Sponsorship’s Financial Sustainability for Cultural Conservation and Enhancement Strategies: An Innovative Model for Sponsees and Sponsors

: The topic of the paper is sponsorship for the requaliﬁcation/conservation of historical-architectural heritage. In the literature, there are many models for evaluating the ﬁnancial efﬁciency of sponsorship from the point of view of the sponsor (mostly in the sports ﬁeld), but none of these jointly support both the sponsor and the sponsee in the selection of ﬁnancially sustainable cultural sponsorships. Trying to reduce this gap, an innovative model is proposed for estimating the proﬁtability of cultural sponsorship. The model consists of three phases. In the ﬁrst, which consists of the ﬁnancial analysis of the investment for the sponsee, the minimum amount that the sponsee can request from the sponsor is established. The second phase analyzes the ﬁnancial performance of potential sponsors, estimating the optimal sponsorship budget that maximizes proﬁts. In the ﬁnal phase, where the results of the two analyses are compared, the sponsee eventually reformulates his offer and decides which company to sign the contract with. The model is tested through a case study: the sponsorship of the restoration of the Don Tullio Fountain in Salerno (Italy). It is assumed that two companies are interested in sponsorship. The results show that the investment is ﬁnancially sustainable for both companies.


Introduction
The increasing focus on corporate social responsibility (CSR) has rekindled corporate interest in the world of culture. The European Commission defines CSR as the mechanism through which companies integrate social, cultural, and environmental issues in their commercial operations and in their interaction with stakeholders [1]. Guided by this principle, many companies are keen to promote their corporate culture through synergies with the arts and culture market. The corporate world meets the cultural world through a variety of actions aimed at protecting and enhancing the historical and artistic heritage. In this way, companies can support the actions and measures of the State and other public bodies in the field of cultural heritage [2]. Collaboration between public administrations and private entrepreneurs about cultural heritage enhancement is now an established practice in several countries and is manifested through various forms of public-private partnership (PPP). According to Klijn and Teisman, PPP is a form of cooperation between public and private actors with a lasting character in which actors develop mutual products and/or services by sharing risks, costs, and benefits [3]. PPPs allow a public work/activity to be built and/or managed with private capital and under the supervision and responsibility of a public body [4][5][6][7]. The use of PPPs allows governments to make complex and financially difficult projects feasible. It is no coincidence that countries with a high level of public debt have recourse to PPPs [8]. Cooperation between the public and private sectors can be achieved through different operational methods, providing opportunities to improve the The purpose of this work is to allow both the sponsor and the sponsee to pursue their financial objectives in the case of sponsorship agreements aimed at enhancing the historical-architectural heritage. The financial objectives of sponsors and sponsee strongly depend on their ability to establish a partnership relationship based on trust and sharing. With this work, we intend to evaluate the financial sustainability of the investment from the point of view of both the sponsor and the sponsee. Financial sustainability is defined as the ability to increase the value of a given organization (public or private) through an optimal combination of sources of financing and invested capital, ensuring a certain continuity of the business [36]. To pursue the objectives of financial sustainability, this work proposes an innovative econometric model that allows both economic actors to maximize the value obtainable from the sponsorship. The main novelties of the study are embedded in the characterization of the model. In the literature, there are many models for evaluating the financial efficiency of sponsorship from the point of view of the sponsor (mostly in the sports field), but none of these jointly support both the sponsor and the sponsee in the selection of financially sustainable cultural sponsorships. Furthermore, the model allows sponsorship players to be able to carry out an ex-ante assessment of the financial sustainability of the investment in a sector, that of the restoration of historical and architectural heritage, which has few operational tools suitable for the purpose.
The model in question is tested through a case study. It is assumed that for a monument located in the city of Salerno (Italy), restoration works are needed to ensure its better preservation. The selected monument is the Don Tullio Fountain located in the Villa Comunale, a few steps from the historical center. Two companies, operating in the same sector, and both interested in signing a sponsorship contract with the municipal administration, are then considered. In the first instance, it is possible to use the model to define the right amount that the municipal administration can request from the private contractor. This amount considers both the design and execution costs of the restoration work and an additional rate proportional to the increase in value that the sponsoring company can obtain from the sponsorship. The latter amount is, therefore, representative of an advertising cost (sponsorship tariff). Therefore, not only the cost of the restoration is considered, but also the advertising return obtained by the sponsor. It is estimated starting from the observation of the main variable that can influence the results of the sponsorships of the architectural heritage: the direct audience. This indicator is expressed as the average monthly number of goers to the location where the monument subject to intervention is located. By goers, we mean both resident citizens and external visitors.
To obtain a considerable level of direct audience and, therefore, a higher sponsorship fee, it was decided that the restoration works of the monument take place in conjunction with the Luci D'Artista event. During this event, Christmas lights of considerable scenic impact are installed in the main streets and squares of the city. Furthermore, ethical issues related to cultural sponsorship are also considered in this way. In fact, it was decided to avoid the direct posting of advertising posters on the scaffolding of the restorations and to integrate the advertising messages with Christmas lights. It is thus possible to promote the name or brand of the company through forms that are totally compatible with the historical-artistic character, appearance, and dignity of the property to be enhanced. The association between the company's brand (and its products) and the image of the monument is indirect and maintains blurred outlines. The distinctive signs and images of the sponsor are not directly attributable to the cultural asset, but the link between the financing company and the restoration work remains known. In this way, the municipal administration promotes a more sustainable intervention method on both a social and cultural level.
For each of the two companies involved, the proposed model makes it possible to estimate the amount to be allocated to sponsorship to maximize profits. In other words, by using econometric formulas, it is possible for the two companies to establish the optimal sponsorship budget. By investing this amount, all other financial variables being equal, the maximum achievable profit is obtained. Each of the companies involved can then decide Sustainability 2021, 13, 9070 5 of 28 whether to sign the sponsorship agreement based on the expected financial returns. The two selected companies, although operating in the same sector, differ considerably in terms of turnover and number of employees. This choice is not accidental, as we are interested in understanding how the sponsorship budget should vary as the company size increases. However, estimating the optimal budget is useful not only for companies, but also for public authorities. This information allows the public body to select as a sponsor of the company that can offer the most funding. Moreover, knowing the amount of money that the sponsor is willing to invest, the sponsee can adjust the sponsorship tariff by offering the company tailor-made advertising solutions. Finally, there is a dialogue phase through which both the sponsor and the sponsee can adjust their requirements to those of their respective counterparts.
The structure of the work is summarized below. In the following section, we analyze the reference literature on sponsorships. Section 3 describes the model, which consists of three phases: financial analysis for the sponsee, financial analysis for the sponsor, and the consultation phase. In Section 4, the model is applied to the case study and the results are presented. Section 5 is devoted to the discussion of the results. Finally, the conclusions follow.

State of Art
This section analyzes the literature on sponsorship, identifying as lines of research of interest for the study those relating to the sponsor-sponsee relationship and to the assessment of the financial sustainability of the investment. The main gaps that emerged from the analysis of the literature are therefore highlighted. Furthermore, it is explained how it is intended to fill these gaps at least partially through the proposed model.

Literature Analysis on the Sponsor-Sponsee Relationship
There are many contributions in the literature on the relationship between sponsor and sponsee, but rarely has this link been studied from a purely financial point of view. Moreover, most research focuses on the effects that sponsorship generates for sponsor, neglecting the sponsee's point of view [37]. Among the exceptions, we highlight the study by Dickenson and Souchon (2019), in which the relationships linking multiple sponsors to a single sponsee are analyzed [38]. In this specific case, multiple sponsors represent an aggregate of social entities perceived as a single whole [39], which, according to social psychology, can be expressed in terms of entitativity [40,41]. However, the study, which shows that the presence of multiple sponsors for an event improves the public's perception of the sponsee, is limited to sports sponsorships. Chavanat and Martinent (2009) analyzed the effects generated by sponsorship in the football sector [42]. The research shows how the link established by a sponsor with multiple sponsees (sporting events, football clubs, individual athletes) can affect the perception of the brand image, brand loyalty, and the intention to purchase products offered by the sponsor. The research carried out by Rajabi et al. (2020), which uses innovative methods to identify the main variables that allow for the mutual adaptation between sponsors and sponsees, also refers to the sports sector [43]. On the other hand, van Rijn et al. (2018) investigate the set of motivations that lead to the end of the partnership relationship [44]. Pappu and Cornwell (2014) analyze the similarities between sponsors and sponsees and extend their research to the cultural and social spheres [45]. In particular, the authors identified the two main variables, similarity and adaptation, which can positively or negatively influence the results of sponsorship. On the other hand, Toscani's (2018) study, which is mainly focused on the artistic-cultural field, analyzes the reciprocity relationship between the sponsor and sponsee [46]. The study shows that shared goals and strong relationships lead to a reduction in the elements of uncertainty and the strengthening of the reciprocity of the relationship. In contrast to most of the publications on the topic of arts and culture sponsorship, in this study, more emphasis is placed on the role of the sponsee. Several strategies are suggested to enable the sponsee to select the right partner. The work of Giannakopoulou and Kaliampakos (2020)  should be noted on the ethical issues arising from the relationship between the sponsors and sponsee in the cultural tourism sector [35]. The authors highlight how cultural heritage is often considered as an ordinary good in sponsorship contracts, following a logic oriented solely to profit. McGuinar (2005) and Urry (1995) share the same opinion, according to whom in sponsorship agreements the goods with a touristic-cultural value are considered as a generic commodity [47,48]. In the modern society devoted to profit, there is a risk that only the cultural heritage capable of generating value for the sponsors and sponsee are preserving.

Literature Analysis on Sponsorship Financial Sustainability Assessment
As far as the study of the purely financial objectives of sponsorship is concerned, there are few examples in the literature, and these refer almost exclusively to the figure of the sponsor. Most of the research conducted, in fact, analyzes the general objectives of the effectiveness of the instrument in terms of marketing and company communication, giving little space to the economic and financial evaluation of the sponsorship investment [49]. One of the exceptions is the study conducted by Olson and Thjømøe (2009), in which the financial return of sponsorship is assessed in comparison with other alternative forms of communication. The research shows empirically that it is possible to convert the exposure time to sponsorship into the equivalent exposure time to television advertising. This conversion allows sponsors to more efficiently evaluate the financial return generated by sponsorship [50]. The analysis of the financial aspects of sponsorship has been addressed in depth by Kourovskaia and Meenaghan (2003). The study defines the tools needed to measure the increase in brand value generated by the sponsorship investment and the value created for shareholders [51]. The financial impact of sponsorship has also been investigated by Nickell and Johnston (2019). Starting from the theory of consumer behavior, the authors built a model that allows for estimating the number of new customers that a sponsorship can generate. In particular, the probability that an individual becomes a future customer of the sponsoring firm is a function of four dependent variables that a sponsorship can influence: awareness, knowledge, liking, and preference of the brand. The mechanism through which sponsorship contributes to customer lifetime value (CLV) is also assessed. Starting from this last parameter and considering the number of new consumers and the overall cost of sponsorship, it is possible to estimate the return on investment (ROI) in the sponsorship [52]. Another interesting work is the one conducted by Blake et al. (2019), in which they evaluate the differences in terms of financial returns between listed South African sports clubs that invest in sponsorship and those that do not. The approach used is quantitative, as the revenues, profits, and share price of the companies surveyed were monitored. The research shows that there were no significant differences in terms of increases in revenues and share prices between the companies involved and those not involved in sponsorship. What does differ, however, are the earnings per share, which are much higher for companies that invest in sponsorship [53].

Limits Emerged from the Literature Analysis
Overall, the analysis of the reading reveals three main limitations of the research conducted to date on sponsorship.
Firstly, most of the studies on sponsorship are of a general nature or focus almost exclusively on the fields of sport and broadcasting. Companies that invest in sports sponsorships can address their messages to a much wider and generalist audience. This allows the sponsors to obtain substantial returns both financially and in terms of image. Cultural sponsorship, on the other hand, plays a marginal role compared to other sectors. It is only recently that we are witnessing a progressive interest of scholars in this field. More specifically, studies about sponsorship for the enhancement of historical and architectural heritage are even rarer. This is probably since this type of sponsorship is not very widespread at the international level. In fact, this peculiar form of cultural sponsorship is almost exclusively diffused in those countries, such as Italy, characterized by a high number of monuments and historical buildings in constant need of restoration and maintenance. Most sponsorship studies focus on the areas that are the most appealing to potential sponsors. The limited interest of companies in sponsoring the historical-architectural heritage is probably due to the lower level of mass emotional involvement that culture can transmit, unlike sports. In this sense, the research conducted by McDaniel (1999) demonstrates how sports sponsorship has a greater impact when a sporting event is associated with a highly emotionally engaging product [54]. High involvement products are defined as products with a high unit value characterized by a high interest in purchasing. On the other hand, the sponsorship of cultural heritage would seem indicated for the formation of favorable attitudes not so much towards a single product, but towards the brand or the company as a whole [16].
Secondly, as mentioned above, scholars mainly investigate the point of view of the sponsor, leaving little room for that of the sponsee. The exceptions in the literature once again refer almost exclusively to the sporting sphere. However, it should be noted that in the cultural field, the sponsor-sponsee relationship plays a central role, since the sponsoring of historical and artistic heritage is characterized by the constant presence of an ethical component in the actions undertaken by the company. The sponsee, therefore, has the delicate task of supervising the work of the sponsor, establishing the operating procedures for the enhancement of the heritage of public interest.
Thirdly, the object of evaluation is often the effectiveness of sponsorship expressed in general terms, i.e., considering several aspects simultaneously in terms of both marketing and corporate communication. In contrast, little attention is paid to the purely financial assessment of the investment. However, in the case of sponsorship in support of historical and architectural heritage, both sponsoring companies and public authorities are primarily interested in the financial aspects during the planning stage.

Contribution of the Work Compared to the Existing Literature
From what has been stated so far, it emerges that it is necessary to define a series of criteria and benchmarks to maximize the returns resulting from sponsorship for both public bodies and private companies [55]. The objective of this work is to overcome, at least partially, the limits found in the field of sponsorship of the architectural heritage, focusing above all on the evaluation of the financial sustainability of the investment. To this end, a model is proposed that includes the following: (i) it allows for evaluating the convenience of the investment specifically as regards cultural heritage restoration sponsorship; (ii) it considers jointly the point of view of the sponsor and the sponsee, also contemplating a phase of dialogue between the two actors; (iii) it analyzes the financial sustainability of the investment while ignoring the effectiveness assessments in terms of communication; (iv) it integrates ethical issues on sponsorship, suggesting forms of promotion compatible with cultural heritage. The proposed model makes it possible to assess whether a specific investment in sponsorship, aimed at enhancing the value of historical and architectural heritage, is financially sustainable for both the sponsor and the sponsee. The objective for the sponsee is to establish the amount to be asked of the sponsor to effectively enhance the heritage being sponsored, improving both its social and cultural value and its relationship with the urban environment. Therefore, we can consider sponsorship in the cultural field as one of the most significant examples of sustainable marketing. The latter has been defined by Charter et al. (2006) as the tool through which a company can offer solutions creating a high sustainable net value and satisfying both customers and other stakeholders [56]. The model assumes that a company that invests in sponsorship, by demonstrating its commitment to socio-culturally sustainable activities, can differentiate itself from other competing companies more effectively and, thus, attract more new customers. The social and cultural improvements resulting from sustainable investments are the added value that customers are willing to pay for by purchasing the products of the socially committed company. Therefore, the investment in sponsorship can result in an increase in turnover and, for the same costs, in profit for the sponsoring company. As a result, the model makes it possible to determine how much the company should spend on sponsorship in the current financial year to maximize profits.

Method
The proposed model consists of three phases:

•
Financial analysis for the sponsee: This consists of establishing the total amount that the public administration can request from the sponsor. This amount should not only consider the cost of designing and carrying out the restoration work, but also include a surcharge that is representative of the counter-value, expressed in terms of the advertising return that the sponsor intends to acquire by signing the sponsorship contract. • Financial analysis for the sponsor: In this phase, the objective is to estimate, through econometric equations, the optimal budget that the sponsor company should invest in the sponsorship to maximize profits. This budget may be higher or lower than the total amount requested by the sponsor. The output of the analysis is expressed in terms of the number of restorations, virtually identical to the one to be financed, that the company should sponsor to obtain the highest possible profit.

•
Consultation phase: A phase in which the sponsor and sponsee talk to reach an agreement. For example, if the sponsor's financial analysis shows that the company is willing to invest more in the sponsorship than the sponsee had originally estimated, the sponsee could reformulate the application for funding asking for a higher amount. Proportionally, the sponsee's counter-performance should also be adjusted to allow the company to obtain a greater return on its image. On the other hand, if the cost of the sponsorship is too high for the sponsor, the public body may decide to reduce the offer of advertising services or to select a new, more likely sponsor.
The three phases of the model are analyzed in detail below.

Financial Analysis for the Sponsee
This phase is linked to Italian legislation on cultural sponsorship. An aspect introduced by the Decree of the Ministry of Cultural Heritage and Activities and Tourism (MIBACT) of 19 December 2012 (Approval of the Technical Standards and Guidelines on Sponsorship of Cultural Heritage and Similar or Related Matters) [57] is considered. This decree governed the provisions contained in Article 199-bis of Legislative Decree No. 163 of 12 April 2006 (old Public Contracts Code) [58], which has now been entirely repealed with the entry into force of Legislative Decree No. 50 of 18 April 2016 (new Public Contracts Code) [59]. Article 199-bis provided that, for works above the threshold value of EUR 40,000, the selection of the sponsor should always take place at the end of a competitive procedure. By virtue of this, the MIBACT Decree of 19 December 2012 governed the way the contracting authority was to define the auction base, i.e., the minimum threshold to be indicated in the public notice of selection of the sponsor. Starting from this threshold, the sponsor candidates could have made their bids upwards. The technical rules stipulated that the basic amount of the selection procedure did not automatically have to coincide with the value of the works, services, and supplies requested, but also had to consider the value of the publicity and image return that the candidate company intended to acquire with its bid. Therefore, in addition to the overall cost of restoring the asset to be enhanced, the minimum threshold had to include a further rate proportional to the monetary and image returns that the company could have obtained from combining its name or brand with the works to be realized. This would have allowed the administration to maximize the benefits, in financial or performance terms, deriving from the sponsorship. Therefore, the offered counter-value had to be estimated based on its plausible attractiveness on the sponsorship market. In this way, it would have avoided both overestimating the overall cost of sponsorship, with the consequent removal of potentially interested companies, and underestimating it by attributing high-value performances to the winner.
With the entry into force of the new Public Contracts Code (Legislative Decree no. 50/2016), which is inspired by a logic of simplification and of not aggravating the administrative procedure for choosing the sponsor, the procedure for selecting the sponsor has been modified. In particular, the awarding of sponsorship contracts for amounts exceeding EUR 40,000 is subject exclusively to the prior publication on the contracting authority's website of a specific notice for at least 30 days. The same publication mechanism is provided for if the public administration receives spontaneous proposals for sponsorship. Once the notice has been published, the contract can be freely negotiated. Therefore, the definition by the contracting authority of the auction base disappears [60]. However, the general rationale for establishing the overall cost of sponsorship would remain valid, although not expressly referred to in the new code. This principle, which allows the public authority to determine whether the offer of a potential sponsor is appropriate or not, was incorporated into the first stage of the model. Formally, therefore, we can consider the following relationship to be valid: where STC is the sponsorship total cost, RC is the restoration cost, and ST is the sponsorship tariff. However, the latter, which for the sponsor company represents an advertising cost, is not immediately determinable. In fact, the value of the services offered by the sponsee can depend on different market conditions, which are extremely changeable. The estimation of the sponsorship tariff cannot follow univocal criteria that are valid for all sponsored restoration work throughout the country. Furthermore, the results of the sponsorship, upon which the fee should be defined proportionally, are generally difficult to measure [61,62]. For this reason, public authorities often prefer to avoid making an economic assessment of the counter-performance they offer. In fact, most of the time, the total cost of the sponsorship is set equal to the cost of the restoration work alone. However, this approach does not allow the sponsee to maximize the funding due to him. It is, therefore, necessary to consider the economic attractiveness of the initiatives or assets to which the sponsor can attach his name or brand. The surplus collected by the sponsee can be used either to improve the way in which restoration work is carried out or for financing future maintenance work on the asset. The approach suggested for estimating sponsorship tariffs consists first in identifying the set of critical variables that can influence the results of the sponsorship and, therefore, the economic and image return due to the sponsoring company [63]. With regard to the sponsorship of historical-architectural heritage, the main critical variables that influence the outcome of the initiative can be grouped into the following three classes: the location characteristics (average number of goers, the relevance of the location, and coverage of the target audience), the monument characteristics (importance of the architect/designer, architectural quality, and relevance of the monument), and the sponsorship characteristics (size of the billboards, media coverage, image congruence between brand and monument, and amount of funding) [64].  showed that these variables do not always produce significant effects in terms of results [65]. For example, in specific cases of sponsoring restoration work, there may be a total absence of media coverage. In general, it was found that in the case of sponsorship of minor monuments-that is, of monuments relevant only to the local community, but with little known on a supra-municipal scalemost of the characteristics of the monument and those of the sponsorship can be neglected. This is because their effects in terms of monetary returns to the sponsor are minimal. The parameter that is most likely to have a significant effect on the financial performance of the sponsor is the average number of goers to the location hosting the monument. In the study mentioned above, several cases of sponsorship of restoration work on monuments with similar characteristics and located in locations with the same degree of attractiveness were analyzed. For these monuments, an almost linear relationship was found between the number of goers (direct audience) and the sponsorship tariffs per square meter. Therefore, for smaller monuments located in locations and cities with similar characteristics and in the total absence of media coverage, the following relationship can be considered valid: where ST is the sponsorship tariff and N is the direct audience. Equation (2) represents the equation of a straight line where a > 0 is the angular coefficient and b > 0 the intercept with the x-axis. To estimate the advertising cost due to the sponsor, it is necessary to make a comparison with similar cases of sponsorship for which the unit tariffs are known.
Once the direct audience has been measured both for the location of interest and for those selected for the comparison, it is possible to estimate the sponsorship tariff (ST) through linear interpolation. Next, the restoration cost (RC) is estimated by drawing up an estimative metric computation, expressed briefly in the following formula: where q i is the quantity of the generic working i and p i is the respective unit price. Finally, adding the sponsorship tariff (ST) to the restoration cost (RC) gives the sponsorship total cost (STC).

Financial Analysis for the Sponsor
The financial performance of the sponsor is assessed through an econometric model. This type of model applied to the field of advertising is strongly supported by the literature [66][67][68][69].
The objective of the second stage of the model is to estimate the optimal budget to be allocated to the sponsorship of the monument to maximize the company's profit. Firstly, we consider a production function of the Cobb-Douglas type [70], with three production factors: capital, labor, and sponsorship. This function follows the version proposed by Romer (1986), used to explain the mechanism of endogenous growth that is attributable to the positive externality produced by the so-called learning by doing. According to Romer, knowledge linked to the accumulation of physical capital would generate economic development by increasing labor productivity [71]. In the case under analysis, however, we assume that it is the investment in intangible capital that leads firms along a growth path. This is because, for the same objective quality, the products of a socially committed firm are more deserving of choice. Companies that invest in sponsorship, therefore, have an additional competitive advantage over others that do not consider this type of investment. Given that in this study we are interested neither in analyzing aggregate economic growth nor in carrying out an analysis of long-term financial profitability for the company (we will therefore neglect the effects of learning by doing), it is possible to introduce the production function defined above as: where R is the revenue, K is the tangible capital stock, L is the labor production factor, and S is the sponsorship intangible capital stock (number of sponsored restorations). The marginal returns of each individual factor of production are decreasing. In particular, α < 0 is the rate of change of the marginal returns of capital, while 1 − α < 0 is the rate of change of the marginal returns of both labor and sponsorship. If we consider only the two factors of production capital (K) and labor (L), the function preserves constant returns to scale. It is the same if we consider only K and S. However, if we consider the three factors of production jointly, we obtain increasing returns to scale. The price is normalized to one, so the revenue coincides with the quantity sold. We define the total profits (π) as follows: where r, w, and s respectively represent the unit costs of the production factor capital, the labor, and the sponsorship, while rK, wL, and sS are the respective total costs. Since s is the cost of a single sponsorship, we can consider the latter equal to the sponsorship total cost estimated in the financial analysis phase for the sponsee: The parameter s therefore represents the link between the first two phases of the model. It is the single sponsorship total cost and includes both the restoration cost and the sponsorship tariff per location. All terms in Equation (4), except α, s, and S, can be easily extrapolated from the company's latest available financial statements. The parameter s is calculated from Equation (6), and therefore from Equation (1), while the production factor S is known a priori, being equal to the number of restoration projects sponsored by the company in the year of analysis (each sponsorship is considered virtually similar in characteristics and unit price to the last one proposed by the sponsee). It remains to define the exponential coefficient α, which can be calculated as follows considering the log-linearity property of the production function: Given all the variables of the problem, let us set the derivative of Equation (4) with respect to S equal to zero (condition of economic optimum with respect to S), remembering that if the marginal profit is zero, the total profit is maximum: By solving Equation (8) with respect to S we obtain the optimal number of restorations to sponsor (S*) to maximize the entrepreneurial profit: Furthermore, knowing S*, it is possible to estimate the optimal sponsorship budget (s*) capable of maximizing the business profit: The s* budget plays a crucial role in the final consultation phase between the sponsor and sponsee.

Concertation Phase
The last step of the model is to compare the optimal budget for the company (s*) with the minimum budget required by the public administration (s). Two different situations can arise, as follows: • If s* > s, the public authority can ask the potential sponsor for higher funding by offering him/her a better advertising counter-performance (e.g., by enlarging the display area to be installed on the scaffolding of the restoration site). • If s* < s, the public authority can scale back its request by offering a smaller advertising counter-performance (e.g., by reducing the exhibition space to be devoted to the sponsor's message). In any case, the cost of the sponsorship cannot be less than the cost necessary to carry out the restoration work. Alternatively, the administration may reject the company's proposal and enter into the sponsorship agreement with another company that can offer more funding.
This phase is therefore characterized by a close dialogue between the sponsor and sponsee aimed at reaching a shared understanding. The partnership will only be successful if satisfactory levels of mutual trust, commitment, effective communication, general satisfaction, and cooperation between the sponsor and sponsee are achieved in this final step [72]. Figure 1 describes the general logic of the model.
the cost necessary to carry out the restoration work. Alternatively, the administration may reject the company's proposal and enter into the sponsorship agreement with another company that can offer more funding.
This phase is therefore characterized by a close dialogue between the sponsor and sponsee aimed at reaching a shared understanding. The partnership will only be successful if satisfactory levels of mutual trust, commitment, effective communication, general satisfaction, and cooperation between the sponsor and sponsee are achieved in this final step [72]. Figure 1 describes the general logic of the model. In the next section, the model is applied to the case study. In addition, the main results obtained are reported.

Application and Results
For the case study, we assume that the Municipal Administration of Salerno (Italy) intends to restore a monument of the city-specifically, the Don Tullio Fountain located in the Villa Comunale (Municipal Villa)-and to look for a sponsor who will finance the work. Suppose, moreover, that the administration has received two sponsorship pro- In the next section, the model is applied to the case study. In addition, the main results obtained are reported.

Application and Results
For the case study, we assume that the Municipal Administration of Salerno (Italy) intends to restore a monument of the city-specifically, the Don Tullio Fountain located in the Villa Comunale (Municipal Villa)-and to look for a sponsor who will finance the work. Suppose, moreover, that the administration has received two sponsorship proposals from two different companies operating in the same region (Campania, Italy). We apply the three stages of the model, first establishing what is the minimum sponsorship total cost (STC) required by the public body. The sponsorship tariff for the Villa Comunale and the restoration cost of the monument are then estimated. Subsequently, the second phase is applied to the two companies, establishing the optimal sponsorship budget for both. Finally, in the consultation phase, judgements are made on the financial viability for the sponsee and the two potential sponsors. The public authority can choose which company to sign the sponsorship contract with, possibly reformulating the amount of funding required. The following section provides the main information about the monument and its location.

Area of Application
The Don Tullio Fountain (see Figure 2) is in Salerno's Villa Comunale. The monument, built in 1790, is in the Baroque style and made entirely of stone. It was installed at the expense of a certain Don Tullio, from whom it takes its name. The fountain was originally located near the Salerno seafront, near the western gate (now disappeared) of the city. Immediately after the unification of Italy, municipal gardens were created around the Don Tullio Fountain, which was rotated towards the city and moved a few dozen meters from its original position. It is now considered one of the most characteristic fountains of ancient Salerno [73]. Although the fountain is not in a bad state, some forms of deterioration due to atmospheric agents and human action are evident.
amount of funding required. The following section provides the main information about the monument and its location.

Area of Application
The Don Tullio Fountain (see Figure 2) is in Salerno's Villa Comunale. The monument, built in 1790, is in the Baroque style and made entirely of stone. It was installed at the expense of a certain Don Tullio, from whom it takes its name. The fountain was originally located near the Salerno seafront, near the western gate (now disappeared) of the city. Immediately after the unification of Italy, municipal gardens were created around the Don Tullio Fountain, which was rotated towards the city and moved a few dozen meters from its original position. It is now considered one of the most characteristic fountains of ancient Salerno [73]. Although the fountain is not in a bad state, some forms of deterioration due to atmospheric agents and human action are evident. As for the location of the monument (see Figure 3), Salerno's Villa Comunale was designed in 1870 at the entrance to the city coming down from Vietri sul Mare. Covering an area of approximately 15,000 m 2 , it is bounded by two main roads: Via Roma and Lungomare Triste. Salerno's Villa Comunale is a favorite spot for citizens, who come here to stroll and play sports in the dense vegetation it contains. The park has a very large catchment area, both local and tourist, given the presence, in the immediate vicinity, of the city's seafront and the city's shopping area.
The Villa Comunale becomes particularly evocative during the renowned Luci D'Artista event. During the Christmas period, some of the city's squares and streets are dressed in lights, which go beyond the usual end-of-year illuminations: they are works conceived by contemporary artists, which stand out for their high scenic value or for strongly symbolic and conceptual values. In particular, the Villa Comunale is home to the "Enchanted Garden", the main attraction of the event that surprises thousands of goers every year [74,75]. It can be deduced that the location has a very high level of attractive- As for the location of the monument (see Figure 3), Salerno's Villa Comunale was designed in 1870 at the entrance to the city coming down from Vietri sul Mare. Covering an area of approximately 15,000 m 2 , it is bounded by two main roads: Via Roma and Lungomare Triste. Salerno's Villa Comunale is a favorite spot for citizens, who come here to stroll and play sports in the dense vegetation it contains. The park has a very large catchment area, both local and tourist, given the presence, in the immediate vicinity, of the city's seafront and the city's shopping area.  In normal practice, public administrations allow sponsors to install posters on scaffolding at restoration sites. The companies acquiring the display space take advantage of the location of the billboard (often in a central or otherwise busy area), as in ordinary advertising space concessions. Sometimes, public administrations may turn to advertise companies, which make a profit by selling the advertising space to third parties. For the case study, it is preferred to avoid the direct posting of advertising billboards on scaffolding. In particular, the sponsor is expected to promote its image during the Luci D'Artista event, integrating the advertising message with the illuminations installed in the Villa Comunale. In doing so, the companies must comply with the design of the light installations. The sponsor becomes a part of the event, reflecting its artistic and cultural The Villa Comunale becomes particularly evocative during the renowned Luci D'Artista event. During the Christmas period, some of the city's squares and streets are dressed in lights, which go beyond the usual end-of-year illuminations: they are works conceived by contemporary artists, which stand out for their high scenic value or for strongly symbolic and conceptual values. In particular, the Villa Comunale is home to the "Enchanted Gar-den", the main attraction of the event that surprises thousands of goers every year [74,75]. It can be deduced that the location has a very high level of attractiveness for a potential sponsor, especially if the sponsorship were to take place during the Christmas season.
In normal practice, public administrations allow sponsors to install posters on scaffolding at restoration sites. The companies acquiring the display space take advantage of the location of the billboard (often in a central or otherwise busy area), as in ordinary advertising space concessions. Sometimes, public administrations may turn to advertise companies, which make a profit by selling the advertising space to third parties. For the case study, it is preferred to avoid the direct posting of advertising billboards on scaffolding. In particular, the sponsor is expected to promote its image during the Luci D'Artista event, integrating the advertising message with the illuminations installed in the Villa Comunale. In doing so, the companies must comply with the design of the light installations. The sponsor becomes a part of the event, reflecting its artistic and cultural needs and, at the same time, effectively promoting its brand. In this way, both parties involved in the sponsorship obtain immediate benefits: the sponsor is guaranteed greater visibility due to the high number of goers, while the sponsee is given the opportunity to increase the sponsorship tariff due to the greater economic and image returns due to the company. Furthermore, the municipal administration can promote a more socially and culturally sustainable form of intervention. In fact, by avoiding the direct posting of advertising posters on scaffolding, it is possible to promote the company's name or brand in a way that is totally compatible with the historical and artistic character, appearance, and decorum of the building to be enhanced. Unfortunately, the ethical questions on how to implement cultural sponsorship are not always sufficiently considered in practice. The awareness of the potential of the exploitation of cultural heritage is one of the main factors that conditions the enhancement of the historical-architectural heritage. On the other hand, this awareness leads us to witness the progressive transformation of monuments into banal supports for advertising. In this sense, the historical-architectural heritage risks undergoing a shift in meaning, from a place where the citizen's identity was built to a customer factory. The image of cultural heritage should be better protected. In theory, public administrations should identify potential sponsors in relation to the characteristics of the monument, verifying the compatibility between the image of the monument and the image of the brand. Numerous examples of sponsorship undertaken in recent years have revealed that not all businesses are suitable for sponsoring cultural heritage. A strong coherence of meaning is required between brands, products offered, and cultural instances to be preserved. In this sense, those companies that operate in sectors close to the cultural or tourism sector would be indicated as potential sponsors (for example, journals, publishing houses, travel agencies, and design studios). Furthermore, it is advisable to avoid advertising individual product lines, as it is well known that the benefits of cultural sponsorship are manifested above all at the corporate level. The entire cultural heritage in a state of deterioration should be preserved, and not just those assets that can guarantee the sponsor a high return of image. The historical-architectural heritage is not always perceived by the public in the same way. Some monumental works are known nationally and internationally, while others have a very high value only for local communities. However, even the so-called "minor monuments" should be preserved in the same way as the more famous ones. For these works, local companies could prove to be excellent sponsors, further strengthening the link with their territory. The sponsee should also consider the ethical issues when selecting sponsorship opportunities. In fact, however, the administrations do not always consider these aspects, often moved by the urgency of safeguarding part of the heritage destined for decay and abandonment [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].
Ethical issues on cultural sponsorship were considered in the application phase of the model. It was decided to opt for a sponsorship method that is more respectful of the historical and cultural value of the monument, associating the sponsor's advertising message with the lights of the Luci D'Artista event. However, the association between sponsoring companies and sponsored monuments remains clear and in the public domain.
The sponsorship method chosen therefore appears further away from traditional advertising and virtually closer to patronage (although in fact, the economic and image return for the sponsor remains). In addition, all sponsors were given the same square meters of exhibition space. In this way, all the monuments have the same chance of being preserved, beyond their deemed desirability in terms of economic return and image.

Results of the Financial Analysis for the Sponsee
To estimate the sponsorship tariff for the Salerno's Villa Comunale, the first step was to measure the monthly goers' average number to the location during the last edition (2019) of the Luci D'Artista event. The monthly data were estimated starting from the daily ones. In fact, the direct audience was measured on two midweek days (Monday and Tuesday) and three coinciding with the weekend (Friday, Saturday, and Sunday). The week in which the measurements of the goers' numbers were carried out was the one from 16 to 22 December 2019. For each day, the revelations were carried out in the two time slots of the highest attendance: morning and afternoon-evening. Each slot consists of four hourly revelations carried out by means of video recordings in the Villa Comunale. Specifically, a video camera was placed on a fixed tripod to frame all the access routes to the location. The number of passers-by was then quantified remotely using freeze-frame technology. For each day, the data obtained for the two-time slots were subsequently extended to 24 h, considering that attendance is generally still high between 19:00 and 24:00 and between 08:30 and 10:30, while it can be considered negligible between 24:00 and 08:30. For the remaining days of the week (Wednesday and Thursday) the number of goers to the location was assumed to be equal to the average number of recorded passers-by on Monday and Tuesday. The results obtained were then averaged to obtain the average goers' number on Monday to Thursday (low-frequency days), the average goers' number on Friday (medium-frequency days), and the average goers' number on Saturday to Sunday (high-frequency days). The daily data were extended to the following three weeks to obtain the monthly goers' average number.
The next step was to identify sponsorships comparable to the one under study. In particular, a selection was made of similar restoration projects for which sponsorship tariffs were known. Similar cases were not found in the city of Salerno, so it was decided to extend the search to the nearby city of Naples. Although the regional capital of Campania is characterized by an undoubtedly higher population than that of Salerno, the comparison between the flow of goers of the locations of the two cities is consistent. This is because, during the Luci D'Artista event, the goers' number to the Salerno's Villa Comunale is of the same order of magnitude as the goers' number to the selected locations in Naples. In the latter city, two locations were identified, each of which has a monument that has been restored through sponsorship [76]. The locations in question are the Naples' Villa Comunale, where the Virgil's Temple is located, and Via Chiaia, where the bridge named after the street is located. The two selected monuments present some similar characteristics to Don Tullio Fountain, such as the fact that they belong to municipalities located in the Campania Region, their limited size (such as to be considered 'minor monuments'), their location in areas excluded from vehicular traffic and near the shopping area, their state of preservation and level of architectural quality, the historical period of their construction not too far away, and the fact that they are not too well-known both among the local population and among tourists. Following the same procedure described for the Salerno's Villa Comunale, the direct audience was measured for the two locations in Naples in the week from 9 to 15 December 2019. As in the case of Salerno, the monthly goers' average number of each location was obtained from the weekly one. The results of the measurement campaigns conducted in Salerno and Naples are shown in Table 1. The Technical Department of the city of Naples has published on its institutional website the main data concerning the sponsorship of the restoration works of the Via Chiaia Bridge and the Virgil's Temple. In particular, the sponsorship total cost, the restoration cost, and the sponsorship tariff for both monuments are reported [77]. An advertising agency won the public call for tenders issued by the Naples municipal authorities and was awarded the sponsorship of the works on both the Via Chiaia Bridge and the Virgil's Temple. The official website of this agency provides further data, such as the surface area of the advertising posters, the display period, and the unit and total resale prices of the display spaces [78]. The latter indicate that the winner of the tender is given the possibility to sell the sponsorship rights to other companies that want to promote their image. It could be considered to allow for the resale of the exhibition space also for the Salerno case study. The data collected on the sponsorship of monuments in Naples are shown in Table 2. In addition, an inspection of the Salerno's Villa Comunale during the Luci D'Artista event made it possible to estimate the surface area of the illuminations. In particular, the illuminations cover a total area of 7% of the surface of the location, i.e., approximately 1000 m 2 . This is the exhibition area available to the sponsor to integrate its distinctive signs into the illuminations. Table 3 shows the sponsorship rate for Salerno's Villa Comunale, estimated from Equation (2). Similarly, applying the same procedure, it was also possible to estimate the resale price of the exhibition space. The restoration cost was estimated by applying (3), i.e., by means of an estimative metric computation. To draw up the latter, it was necessary to carry out an analysis of the deterioration as well as to identify appropriate conservation measures. The restoration cost (RC) was then added to the sponsorship tariff (ST) to obtain the sponsorship total cost (STC), as reported in Table 4. The sponsorship total cost (STC), which for Equation (6) coincides with the sponsorship unit cost (s), was used as a starting point in the financial analysis phase for potential sponsors, the results of which are given below.

Results of the Financial Analysis for Potential Sponsors
As anticipated, the financial analysis phase aims to reveal to the companies interested in sponsorship what the budget to invest in the sector should be to maximize profits. The econometric model illustrated in Section 2.2 is herein applied to two companies operating in the same region (Campania) and in the same product sector (production and sale of wholesale coffee). Both companies, Alpha and Beta, intend to sponsor the restoration of the Don Tullio Fountain in Salerno. Alpha has already made similar investments in the past. It has sponsored three restorations of monuments located in the city of Naples between 2014 and 2016. In contrast, Beta is uninvolved in sponsoring architectural heritage, although it has more media coverage and invests heavily in traditional advertising. The turnover of the latter is about 12 times higher than that of the Alpha company. Most of the data needed for the analysis can be extrapolated from the latest available financial statements for each of the companies (closing date 31 December 2019) [79]. In the financial year under review, both companies did not invest in sponsorship. Therefore, if selected, the two companies would sponsor a single event. We can therefore set S = 1. Consequently, the sponsorship unit cost coincides for both companies with the sponsorship total cost, i.e., s = sS = EUR 171,000. The data necessary for the financial analysis of both companies are shown in Table 5. The constant α is estimated for both companies from Equation (7). For the Alpha company, we obtain: Instead, for Beta company, we have: If we apply Equation (9), we get S ALPHA * = 4.17 for Alpha. The relative optimal sponsorship budget for Equation (10) is s (ALPHA) * = EUR 713,581, while the maximum achievable profit for Equation (5) is π ALPHA * = EUR 1,512,912.
In the next subsection, the optimal budget for each of the two companies is compared with the sponsorship total cost requested by the sponsee.

Results of the Concertation Phase
The last phase of the model, focusing on the dialogue between the sponsee and potential sponsors, is rather delicate as the outcome of the sponsorship may depend on it. The administration must decide with which company to conclude the sponsorship contract, assessing how it can maximize the funding requested. On the other hand, the companies involved are only willing to accept the sponsorship proposal if it allows them to obtain a positive ROI that is higher than that obtainable from other investment opportunities of the same cost. Table 6 shows the results of the financial analysis for the two companies.
To maximize profits, Alpha would have to invest in sponsorship an amount that is about four times higher than that requested by the public administration and equal to 5% of the turnover. As it is advisable for medium-sized companies to allocate a maximum of 10% of their revenues to the marketing budget [80], this implies that for the case under consideration a substantial portion (at least half) of this amount should be allocated to sponsorship. Moreover, the investment would generate a profit increase of about 18%. Again, for every EUR 1 spent, the company would get EUR 38. The investment is certainly worthwhile for Alpha if it were to use the optimal budget, since investing a tolerable amount would generate substantial profits. Similarly, to pursue the goal of profit maximization, the Beta company should invest about 78 times more in sponsorship than the sponsee requires, with an impact on turnover of about 6%. For large companies, the marketing budget should be a maximum of 5% of revenues [81]. Therefore, the optimal investment in sponsorship would exceed, even if only slightly, the maximum threshold to be allocated to marketing and corporate communication in total. As a result, large companies could concentrate on sponsoring large events rather than on other strategies in the marketing mix. Furthermore, the investment would generate a profit increase of about 47%. The ROI of the investment is also high: for each euro invested there is a profit of EUR 284. The investment for Beta would appear to be very cost-effective since it only needs to invest a low percentage of turnover (roughly the same as for Alpha) to obtain profits that are almost halved. Although sponsorship affects the turnover of the two companies in approximately the same way, in absolute terms the optimal budget for Beta is about 19 times higher than for Alpha. On the other hand, the increase in profit is about 139 times greater for Beta than for Alpha. The larger the company, the more funding should be provided to achieve optimal profitability. Sponsoring the restoration of the Don Tullio Fountain would generate such low profits for Beta that it would be considered negligible. On the contrary, the company would be better off sponsoring the restoration of monuments of greater importance (both for the resident population and for tourists) that would have a greater influence on the growth of sales volumes.
Although the investment in sponsorship is convenient for both companies, at a first analysis it seems more appropriate for Alpha. By financing four times the amount requested by the municipality, Alpha would maximize its profits through a financial sacrifice that is not too costly. For Beta, on the other hand, the excellent condition requires a greater effort. The municipality of Salerno's sponsorship offer, as formulated, is not able to meet the requirements of the latter company.
Finally, from the sponsee's point of view, the choice of sponsor may depend on several factors. If the public administration were only willing to sponsor the monument under analysis, it would be better to select Alpha. Since s* > s, the sponsee can ask for a higher amount of funding, equal to the optimal amount for the company. Therefore, the administration should offer a better advertising counter-performance to the sponsor (e.g., by enlarging the exhibition area or guaranteeing media coverage at its own expense). However, the city of Salerno could also be interested in sponsoring other smaller monuments in the same location. In this case, it could always ask for an amount equal to the sponsor's optimal budget, but this time increasing only the amount earmarked for restoration work, since the monuments on which the work is to be carried out have increased. By sponsoring more monuments, Alpha would certainly obtain a greater image return. However, even for Beta, we have s* > s. It would be advisable for the sponsee to select the latter in two situations: if a considerably high number of restorations are planned or if the object of the intervention is a monument of great fame and great historical and cultural importance (national monument). In these two cases, the image return would be sufficient to justify a high expenditure.

Discussion
In the previous section, we established what is the optimal amount for both companies to invest in sponsorship to maximize profits. We now proceed to identify the range of investment acceptability for the two companies. The logic followed is that companies should accept any investment offer capable of generating higher profits than those obtained in the absence of sponsorship.
We have previously established that the optimal investment for Alpha exceeds 4.17 times the one requested by the municipal administration. Applying Equation (5) several times, it is evident how different values of π can be obtained when S varies (as shown in Figure 4). However, only for values of S between 1.5 and 9 are profits higher than those obtained at S = 0, i.e., in the absence of sponsorship. In other words, the Alpha company should invest in sponsorship an amount not lower than EUR 256,500 and not higher than EUR 1,539,000 to generate acceptable profits. In fact, below the first threshold, the incidence on sales of sponsorship is still not very effective, while above the second threshold the investment costs are disproportionate to revenues, although the latter are high. It is observed that the current offer of sponsorship by the municipal administration (S = 1) is below the minimum threshold of acceptability. Alpha should accept the sponsorship proposal only if it is guaranteed a better advertising service through which it can reach a wider public.  This shows that the phase of defining sponsorship expenditure is particularly sensitive for smaller companies. In the day-to-day running of a small company, the entrepreneur often underestimates the importance of planning the marketing budget. However, the correct and careful planning of the company's promotional strategies is necessary to For the Beta company, the optimal investment is 78.22 times higher than the one required by the municipality of Salerno. Applying Equation (5) for different values of S yields the profits π shown in Figure 5. In this case, too, it is possible to define an acceptable range of S. In particular, the minimum acceptable investment threshold is S = 1. This implies that the sponsorship of the restoration of the Don Tullio Fountain generates negligible effects since the profits are approximately equal to those that would be generated in the absence of sponsorship. The revenues generated for S equal to 1 immediately equal the investment costs. From Figure 5 it is evident that the maximum threshold is so high that it is not necessary to define it. Moreover, it is possible to note that the slope of the tangent to the curve is very high in its initial part. In fact, if the company Beta decided to invest the optimal amount for the company Alpha, it would obtain a profit of just over EUR 56 million. However, the curve immediately tends to stabilize, assuming an almost horizontal trend. In this part of the curve, every minimum increase in profit corresponds to a very high cost of sponsorship for the company. The maximum achievable profit, of around EUR 81 million, can be obtained by spending 78 times the minimum amount requested by the sponsee. component that allows you to dynamically check the evolution of financial performance indicators over time following an investment in sponsorship. Beyond this, the benefits that can be pursued over the years by the local community and by the visitors of the monument following the restoration work are of primary importance. These benefits will certainly be the subject of future investigations. Figure 5. Variation in profits π as the sponsorship stock S changes for the Beta company.

Conclusions
The issue of allocating financial resources to support the historical and architectural heritage is highly topical. In the Italian context, the artistic and cultural heritage is not a resource but a cost, since large amounts of funding are needed for its conservation. However, although the maintenance and protection of this heritage has an impact on public spending, there is considerable economic potential that has not yet been adequately exploited [88,89]. This shows that the phase of defining sponsorship expenditure is particularly sensitive for smaller companies. In the day-to-day running of a small company, the entrepreneur often underestimates the importance of planning the marketing budget. However, the correct and careful planning of the company's promotional strategies is necessary to avoid overly expensive campaigns that do not produce the desired results. Ultimately, smaller companies need to pay more attention to sponsorship budgeting, as the risk of poor financial performance is higher. In this sense, the results obtained would seem to be in line with the observations of various researchers, including Bjerke and Hultman, (2002) and Coviello et al. (2000). They agree that marketing in small firms is distinct from marketing in large firms. Overall, small firms make less use of ordinary marketing tools (i.e., socalled managerial marketing) for the following reasons: limited resources (financial and human) and capacities, the absence of formal organizational structures and communication systems, simplified structure of the decision-making process, fewer decision-makers than larger firms, and easier access to customer information [81,82]. In essence, small-and medium-sized enterprises adopt an entrepreneurial rather than managerial marketing model, which, according to Mattiacci and Ceccotti (2003), is reactive (rather than proactive), tactical (rather than strategic), empirical, and intuitive (rather than structured) [83]. In entrepreneurial marketing, the personal dimension of relationships prevails, strengthened by social and territorial mechanisms, and market and brand power are missing [84]. As a result, since this type of marketing is not aimed at the general public, the profit levels obtained are certainly lower than those of larger firms that make use of more efficient managerial marketing techniques. Moreover, it is not obvious that strategies focusing on the entrepreneur-customer relationship are less costly. In fact, small enterprises do not have strong brand awareness and are therefore often forced to use more sophisticated, and therefore expensive, marketing strategies to communicate directly with their target audience. This argument can be extended to sponsorship since our intention here is to evaluate the effects of sponsorship in terms of marketing and not in terms of corporate communication. For example, in the case under consideration, it might be sufficient for Beta to integrate its company logo into the illuminations of the Villa Comunale to be immediately recognized by goers to the location, while Alpha, which is less well-known to the general public, would have to construct a more complex message highlighting the company's social responsibility objectives. This second solution is more expensive. There are, therefore, economies of scale: single sponsorship costs less for companies with high production volumes. The Cobb-Douglas production function used in the model takes this effect into account, making it consistent with reality and in agreement with both business practice and most studies in the literature. In addition, even those positions that differ from the theories outlined above do not contradict what is shown in Figures 4 and 5. This is the case, for example, with Kilenthong et al. (2010), who showed in an empirical study that smaller companies do not make greater use of entrepreneurial marketing than larger ones [85]. This is because small firms generally have a lower growth orientation and market immersion than large firms. According to the authors, this tendency is inherent in the personal preferences of managers. Thus, large firms are large because they want to expand, while small firms are smaller because they want to remain small. Therefore, the latter, not wanting to expand their sales volume, are less likely to invest in entrepreneurial marketing strategies. Furthermore, the marketing of the products of smaller enterprises is strongly influenced by the production techniques employed rather than by market demand. Even if we follow this last line, we can still see that smaller enterprises obtain lower profits from a marketing investment than larger ones. What changes is that in this case, the profits are lower simply because of the choice of the entrepreneur. Moreover, even if small firms were to use managerial marketing in the same way as large firms, the scale effects in terms of costs remain valid. In fact, smaller companies, having a lower level of technology, have higher marketing unit costs.
At this point, it is useful to remember that the results shown in Figures 4 and 5 are also useful information for the sponsee. In fact, they constitute further analysis tools on the basis of which the public administration can select the company with which to sign the sponsorship agreement. In this specific case, if the sponsee does not intend to increase the unit sponsorship cost by much, he should choose Alpha as the sponsor. On the other hand, if the municipality wishes to upgrade additional monuments or make the sponsorship more sustainable in socio-cultural terms, the choice should fall on Beta, since its eligible budget is defined in a wider range.
Finally, it should be emphasized that the research focuses on short-term financial objectives and does not consider the effects on sales (and therefore on profits) that sponsorship could generate considering a longer time horizon. Since this is a static analysis, the results obtained from the model refer only to the financial year in which the investment is made. The goal of this type of models is to define a logical path that directs the choices of the involved actors through streamlined modelling, which is quick to apply and easy to understand for the interested parties [86,87]. Therefore, not considering the long-term benefits of the investment, we are in a sense working to the advantage of safety. Moreover, the long-term effects of sponsorship are much more incisive on the corporate image and reputation than on actual sales. In fact, a previous study shows that ordinarily most of the profits generated by sponsorship occur within the third year, showing a significant increase during the first year [33]. One could therefore think of applying the static analysis in the three years following the sponsorship activity. In addition, the financial analysis phase for the sponsor can be integrated with an econometric component that allows you to dynamically check the evolution of financial performance indicators over time following an investment in sponsorship. Beyond this, the benefits that can be pursued over the years by the local community and by the visitors of the monument following the restoration work are of primary importance. These benefits will certainly be the subject of future investigations.

Conclusions
The issue of allocating financial resources to support the historical and architectural heritage is highly topical. In the Italian context, the artistic and cultural heritage is not a resource but a cost, since large amounts of funding are needed for its conservation. However, although the maintenance and protection of this heritage has an impact on public spending, there is considerable economic potential that has not yet been adequately exploited [88,89].
In this paper, the issue of sponsorship for the restoration of historical-architectural heritage is explored by focusing on the financial sustainability of the investment for both the sponsor and the sponsee. A model is proposed for estimating the profitability of the investment which consists of three phases. The first is the financial analysis of the sponsorship from the point of view of the sponsee. The objective is to establish the minimum amount that the public administration can request from the sponsor. This amount includes both the financial capital necessary for the design and execution of the restoration work and a further rate (sponsorship tariff) proportional to the economic and image return due to the sponsor. The latter fee is defined based on the number of individuals who view the sponsorship message (direct audience). Given this parameter, the sponsorship tariff for a given location, and therefore for a specific monument, can be established if the advertising costs of other locations with similar characteristics to the one being sponsored are known. The second phase analyzes the financial performance of potential sponsors, estimating the optimal sponsorship budget to maximize profits. This amount is defined based on an econometric function. A Cobb-Douglas production function is assumed, introducing as an additional production factor the number of restorations sponsored by the firm. Once the economic optimum condition has been set (first-order condition), it is possible to estimate the amount to be allocated to sponsorship to maximize profits. In the last stage, the concertation phase, the results of the two financial analyses are compared. Depending on their needs, the sponsee can modify the initial request to meet the sponsor's needs. The administration can also establish with which company it is more convenient to sign the sponsorship contract.
The proposed model is tested through a case study. It is assumed that the municipal administration of Salerno intends to seek a sponsor to finance the restoration of the Don Tullio Fountain located in the Villa Comunale. The estimated sponsorship cost (the minimum amount that the sponsee should request) is EUR 171,000. Of this, EUR 60,000 is needed for the restoration work. The remainder (EUR 111,000), representing the sponsorship tariff, is commensurate with the attractiveness of the location. Furthermore, it is assumed that two companies are interested in sponsoring the work. Both companies operate in the same sector, although they differ in size (in terms of both turnover and number of employees). Having estimated the economic performance indicators, it is possible to make a judgement of financial viability for each of the companies. The application shows that, to pursue the objective of profit maximization, the smallest company would have to invest EUR 713,581 in sponsorship (5% of turnover), i.e., 4.17 times the amount requested by the sponsee, resulting in an ROI of 38%. In addition, the company would have to invest no less than EUR 256,500 and no more than EUR 1,539,000 in the sponsorship to obtain higher profits than without the sponsorship. The investment proposed by the city of Salerno of EUR 171,000 is therefore not within the acceptable range. On the other hand, to maximize profit, the largest company would have to invest EUR 13,374,912 (6% of turnover) in the sponsorship, which would be 78.22 times more than the minimum funding required by the city council. The ROI of the investment is 284%. Moreover, for the larger company, the investment proposed by the sponsee coincides with the minimum threshold of acceptability. Therefore, both companies would benefit from investing more than EUR 171,000. For this reason, the municipality could reformulate its initial request. Of course, the advertising compensation offered by the sponsee must be appropriately commensurate with the higher price that the two companies are willing to pay. Furthermore, it should be considered that the larger company might lose interest in the proposed initiative and opt for other sponsorship opportunities that allow it to achieve higher levels of profit.
In the application phase, an attempt was made to also make the sponsorship sustainable on an ethical level, reducing the negative impacts with respect to the socio-cultural dimension. Specifically, it was decided to integrate the sponsor's advertising message to the illuminations that are installed in the Villa Comunale of Salerno for the Luci D'Artista event during the Christmas period. In this way, the direct posting of advertising billboards on scaffolding is avoided, preserving the artistic, cultural, and historical value of the monument. Furthermore, all restoration interventions have equal funding opportunities, from the moment in which all potential sponsors are assigned the same square meters of exhibition space. The overall cost of sponsorship depends solely on the scope of the works and the attractiveness of the location, and not on the alleged attractiveness of the monument on the sponsorship market. Thanks to the Luci D'Artista event, the company's advertising message could have greater visibility and enjoy greater freedom of expression. Close collaboration is therefore envisaged between the marketing managers of the sponsoring company and the artists of the illuminations.
In addition to the specific objectives described above, the model makes it possible to pursue the following general aims: to analyze the dynamics that characterize cultural sponsorship, differentiating it from sports sponsorship; to assess the financial efficiency of sponsorship (increase in profit), offering a different point of view from that of most literature studies, which focus mainly on measuring overall effectiveness (return of image, return in terms of reputation, and impact on brand awareness); and to give greater importance to the role of the sponsee and the sponsor-sponsee interaction. The proposed model allows for us to consider the correct definition of sponsorship objectives in the planning phase, ensuring their alignment and sharing for both economic actors. This contributes to reducing elements of uncertainty and strengthening the reciprocity of the relationship.
Finally, future research directions are highlighted. The first goal is to overcome some limitations imposed by econometric modelling. Production functions other than the Cobb-Douglas type could be used for the model in the financial analysis phase for the sponsor. It should then be checked which of these functions best represents the actual behavior of the sponsor company. Further validation of the model through traditional ex post measurements of the results obtained is also necessary. Another aspect to be considered in the future concerns the definition of the rate of change of the marginal returns of the sponsorship, which in this discussion was set equal to that of the labor factor. By setting up a sensitivity analysis, it could be possible to assess how investment costs and profits change as the exponential coefficient of the production factor S varies. In addition, the other critical variables, which, in addition to the direct audience, can affect the determination of rates (media coverage, the relevance of the monument, size of the billboards, etc.) will be considered. The model could also be used to assess the long-term effects of the investment, always bearing in mind the mechanisms of interaction between sponsee and sponsor.