Rental and sale prices of agricultural lands under spatial competition

Graubner, Marten; Hüttel, Silke Article — Published Version Rental and sale prices of agricultural lands under spatial competition Letters in Spatial and Resource Sciences Provided in Cooperation with: Springer Nature Suggested Citation: Graubner, Marten; Hüttel, Silke (2024) : Rental and sale prices of agricultural lands under spatial competition, Letters in Spatial and Resource Sciences, ISSN 1864-404X, Springer, Berlin, Heidelberg, Vol. 17, Iss. 1, https://doi.org/10.1007/s12076-024-00396-6 This Version is available at: https://hdl.handle.net/10419/318870 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) Letters in Spatial and Resource Sciences (2024) 17:32 https://doi.org/10.1007/s12076-024-00396-6 ORIGINAL PAPER Rental andsale prices ofagricultural lands underspatial competition MartenGraubner1 · SilkeHüttel2 Received: 16 May 2024 / Accepted: 6 November 2024 / Published online: 28 November 2024 © The Author(s) 2024 Abstract Much of the land economics literature has largely ignored the spatial nature of competition and related differences between farmland rental and sales markets when assessing return rates from farming, the capitalization of agricultural, environmental and energy policy into land values, and climate change impacts. We propose a model for price formation in both markets under a spatial competition framework. We demonstrate that price formation differs, particularly under policy-induced output price shocks.We suggest that using the rent-price ratio as an approximation for expectations in the net returns of farming, based on the net present value model, may produce biased results. In consequence, studies relying on land prices need to control for local land competition, farming structure, and policies. Keywords Land markets· Rent-price Ratio· Spatial competition· Policy capitalization· Price formation JEL Classification L13· Q12· Q18 1 Introduction In this note, we investigate the land market from an industrial organization perspective. Land is a scarce resource with declining overall supply, fixed location and other heterogeneous attributes. As a consequence, every transaction is specific, location matters and in a typical constellation a single seller meets several potential buyers. * Marten Graubner [email protected] 1 Institute ofAgricultural andNutritional Sciences, Chair ofFarm Management, Martin-LutherUniversity Halle-Wittenberg, Karl-Freiherr-von-Fritsch-Str. 4, 06120Halle, Germany 2 Department ofAgricultural Economics andRural Development, Agriculture andFood Business Management Group, Georg-August-University Göttingen, Platz der Göttinger Sieben 5, 37073Göttingen, Germany M.Graubner, S.Hüttel 32 Page 2 of 12 In the following, we elaborate the difference between the short-run leasing market and the long-run sales market.1 The spatial aspects of competition and associated distinctions between the rental and sales markets for agricultural lands are as important as location specific characteristics and spatial dependencies (cf. Nickerson etal. 2012). For instance, rents may be the results of less competitive market settings compared to sales markets, since local farms compete primarily in the rental market, while non-local agricultural and non-agricultural investors compete primarily in the sales market. Ignoring the spatial nature of competition may challenge the results given by the net present value model of farmland prices (cf. Deaton and Lawley 2022), i.e. relying on the land-price ratio to approximate the returns from farming (e.g. Borchers etal. 2014; Plogmann etal. 2020; Schaak and Mußhoff 2022). This may for instance explain the noted divergence in policy capitalization rates in rental and sales markets (e.g. Salhofer and Feichtinger 2020; Ciaian etal. 2021 ). Assessments of climate change on agriculture which use Ricardian approaches based on rental rates or land values ignoring spatial aspects of the markets may also give biased results (e.g. Ortiz-Bobea 2020; Bareille and Chakir 2023 ). To demonstrate how changes in marginal revenues may affect equilibrium rental and sales prices, we develop a model for price formation in farmland markets under a spatial competition framework. Unlike existing models of spatial competition under farm policies (Graubner 2018) and approaches attempting to explain the behavioural differences of agricultural and non-agricultural bidders in farmland markets (Curtiss etal. 2021; Seifert etal. 2021; Balmann etal. 2021; Deininger etal. 2023), our model is better able to account for previous empirical findings of the differences in policy capitalization rates on land prices and rental rates, respectively, and the bidding behaviours of owners, buyers and renters. This leads us to propose the following hypothesis: given the spatial nature of competition in rental and sales markets for agricultural lands, compounded rents differ systematically from sales prices, but particularly under an output price shock and alternative future use of land. This note is organized as follows. Section2 describes our theoretical framework, introduces the graphical models of spatial competition in the rental and sales farmland markets as well as our hypothesis. In Sects.3 and 4 we demonstrate the effects of shocks in downstream markets and alternative uses of land on rental and sales prices, respectively. Section5 discusses the results, and Sect.6 concludes with suggestions for future research. 1 While the paper focuses on agricultural land markets, the model and its results can be relevant for markets with similar characteristics, e.g., the forestland, housing, and urban land market in particular or other markets of horizontal product differentiation and the possibility for price discrimination in general. Rental andsale prices ofagricultural lands underspatial… Page 3 of 12 32 2 A spatial competition framework ofland markets 2.1 Land rental market Following Graubner (2018), we assume two farms, A and B, located at the endpoints of a line market with unit length and uniformly distributed land along this segment. Bothfarms operate under distance cost t reflecting their decreasing willingness to pay (WTP) for land with increasing distance to the farmstead.2 Under perfect competition in the agricultural output market, they receive a net marginal revenue from land MR, i.e. the marginal revenue for land net of production costs but the rental price r for land. At each location x=[0, 1] , a landowner supplies one unit of land to the farmland rental market, given the rental price r(x) exceeds the landowner’s reservation price v. Farms can set the rental price for land at each location, i.e. for each individual plot. This decision is influenced by their linear distance costs t and gives: WTPA(x)=MRA−tx and WTPB=MRB−t(1−x) . Depending on their cost and production structure, their net marginal revenue might differ, i.e. MRA≠MRB . We find the location x where A and B have the same willingness to pay for land in the rental market by: Fig. 1 A spatial model of the land rental market 2 Distances depicted in our model do not necessarily measure the distance between farmstead and field but, more broadly, include any reference location relevant for farm operations such as staples or produce magazines as well as the distance to similarly farmed land owned or rented by the same farm. M.Graubner, S.Hüttel 32 Page 4 of 12 With sufficiently low v, the market is covered and A and B can profitably rent land neighbouring the farmstead of their competitor as shown in Fig.1, formally v+t≤min[MRA,MRB] . Given the distance cost, farm A (B) on the left (right) of x has a higher WTP, e.g. if MRA=MRB=MR , x=1∕2 and the maximum WTP for land is WTPA(x1) at location x1 for farm A, but B is only able to pay WTPB(x1) and the landowners’ willingness to accept (WTA) at x1 is v (see Fig.1). Because of the (perfectly) price-inelastic local land supply, uniform pricing is the profit maximizing price strategy for farms (Espinosa 1992; Graubner etal. 2011). Under uniform pricing, a farmer offers the landowner an identical rental price irrespective of the distance from the landowner’s plot to the farmstead as long as it generates (local) surplus to the farm. In a non-cooperative setting, no Nash equilibrium under uniform pricing exists (Schuler and Hobbs 1982; Zhang and Sexton 2001).3 If farms A and B decide their rental prices according to an average of the prices of neighbouring farms (Balmann etal. 2021), spatially-cooperative price matching competition emerges (Gronberg and Meyer 1981; Graubner etal. 2011). In equilibrium, farms set rental prices at the landowners reservation price (Graubner 2018) to capture all of the suppliers’ (landowners’) surplus (Zhang and Sexton 2001). For instance, at location x1 the owner’s surplus is zero because ru =v , but both farms could yield non-zero profits if they offer ru =v and rent that land (see Fig. 1). The potential surplus of farm A is MR −tx1−v and larger compared to farm B: MR −t+tx1−v . Tie-breaking rules determine which farm rents land at location x1 (Gronberg and Meyer 1981; Iozzi 2004). Since both farms offer the same price ru , one could assume that landowners randomly select the tenant, but farmers (e.g. in Eastern Germany) often exchange rented land to round off their farmland area (Margarian 2008). The practice corresponds to the efficient tie-breaking rule (Iozzi 2004), i.e. the farm with the lowest distance costs rents the plot. Hence, farm A obtains the surplus from the plot at x1 . If all land in the market is rented so that no farm owns (at least part of) its operated land, the equilibrium rental price ru =v yields landowners surplus in the market of while the surplus of the farmers is (1) x = MR A −MR B +t 2t . (2) ∫1 0 (ru−v)dx = 0 3 For instance, Farm A could offer rA (see Fig.1) and rent all land left of x1 . Farm B’s maximum WTP at x1 is rB , which facilitates to rent all land right of x1 . Neither price is an optimal response to the competitor’s price though. Farm B is better off with rB = v , which incentives Farm A to lower its price as well and to marginally overbid B. Rental andsale prices ofagricultural lands underspatial… Page 5 of 12 32 with xi=[0, 1] . 2.2 Land sales market Instead of renting land, farmers may prefer buying it due to the transaction costs of negotiating rental contracts, the search costs associated with losing contracts and related risks. Seeking hedges against inflation, storing wealth, stabilizing portfolios, etc., may motivate also non-farmer buyers to acquire farmland. Liquidity reasons or other investment options are incentives for landowners to sell land. The common approach to model land values R is the net present value (NPV) model, which discounts a stream of expected returns over an infinite time horizon (Goodwin etal. 2003); cash rents are an observable option for such returns (Borchers etal. 2014). Accordingly, any rental price r(x) in Fig.1 represents the potential annual returns from owning land. Using the NPV model yields a local sales price: where d is a constant discount factor. Lands immobility, local specificity, spatial distribution and low market liquidity (Bigelow etal. 2020; Kionka etal. 2022) characterize farmland sales markets as a (3) ∫1 0 (max[WTPA(x),WTPB(x)] − v)dx =MR −t 4− v (4) p (x)= ∞ ∑ n=1 r(x) (1+d)n Fig. 2 A spatial model of the land sales market M.Graubner, S.Hüttel 32 Page 6 of 12 static, one-shot game. In this setting, farms have less incentives for collaboration (Espinosa 1992). In terms of local returns, the lowest WTP at any location determines the non-cooperative, Nash-equilibrium sales price p∗(x) (Graubner etal. 2021; Lederer and Hurter 1986; Thisse and Vives 1988). The red lines in Fig.2 show the resulting local land price schedule. Farm A (B) can profitably purchase land left (right) of x . At location x1 the surplus of farm A, pricing marginally above WTPB(x1) , is WTPA(x1)−p∗(x1) and the landowner’s surplus is p∗(x1)−v . Under perfect information, all landowners and potential buyers can observe the local prices. The cost of search and information gathering, however, may be asymmetrically distributed among market participants; sellers and buyers might not be able to acquire all the information about market conditions and specific attributes of the respective land plot (Meissner and Musshoff 2022). For instance, local farmers can be better informed than non-local farmers and other buyers (Seifert etal. 2021). Accordingly, these groups only observe the average sales price p in a region shown as the dotted line in Fig.2 given by: We observe that p increases with increasing marginal revenue from the land but decreases with distance costs. We can make qualitatively similar observations for the farmer’s WTP and thus the equilibrium sales prices, but not for the equilibrium rental prices that are independent of MR or t (2). The landowner surplus in the sales market is where p(x)=min{WTPA(x),WTPB(x)} . The surplus of the farmers is which is always smaller compared to the (discounted) surplus of farms in the rental market (3). In other words, renting is preferable to buying in an atomistic landownership structure and under the assumption that the rental market is less competitive than the sales market. 3 Shocks infarm output markets Many empirical studies identify substantial capitalization of price shocks in farm output markets caused by farming policies or other factors on land rentals. However, capitalization is lower than theoretically expected (Ciaian etal. 2021; Latruffe and Le Mouël 2009). This has been attributed to imperfect competition in local land rental markets (Kirwan and Roberts 2016): if the marginal revenue for land MR changes due to external price shocks, farms’ WTP changes as well. But if the (5) p= MR(0)+MR(x) 2 x+ MR(x)+MR(1) 2 (1−x)=MR −3 4 t . (6) ∫1 0 [p(x)−v]dx =1 4(4MR −3t−4v)> 0, (7) ∫1 0 | WTPA−WTPB | dx = t 2 , Rental andsale prices ofagricultural lands underspatial… Page 7 of 12 32 landowners’ reservation price v is independent of a plot’s marginal revenue, the equilibrium rental price r does not change, and no price transmission from the farm output market shock to the rental market occurs (Graubner 2018). If, however, landowners believe that an external shock or policy may affect a plot’s future use and its return the reservation price does change.4 The resulting effects on the land sales prices p will depend on whether all or only a part of the farm population benefits or loses by the external shock.5 Figure3 shows that when farm B benefits by a higher net marginal revenue of land, its WTP shifts by s for each location. Not receiving a higher return, farm A’s WTP does not change, but does alter the local price p(x) it has to pay to obtain land (for x=[  x� ,  x] ) and also increases the area where farm B has a cost advantage over farm A to 1−x� . The corresponding Fig. 3 Effect of shocks in the output market on rental and sales prices 4 The reservation price reflects alternative uses (opportunity costs) of agricultural land, e.g. forestation, subsistence or hobby agriculture, building land or renewable energy production. In the short run and depending on a plot’s location, some alternative uses may be limited, and the reservation price may not account for changes in external conditions of farming (Graubner 2018). In the long run, however, landowners may adjust their reservation price by incorporating government payments, potential alternative land designations, and the like, in expectations of future earnings (Hendricks etal. 2012; Kirwan and Roberts 2016; Hüttel etal. 2016). 5 For instance, price shocks in certain markets may affect farms differently depending on their production portfolio. Under farming policies, benefits might unevenly be distributed among farms given their willingness to participate in such programs or if the policy supports specific location characteristics, e.g. peatlands for carbon sequestration. Another example poses renewable energy subsidies, where farms investing in biogas receive subsidies for their energy crops. M.Graubner, S.Hüttel 32 Page 8 of 12 Nash-equilibrium sales prices p∗(x) also causes the average observed sales price p′ to increase but the difference p�−p<s due to the asymmetric effect on local prices, i.e. in Fig.3, left of x′ the price effect is s but right of x it is zero. 4 Location specific effects ofalternative uses ofland We assume landowners expect land will be used for urban or infrastructural purposes, renewable energy production, etc., and that future returns will exceed agricultural returns, i.e. the WTP of potential buyers and the landowners’ opportunity cost (WTA) increase. Figure4 shows the locations for alternative uses and the respective sales prices p(x) in area xR∈[x1,x2] ; these prices typically do not depend on the distance to either farm. More profitable alternative use at some location also increases the average observable sales price in the region, but the level of increase depends on the difference in returns and the size of xR relative to the size of the region. Similarly, the rental price r(x) increases in xR to vR according to Eq.4 but remains at v everywhere else. The effect on the average rental price in the region then depends on the difference of vR −v and, again, the size of xR relative to the size of the region. Fig. 4 Location specific effects