in ce ain ma ke s may a ec a ms di e en ly depending on hei p oduc-
ion po olio. Unde a ming policies, bene i s migh une enly be dis ibu ed among a ms gi en hei
willingness o pa icipa e in such p og ams o i he policy suppo s speci ic loca ion cha ac e is ics, e.g.
pea lands o ca bon seques a ion. Ano he example poses enewable ene gy subsidies, whe e a ms
in es ing in biogas ecei e subsidies o hei ene gy c ops.
M.G aubne , S.Hü el
32 Page 8 o 12
Nash-equilib ium sales p ices
p∗(x)
also causes he a e age obse ed sales p ice
p′
o inc ease bu he di e ence
p�−p<s
due o he asymme ic e ec on local
p ices, i.e. in Fig.3, le o
x′
he p ice e ec is s bu igh o
x
i is ze o.
4 Loca ion speci ic e ec s o al e na i e uses o land
We assume landowne s expec land will be used o u ban o in as uc u al pu -
poses, enewable ene gy p oduc ion, e c., and ha u u e e u ns will exceed ag i-
cul u al e u ns, i.e. he WTP o po en ial buye s and he landowne s’ oppo u-
ni y cos (WTA) inc ease. Figu e4 shows he loca ions o al e na i e uses and
he espec i e sales p ices p(x) in a ea
xR∈[x1,x2]
; hese p ices ypically do no
depend on he dis ance o ei he a m.
Mo e p o i able al e na i e use a some loca ion also inc eases he a e age
obse able sales p ice in he egion, bu he le el o inc ease depends on he di -
e ence in e u ns and he size o
xR
ela i e o he size o he egion. Simila ly,
he en al p ice (x) inc eases in
xR
o
R
acco ding o Eq.4 bu emains a e e-
ywhe e else. The e ec on he a e age en al p ice in he egion hen depends on
he di e ence o
R
−
and, again, he size o
xR
ela i e o he size o he egion.
Fig. 4 Loca ion speci ic e ec s