COVID-19 and Its Effects on Rent Prices for the Hospitality Industry: An Economic Model for the Rebus Sic Stantibus Clause

Abstract

The COVID-19 pandemic made hotels around the world to experience a huge drop in revenues as lockdowns restricted mobility. For many hotel operators, the rent of the building is one of the most important fixed costs. The Rebus Sic Stantibus clause allows judges to rule that changes can be made to the economic conditions of contracts when a supervening event, not foreseen by the parties, causes economic hardship. This paper analyses, considering different market structures and the degree of product differentiation, how the rent for hotel facilities agreed in long-term contracts will change if the clause is applied now, reducing by law current rents.

JEL Classifications: K12, K22, D43, L83

Keywords

oligopolistic competition equilibrium price product differentiation

Introduction

The COVID-19 pandemic has represented the biggest challenge to society since the Second World War. It caused the global GDP to shrink by 4.4%—a yearly fall with no precedent in any prior crisis. Our way of living has been threatened in almost every way, from the unprecedented pressure on public health systems to restrictions on mobility, with traffic at European airports dropping on average by nearly 90%, driving the tourism industry to the worst global crisis it has suffered in a century (Nižetić, 2020). Many of the most important economic analysis organizations have pointed out that one of the major risks for European economies is a liquidity crisis becoming a solvency crisis, increasing the likelihood of bankruptcy to levels not seen in recent economic crises.

Tourism is one of the industries to have been most severely affected by the COVID-19 pandemic. Data from European countries where tourism is highly important as a percentage of GDP show how the loss of economic activity for several months threatens the continuity of a large number of medium-sized and small businesses associated with tourism. One of the key players in the tourism industry is the hotel sector. Solvency and profitability in this sector are highly sensitive to changes in revenues, as fixed costs comprise a large part of their cost structure. These fixed costs include depreciation of fixed assets such as the building, equipment or IT hardware; and financial expenditure mainly associated with mortgages when the hotel operator owns the building, labour costs and the rent of the building (if the hotel operator is not the owner of the building). The fixed costs are the same, whatever the occupancy rate or the price the hotel charges its customers (average daily rate [ADR]). Most hotels in areas where international tourist arrivals significantly exceed national tourism have experienced a drop in revenues of over 70% year-on-year in many cases. This situation represents a threat to the survival of many medium-sized and small hotel companies.

Table 1 shows the occupancy rate evolution—the average values for June, July and August, in hotels for some European countries, according to the tourism database available at EUROSTAT. Occupancy rate experienced a massive drop; in one year, 2020, compared with 2019, the rate went down from 75% to 36% for Spain, from 89% to only 27% on the island of Malta, and from 60% to 42% for Finland. The COVID-19 shock was temporary. Just one year later, most countries showed a positive trend, with countries such as Greece or Finland only 10 points below pre-pandemic levels. Figure 1 shows the occupancy rate trend for some selected countries.

Table 1.

Occupancy Rate Evolution, June to August Average Values, for a Selection of European Countries.

Country	Summer 2018	Summer 2019	Summer 2020	Summer 2121
Greece	70%	69%	30%	60%
Spain	74%	75%	36%	55%
France	70%	70%	49%	55%
Italy	70%	68%	42%	59%
Malta	89%	89%	27%	53%
Portugal	72%	72%	31%	48%
Finland	59%	60%	42%	50%

Source: Author’s elaboration with information from EUROSTAT.

Figure 1.

Source: Author’s elaboration with information from EUROSTAT.

The effect on hotels revenues came not only from lower occupancy rates at the same time but also because hotels reduced their prices and average daily rate to capture a demand that is just a fraction of what it was before the pandemic; as a result, revenues show an unprecedented drop, while at the same time many of the cost remains at similar levels—depreciation and interest payments associated to debt or rents, to cite a few. While hotels belonging to multinational companies such as Marriot or Hilton benefit from the higher capacity these firms and must handle the drop in revenues, small and independent hotels face a risk of bankruptcy, and therefore they can either lower their fixed expenditures or shut down. Although it is now clear that the pandemic shock has been temporary, and many destinations show a trend to recover from previous levels, at the beginning of the pandemic, the huge level of uncertainty combined with some degree of risk aversion made many hotel managers reluctant to borrow money as a solution to avoid a liquidity crisis that may end in the closure of the business.

Rental contracts are based on the general principle of Pacta Sunt Servanda. According to this principle, the two parties of a contract must fulfil the obligations of the contract they have agreed on, regardless of any changes in the circumstances and the risks each party assumes in the contract (Castiñeira Jerez, 2015). When the owner of a real estate property sells the use of those premises to a company that operates a shop, it is common that the buyer of the right to use the premises assumes the risks of demand and supply fluctuations that may affect the selling price, the amount sold or changes in input prices. The flexibility of contracts allows both parties, if they agree on these terms, to share the risks, for instance, by adopting a rent price that is variable based on the shop’s sales; however, in the hotel industry, it is common that the rent price is fixed and not related to the demand factors. The principle of Pacta Sunt Servanda guarantees the stability of the legal contractual system and reduces the uncertainty associated with economic activity (Pillay, 2015).

When there is a change in the conditions that were explicitly or implicitly relevant,¹ when the terms of a given contract were agreed, the application of the Rebus Sic Stantibus doctrine or similar may justify a change in the conditions of the contract, adapting it to the nature of the new situation. For example, a situation like the COVID-19 pandemic and its direct consequences on mobility may imply a sudden change in hotel demand, leading to the application of the Rebus Sic Stantibus doctrine. This reduction in demand and prices would be so huge that, under the current rent terms, it could lead to solvency and profitability difficulties that may end in the hotel operator’s bankruptcy.

Many hotel operators have stated that, in the new scenario, they cannot afford the rent they paid prior to the pandemic, and they have asked for the Rebus Sic Stantibus doctrine to be applied, even in cases where a fixed rent had been agreed. This doctrine allows rent that was previously agreed by parties to be adjusted due to extraordinary circumstances when the economic equilibrium of the transaction has changed significantly. The COVID-19 crisis, with businesses incapable of generating a sufficient stream of income to pay the rent, agreed in contracts, has created a favourable environment for a surge in judicial demands requesting the application of the Rebus Sic Stantibus doctrine (Lasante, 2020), specifically in the context of rental contracts between building owners with hotel facilities and hotel operators (Agredano, 2021). From an economic perspective, understanding how rent may change due to the application of the Rebus Sic Stantibus doctrine is important. Rent prices depend on the future stream of cash-flow that hotel operators can expect from the demand side and on the alternative uses the building owner may consider. This paper will develop a theoretical model to analyse how the average rent will change if judges tend to apply the Rebus Sic Stantibus doctrine. Considering that the optimum strategies for the parties involved in contract negotiations depend on the market structure in which these negotiations take place and ultimately on the individual conditions of the parties, in the short term, the application of the Rebus Sic Stantibus doctrine can contribute to the survival of many small companies by adapting the rent they pay to the new economic scenario, lowering fixed costs and keeping companies operating, which also contributes to less job destruction and increases the resilience of aggregate demand in difficult times. However, the fact that economic agents act according to expectations should not be underestimated, as owners of buildings that can be used as hotels may include the effects of this application of the doctrine in their expected profits, depending on their market power to set prices.

An unexpected event, such as the COVID-19 pandemic, can modify economic agents’ perception of risk and influence decision-making. The pandemic is an extraordinary and unique event with consequence on economic activity, policy decisions and social habits. This paper considers the two firms agreeing on the hotel rent as risk-neutral; future research can explore how extraordinary negative events may change risk perception and the decision-making process of economic agents.

The final impact on the price that a possible adjustment to a contract may have following the application of the Rebus Sic Stantibus doctrine will depend on the market structure. If the owner of a property is in a position that resembles a monopoly, being the sole proprietor offering to rent a building to hotel operators, it can be assumed that the rent will increase as a way of counterbalancing the negative effect application that the Rebus Sic Stantibus doctrine may have on expected profits. The change in price may differ if the owner of the property, who wants to be protected from the risk associated with the general application of the Rebus Sic Stantibus doctrine, operates in an oligopolistic market with companies competing aggressively or even in a more monopolistic competition framework. This article is a first attempt to develop a theoretical model that analyses the optimum pricing strategy from the building owner’s perspective and the risks associated with the general application of the Rebus Sic Stantibus doctrine on the expected level of profits within different market structure frameworks.

The Model

The rent for a building that can be used as a hotel is a direct consequence of the agreement between the owner of the asset and the company managing the hotel. The final price will depend on the market structure. The rent for a hotel in a unique location with a monopoly or near-monopoly would be different from the rent for the building if the hotel competes in an oligopolistic market with other hotels. This section analyses the effect of applying the Rebus Sic Stantibus doctrine in an extraordinary situation in different market structures.

The Effects of Applying the Rebus Sic Stantibus Doctrine When the Owner Has a Monopoly

Let us consider a building in a specific location in which it is not possible to open new hotels due to a privileged geographical situation or, for example, as a consequence of specific regulations forbidding the existence of entrants to the market. The owner of the building can offer the building to different hotel operators interested in running a hotel at this specific location. The willingness to pay will depend on the level of profit the hotel currently generates. In this case, the owner of the building, assuming is the only owner of buildings in a specific location, has price-setting capacity; however, its monopoly power is limited by the existence of substitutes, other locations, for instance, that, although less appealing for tourists, still can allow the hotel operator to generate alternative profitability to the one offered by the building offered by the monopolist.

The model assumes that the reason for the application of the Rebus Sic Stantibus doctrine is a temporary shock. For simplicity, let us assume it last one period, but the model will reach similar conclusions if the shock is temporary and lasts for more than one period. $\emptyset$ represents the percentage of the profits before the event that the hotel keeps if the temporary negative shock takes place. If $\emptyset$ is 0.6, it means that profits have decreased by a 40%. A temporary and unforeseen shock like what has been the COVID-19 pandemic is an event with a low probability; we consider that the probability of such an event is $p$ , and the event can happen at any period as an independent event. If $π$ is the expected profit without temporary shock, the expected value of the profits is:

π p \emptyset + (1 - p) π = π (1 + p \emptyset - p)

(1)

As the temporary shock is an independent event, it may happen again in each consecutive period. Whatever the expected values for the level of profits, we consider that profits grow at a rate g. Appendix A shows the expression for each year’s profits and the net present value of an infinite stream of profits, considering $r$ as the real interest rate. The net present value of the profits for the hotel manager, without considering the rent to be paid to the owner of the building, is as follows:

N P V o f e x p e c t e d p r o f i t s = π \frac{1 + r}{1 + g} \frac{1}{⌊(1 + r) - (1 + g) (1 + \emptyset p - p)⌋}

(2)

To see how an increase in the probability of a negative event decreases the expected value of profits, Figure 2 shows the expected profits for different values of the probability $p$ . As initial values, the numerical simulation considers $π = 100, \emptyset = 0.5, g = 3 % a n d r = 5 %$ .

Figure 2.

Source: Author’s elaboration.

Similarly, Figure 3 shows how an increase in $\emptyset,$ the strength of the temporary negative shock, affects the expected value of profits.

Figure 3.

Source: Author’s elaboration.

The owner of the building, assuming perfect information, knows that the willingness to pay has an upper bound, and the present value of expected profits the hotel manager can achieve is expressed in Equation (2). Assuming that the owner of the building can charge a percentage, $γ, 0 < γ < 1$ , the parameter $γ$ measures the market power of the owner of the building. This value depends on the bargaining capacity of both sides, the owner of the building and the hotel operator, the existence of alternatives buildings in a certain location or nearby that may be alternative options for the hotel manager and the owner alternatives to using the building as an asset in alternative activities. Therefore, the rent both sides will agree on is as follows:

R e n t = R = γ r π \frac{1}{1 + g} \frac{1}{⌊(1 + r) - (1 + g) (1 + \emptyset p - p)⌋}

(3)

One of the economic consequences of the COVID-19 pandemic is that in the hospitality industry, many hotel operators have demanded the application of the Rebus Sic Stantibus doctrine. One option is for the government regulates rent contracts and temporarily limits prices. Alternatively, judges can rule if to apply the doctrine for rent reduction for a concrete period of time. Let’s asume that in this model the negative impact will last one period. As judges can rule in favour of or against the application of the Rebus doctrine, consider that the probability a judge rules in favour of reducing the rent is $α$ . When the judge decides to rule in favour of a rent reduction, judges will normally decide that the owner of the building receive a reduction in the rent paid by the hotel operator, this being a percentage $ψ$ of the rent agreed in the legal contract between the owner of the building and the hotel operator. From the perspective of the hotel operator, if the judges agree to reduce the yearly rent by $ψ R$ , this rent reduction constitutes an increase in yearly profits. As the owner of the building has market power, measured by the parameter $γ$ , it can include this increase in profits expectation in future rent agreements. Appendix B shows the process to find the new rent price.

\begin{array}{l} R = γ \frac{r^{2}}{(1 + r) r - α p ψ {(1 + r)}^{2}} π \frac{1 + r}{1 + g} \frac{1}{(1 + r) - (1 + g) (1 + \emptyset p - p)} \\ R e n t w i t h R e b u s d o c t i r n e = \frac{1}{1 - α p ψ} R e n t w i t h o u t j u d g e d e c i s i o n \end{array}

(4)

The change in the expected rent consequence of the application of the Rebus Sic Stantibus doctrine depends on the value of the probabilities for the unexpected event and the probability of the judge ruling in favour of adjusting the rent ( $p a n d α$ ), the real interest rate $r$ and the percentage of rent reduction $ψ$ .

Proposition 1. The rent price decreases as the probability of a negative extraordinary event $p$ increases and the severity of the negative effect of the extraordinary event, measured by a lower $ϕ$ , increases.

Proof. Appendix C shows that the partial derivative of the rent with respect to the probability of a negative event is negative. If the probability of negative extraordinary events increases, it reduces the expected stream of cash flow the manager hotel can receive, which works as a threshold of the rent. At the same time, the severity of the economic impact of the negative event as measured by $ϕ$ is relevant. The higher the value of $ϕ$ , with $0 \leq \emptyset \leq 1$ , the lesser the reduction of the profits expected consequence of the negative event, therefore a smaller $ϕ$ , meaning a higher economic impact reduces the owner of the building capacity to charge a higher rent.

Proposition 2. If judges rule in favour of applying the Rebus Sic Stantibus doctrine, returning a percentage $ψ$ of the rent to the hotel operator, the rent price increases as the judges’ generosity increases, represented by a higher $Ψ,$ and they rule more often in favour of adjusting the rent, represented by a higher $α$ , and as the probability of the negative outcome $p$ increases.

Proof. Equation (4) expresses the new rent as the new contracts adjust to the application of the Rebus doctrine; from the mathematical expression, the role of each parameter in Proposition 2 can be deduced directly. Figure 4 shows how as the compensation that judges give to hotel operators increases, there is an increase in the annual rent. The numerical simulations consider as initial values 1% probability of a negative event, 30% the probability that judges rule in favour of the hotel and 20% probability of compensation. This percentage is the independent variable, and the vertical axis shows the percentage increase in the rent.

Figure 4.

Source: Author’s elaboration.

Some authors that defend the application of the Rebus Sic Stantibus doctrine argue that thanks to the application of the doctrine, fewer firms shut down, there is a decrease in the number of bankruptcies and, as a consequence, employment destruction is moderated. The previous analysis has not considered how the hotel manager’s lack of liquidity and solvency can imply that the hotel operator stops paying the rent, forcing the owner to find a new tenant. This process implies a cost of searching—a cost that would be higher if the negative impact of the extraordinary event is important, as there is less confidence and therefore less investment, and the total cost will depend on the period of time it takes for a certain economic recovery that facilities to find new tenants. Let us assume that the shock is temporary, and it only takes one year to find a new tenant—an assumption that can be easily changed in the model—and that the cost of searching for a new tenant is $C = β (1 - ϕ) π$ —meaning that the cost of searching for a new tenant is proportional to the expected reduction in profits measured by $(1 - ϕ) π .$

When the owner of the building negotiates a rent, they must consider the effect of the hotel manager, that cannot assume to pay the cancelling the contract, forcing the owner to renounce to the expected profits for the period it takes to negotiate a new contract and the associated cost of searching for a new hotel manager interested in renting the building. The owner of the building may accept lowering the rent in order to avoid the searching cost and the lack of rent for the period (see Appendix D)

R e n t d i s c o u n t = \frac{π (1 + ϕ p - p + β (1 - ϕ)}{{(1 + r)}^{2}}

(5)

Rental Prices in an Oligopolistic Hotel Market with Product Differentiation

The hospitality industry can be characterized as an example of oligopolistic competition with product differentiation (Becerra et al., 2013; Hazledine, 2010; Mazzeo, 2002). Barriers to entry can include high levels of initial investment, the limitation of real estate properties that can be operated as hotels, and increasing regulation and licensing by governments, limiting the number of companies competing in overcrowded destinations. As elements of differentiation, hotels can compete on quality or location (Lee, 2015). Therefore, an analysis of how the rent will change as a consequence of applying the Rebus Sic Stantibus doctrine requires taking a model of oligopolistic competition with product differentiation as a framework.

Let us assume the existence of a duopoly, in which two hotels compete in a specific tourist destination. Although the products have some degree of substitution, we will introduce product differentiation based on the locations of the hotels. Let us assume Hotel 1’s location is where tourists prefer to stay, whereas Hotel 2 is at some distance $d$ from Hotel 1’s location. The parameter $t$ measures the disutility associated with a unit of distance. According to the academic literature, hotel demand depends on the distance to the preferred location by customers (Lee & Jang, 2012, Rigall-I-Torrent et al., 2011); in these papers, hedonic prices are linear to the distance, an assumption captured in demand for the second hotel. Based on these assumptions, the demand functions for Hotels 1 and 2 are, respectively, are as follows:

\begin{array}{l} p_{1} = a - b q_{1} - b q_{2} \\ p_{2} = a - b q_{1} - b q_{2} - t d \end{array}

(9)

Models analysing competition in the hotel industry or in industries in which quality and location are relevant, like in the hotel industry, have considered Cournot competition as a framework for the analysis of firms’ behaviour (Gu et al., 2019, Kawasaki et al., 2019; Nagurney & Li, 2014). This model considers that the two hotels compete à la Cournot, with equal marginal costs $c$ . The Nash equilibrium results in the following profits for the firms:

\begin{array}{l} π_{1} = \frac{1}{b} {(\frac{a - c + t d}{3})}^{2} \\ π_{2} = \frac{1}{b} {(\frac{a - c - 2 t d}{3})}^{2} \end{array}

(10)

The building owner who owns Hotel 1 and rents it to a hotel operator knows that willingness to pay is related to the present value of expected profits. The building owner owning Hotel 1 can charge a higher rent price, as the product is differentiated from the service offered by Hotel 2 in terms of location. The difference in the rent for both leases will depend on $t d$ , as a long distance makes Hotel 1 a more desirable choice, and a higher disutility associated with distance increases the demand function for the hotel located at the preferred location for tourists, increasing the level of profits. To understand the effect a potential pandemic may have on the present value of profits, we assume that each year profits grow for both hotels at a rate $g$ , that the probability of an extraordinary event with a negative impact on profits is $p$ and that the negative extraordinary event implies that companies make a percentage $ϕ$ of profits in normal times. These negative shocks are considered independent events with respect to each other. The rent price the building owner can apply is a percentage $γ$ , which measures the bargaining capacity the owner has to capture the present value of the hotel operator’s profits. $R$ is the yearly rent. The market rent prices for Hotels 1 and 2 would therefore be as follows:

\begin{array}{l} R_{1} = \frac{1}{b} {(\frac{a - c + t d}{3})}^{2} γ r \frac{1}{1 + g} \frac{1}{(1 + r) - (1 + g) (1 + \emptyset p - p)} \\ R_{2} = \frac{1}{b} {(\frac{a - c - 2 t d}{3})}^{2} γ r \frac{1}{1 + g} \frac{1}{(1 + r) - (1 + g) (1 + \emptyset p - p)} \end{array}

(11)

Proposition 3. As the probability of an extraordinary negative event, measured by $p$ , increases, the rent decreases, with a major impact on the hotel located at tourists’ preferred location.

Proof. From Equation (11), $\frac{\partial R_{1}}{\partial p}$ and $\frac{\partial R_{2}}{\partial p}$ are both negative, meaning that as the probability of a negative extraordinary event increases, the present value of the expected level of profits decreases, but as the ratio is $\frac{\frac{\partial R_{1}}{\partial p}}{\frac{\partial R_{2}}{\partial p}} > 1$ , profits at the hotel located at the consumers’ preferred location decrease more than their competitor’s profits.

\frac{\frac{\partial R_{1}}{\partial p}}{\frac{\partial R_{2}}{\partial p}} = \frac{{(a - c + t d)}^{2}}{{(a - c - 2 t d)}^{2}} > 1

(12)

The Effects of Applying the Rebus Sic Stantibus Doctrine in an Oligopolistic Hotel Market with a Growing Supply of Commercial Real Estate

The main limitation of the models analysed thus far is that the building owner renting the hotel building to a hotel operator acted as a monopoly. In this case, the main consequence of applying the Rebus Sic Stantibus doctrine is that the building owner can increase the rent based on their market power to avoid, at least partially, being negatively affected by returning part of the rent to the hotel operator. The building owner’s capacity to set a price will be limited if the model allows for some elasticity in the supply of real estate for the hotel industry. The supply of buildings that can be used as hotels is constrained by several factors—from geographical limitations to a growing set of regulations limiting licenses. Some tourist spots with an important demand have lived a debate between the ones defending the positive effects of tourism and residents complaining about the negative effects of too much tourism in locations such as Paris, Barcelona, Amsterdam or Venice (Farronato & Fradkin, 2018). However, available data suggest that in tourist destinations with increasing demand, supply has increased, with more properties becoming new hotels.

The aim of the model proposed in this section is to capture the effects of a growing supply in real estate for hotels in the context of judges applying the Rebus Sic Stantibus doctrine, ruling a reduction in the rent to be paid by the tenant as a percentage $ψ$ if an extraordinary negative event occurs.

Tourists in a certain destination prefer to stay in a hotel in a specific location, which may be called ‘the centre’. Let us assume there is one hotel, Hotel 1, in this privileged location. Hotel 1 competes with Hotel 2, which is at a distance $d$ from the centre. These hotels compete simultaneously à la Cournot, setting their output levels.

To analyse how greater competition affects rent prices and the effects of applying the Rebus Sic Stantibus doctrine, let us consider now that these hotels decide their output in two periods. In the first period, the two hotels compete, one at the centre and one at a distance $d$ . In the second period, the hotel located at the centre competes with more hotels located at a distance $d$ , assuming that $λ$ is the new number of hotels in the second period. In the second period, there is a probability $p$ of an extraordinary negative event, which may reduce the level of profits by a percentage $ϕ$ .

During the first period, the hotel located at the centre, Hotel 1, competes with a hotel located a certain distance from the centre. $d$ represents the distance to the centre, whereas the parameter $t$ is a measure of the disutility experienced by consumers that buy services from a hotel not located at the best location, Hotel 2. Therefore, the demand for both hotels is the same as in Equation (9).

Let $g$ be the number of hotels at a distance $d$ that enter the market during the second period. The value of $λ$ measures the growth in the supply of real estate that can be used as hotels. As $λ$ increases, the hotel market becomes more competitive, reducing the profitability of the hotel located at the centre and, therefore, the amount the hotel operator is willing to pay in rent. In terms of the cost function, let us assume all the hotels have a marginal cost of $c$ , regardless of their location. Considering that these companies compete à la Cournot, the output, equilibrium price, and level of profits for Hotel 1 in the second period are as follows (see Appendix E):

\begin{array}{l} q_{1} = \frac{a - c + λ t d}{b (λ + 2)} \\ p_{1} = \frac{a + (λ + 1) c + λ t d}{λ + 2} \\ π_{1} = \frac{{(a - c + λ t d)}^{2}}{b {(λ + 2)}^{2}} \end{array}

(15)

Considering that the owner of the hotel can charge a rent that is a percentage $γ$ of the net present value for the profits and that the contract lasts for two periods, the rent is as follows:

R = γ \frac{\frac{{(a - c + t d)}^{2}}{9 b} + \frac{{(a - c + λ t d)}^{2}}{b {(2 + λ)}^{2} {(1 + r)}^{2}}}{\frac{1}{{(1 + r)}^{2}} + \frac{1}{1 + r}}

(16)

Proposition 4. If the distance between the hotel located at the centre and the other hotels is below the threshold $d < \frac{a - c}{2 t}$ , the growth of supply in the hotel industry decreases the rent the building owner can charge to the hotel operator at the centre.

Proposition 4 is important because it highlights the importance of location as a way of differentiation in the hotel industry. When there is enough distance between the hotel located at the centre and the competing hotels at a distance $d$ , when $d > \frac{a - c}{2 t}$ , the hotel at the centre benefits from its exclusive location, and the rent the owner of the building can charge for the building at the centre, therefore, increases. However, if the distance does not reach this threshold, as a consequence of a lower level of differentiation, greater supply in the hotel industry will reduce the rent $\frac{\partial R}{\partial g} < 0$ .

Proof. Equation (16) provides an expression for the rent price. The partial derivative referring to the number of new hotels $g$ competing at a distance $d$ with the hotel at the centre is as follows:

\frac{\partial R}{\partial λ} = γ \frac{\frac{2 (a - c + λ t d)}{b {(1 + r)}^{2} {(2 + λ)}^{2}} (2 t d - a + c)}{\frac{1}{{(1 + r)}^{2}} + \frac{1}{1 + r}}

(17)

This derivative will be positive if:

d > \frac{a - c}{2 t}

Concluding Remarks

The global economic crisis triggered by the COVID-19 pandemic has threatened the survival of many small and medium-sized companies, particularly in the hospitality industry. One of the legal options available to companies facing the burden of fixed costs and shrinking demand is to ask for the application of the Rebus Sic Stantibus doctrine. By reducing the price agreed in the contract, the application of this doctrine can help companies and have positive effects in terms of less employment destruction. However, analysis of the economic consequences of generally applying the Rebus Sic Stantibus doctrine remains a new area of study for scholars in the fields of law and economics.

This article is a first attempt to address the question of how a general application of the Rebus Sic Stantibus doctrine may affect building leasing contract negotiations between a building owner and a hotel operator in the future. The expected increase in price, as the owner knows a future negative extraordinary event may reduce the expected profit stream, depends on the specific market structure and the level of product differentiation.

In a monopoly framework in which building owners can take advantage of their market power to increase the price, this increase will depend on the perceived probability of the extraordinary negative event, the probability of the judges ruling in favour the Rebus doctrine and expectations of the level of the judges’ generosity in protecting the hotel operator. In the hotel industry, operating in oligopolistic markets with product differentiation is common. The model proposed in this paper considers the hotel’s location to be the differentiation variable. Product differentiation plays a key role when market conditions allow for growth in the supply of premises that can be used as hotels. If the distance between a hotel in the consumers’ preferred location and other hotels reaches a minimum threshold, growing supply increases the difference in rent between the hotel at the best location and the rest.

Future research into the economic consequences of a general application of the Rebus Sic Stantibus doctrine could introduce additional variables of differentiation to the analysis, such as the quality of the service provided by hotels (Claver et al., 2006; Fernandez-Barcala et al., 2010).

Appendices

Appendix A. Net Present Value of the Expected Profits for the Hotel Manager.

The profits expression for the first year is as follows:

π p \emptyset + (1 - p) π = π (1 + p \emptyset - p)

In the second year, this value will increase with a growth rate of $g,$ but again, the negative unforeseen shock can happen with a probability $p$ leaving profits to a fraction of just $\emptyset$ the value without the negative shock. Therefore, the expected profits for a year t will be as follows:

E x p e c t e d p r o f i t s y e a r t = π {(1 + g)}^{t - 1} {(1 + \emptyset p - p)}^{t}

The net present value, applying a real interest $r$ , is as follows:

\sum_{t = 1}^{t = \infty} \frac{π {(1 + g)}^{t - 1} {(1 + \emptyset p - p)}^{t}}{{(1 + r)}^{t}} = π \frac{1 + r}{1 + g} \frac{1}{(1 + r) - (1 + g) (1 + \emptyset p - p)}

Appendix B. Rent Value if Judges Rule in Favour of the Rebus Sic Stantibus with Probability $α$ .

Assuming that the temporary negative shock that allows for the application of the Rebus Sic Stantibus doctrine last for one period, the shock is an independent event that can happen each period and the judge can rule in favour of the doctrine with probability $α$ , reducing the rent contract, and therefore increasing the hotel manager profits in $ψ R$ , the expected profits for a giving year $t$ is as follows:

E x p e c t e d p r o f i t s y e a r t = π {(1 - p + ϕ p)}^{t} {(1 + g)}^{t - 1} + α ψ p R

Similarly, in the case in which the owner can charge a percentage of the $γ$ the expected stream of profits, the expression can be written as follows:

\sum_{t = 1}^{t = \infty} \frac{R}{{(1 + r)}^{t}} = γ [\sum_{t = 1}^{t = \infty} \frac{π {(1 + g)}^{t - 1} {(1 + \emptyset p - p)}^{t}}{{(1 + r)}^{t}} + \sum_{t = 1}^{t = \infty} \frac{α p ψ R}{{(1 + r)}^{t}}]

Notice that R, the rent paid by the hotel manager to the owner, is on both sides of the equation. The left-hand side reflects the expected value of the rent. In contrast, the right-hand side expresses the expected value for the hotel manager, which includes the expected profits and the compensation, $ψ R,$ that judges will rule in favor of managers with a probability $α p$ . $ψ R$ can be understood as higher profit for the hotel manager, a consequence of judges being favourable to them, or can be moved to the left-hand side as a reduction on the rent.

Applying some algebra, the expression for the rent is as follows:

\begin{array}{l} R = γ \frac{r^{2}}{(1 + r) r - α p ψ {(1 + r)}^{2}} π \frac{1 + r}{1 + g} \frac{1}{(1 + r) - (1 + g) (1 + \emptyset p - p)} \\ R e n t w i t h R e b u s d o c t i r n e = \frac{r (1 + r)}{(1 + r) r - α p ψ {(1 + r)}^{2}} R e n t w i t h o u t j u d g e d e c i s i o n \end{array}

Appendix C. Proof of Propositions 1 and 2.

Considering Equation (3), the expression for the relevant partial derivatives in terms of proposition 1 are as follows:

\begin{array}{l} \frac{\partial R}{\partial p} = Υ r π \frac{\emptyset - 1}{(1 + r) - (1 + g) (1 + \emptyset p - p} < 0 \\ \frac{\partial R}{\partial \emptyset} = Υ r π \frac{p}{(1 + r) - (1 + g) (1 + \emptyset p - p)} > 0 \end{array}

Appendix D. Discount in the Rent When the Owner Faces the Risk of Contract Cancellation.

If, as a consequence of the liquidity and solvency situation and the drop in profits, the hotel manager is incapable of making the rent payment, they may decide to cancel it, which means that the owner of the hotel faces the opportunity cost of not receiving $π (1 + p \emptyset - p)$ and the additional searching costs $(1 - ϕ) π$ . The maximum yearly discount on the rent must be equal to the cost associated with the contract cancellation.

\begin{array}{l} \sum_{t = 1}^{t = \infty} \frac{R d i s c o u n t}{{(1 + r)}^{t}} = \frac{π [1 + p \emptyset - p + (1 - \emptyset)]}{(1 + r)} \\ R e n t d i s c o u n t = \frac{π (1 + ϕ p - p + β (1 - ϕ)}{{(1 + r)}^{2}} \end{array}

Appendix E. Oligopolistic Model for Hotels When the Supply of Real Estate Can Increase.

Hotel 1 is located in the centre and in the second period competes with $λ$ hotels situated at a distance $d$ from the centre; therefore, the demand for Hotel 1 and the $λ$ hotels is as follows:

\begin{array}{l} p_{1} = a - b q_{1} - b \sum_{I = 2}^{λ + 1} q_{i} \\ p_{i} = a - b q_{1} - b q_{i} - \sum_{j \neq i}^{λ + 1} q_{j} - t d \end{array}

Considering all firms face the same marginal cost, $c$ , and that firms decide simultaneously, the first-order condition (FOC) for firm1 and any other of the firms $i$ located at a distance $d$ of the centre are as follows:

\begin{array}{l} a - 2 b q_{1} - b λ q_{i} - c = 0 \\ a - b q_{1} - (b + λ b) q_{i} - c - t d = 0 \end{array}

Solving for quantities and doing the corresponding substitutions on the demand functions, output, price and profits for Hotel 1—located at the centre—are as follows:

\begin{array}{l} q_{1} = \frac{a - c + λ t d}{b (λ + 2)} \\ p_{1} = \frac{a + (λ + 1) c + λ t d}{λ + 2} \\ π_{1} = \frac{{(a - c + λ t d)}^{2}}{b {(λ + 2)}^{2}} \end{array}

Footnotes

Acknowledgements

Thanks to law Professor Jorge Castiñeira, an Expert in the Rebus Sic Stantibus, for reading the different versions of the paper, for giving his comments and suggestions and for helping the author understand the legal aspects in the application of the Rebus Sic Stantibus.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

Notes

ORCID iD

Juan Pedro Aznar Alarcon

References

Agredano

F. V.

(2021). Rebus sic stantibus and tourist resilience. Journal of Tourism and Heritage Research , 4(2), 148–161.

Becerra

, Santaló

, & Silva

(2013). Being better vs. being different: Differentiation, competition, and pricing strategies in the Spanish hotel industry. Tourism Management , 34, 71–79.

Jerez Castiñeira

(2015). La inexigibilidad de la prestación contractual ante la alteración sobrevenida de las circunstancias [The enforceability of the contractual provision in the event of alteration of occurrence of circumstances]. Doctoral dissertation, Universitat Ramon Llull ].

Claver

, Tari

J. J.

, & Pereira

(2006). Does quality impact on hotel performance? International Journal of Contemporary Hospitality Management , 18(4).

Farronato

, & Fradkin

(2018). The welfare effects of peer entry in the accommodation market: The case of Airbnb (Working Paper No. w24361). National Bureau of Economic Research.

Fernández-Barcala

, González-Díaz

, & Prieto-Rodríguez

(2010). Hotel quality appraisal on the Internet: a market for lemons? Tourism Economics , 16(2), 345–360.

, Sheng

, & Yuen

C. Y.

(2019). Inbound tourism, hospitality business, and market structure. Journal of Hospitality & Tourism Research , 43(8), 1326–1335.

Hazledine

(2010). Oligopoly price discrimination with many prices. Economics Letters , 109(3), 150–153.

Kawasaki

, Ohkawa

, & Okamura

(2019). Inter-group competition through joint marketing efforts and intra-group Cournot competition. Journal of Economics , 128(3), 203–224.

10.

Lasarte

(2020). Incidencias contractuales del coronavirus y cláusula rebus sic stantibus [Contractual incidents of the coronavirus and rebus sic stantibus clause]. Ius et Praxis , (50–51), 81–87.

11.

Lee

S. K.

(2015). Quality differentiation and conditional spatial price competition among hotels. Tourism Management , 46, 114–122.

12.

Lee

S. K.

, & Jang

(2012). Premium or discount in hotel room rates? The dual effects of a central downtown location. Cornell Hospitality Quarterly , 53(2), 165–173.

13.

Mazzeo

M. J.

(2002). Product choice and oligopoly market structure. RAND Journal of Economics , 33, 221–242.

14.

Nagurney

, & Li

(2014). A dynamic network oligopoly model with transportation costs, product differentiation, and quality competition. Computational Economics , 44(2), 201–229.

15.

Nižetić

(2020). Impact of coronavirus (COVID-19) pandemic on air transport mobility, energy, and environment: A case study. International Journal of Energy Research , 44(13), 10953–10961.

16.

Pillay

M. M.

(2015). The impact of pacta sunt servanda in the law of contract [Doctoral dissertation, University of Pretoria].

17.

Rigall-I-Torrent

, Fluvià

, Ballester

, Saló

, Ariza

, & Espinet

J. M.

(2011). The effects of beach characteristics and location with respect to hotel prices. Tourism Management , 32(5), 1150–1158.