Roberto Ezcurra

Belen Iraizoz

Pedro Pascual

Manuel Rapún

Spatial disparities in the European agriculture: A regional analysis

Keywords: Agricultural productivity, regions, European Union. JEL code: Q10, R11, R12

published or not. The documents may come   L'archive ouverte pluridisciplinaire

In light of these circumstances, this paper aims to perform a fairly detailed analysis of the regional distribution of agricultural productivity in the European Union. Our ultimate goal, in doing so, is to draw some kind of inference that might be applied in the design of Community policy within the framework of the recent enlargement of the Union toward Central and Eastern Europe.

The few existing studies of regional disparities at sectoral level in the European context apply the concepts of sigma convergence and beta convergence introduced by Barro andSala-i-Martin (1991, 1992), combining the information provided by various dispersion statistics with the estimation of convergence equations. However, as [START_REF] Quah | Empirical cross-section dynamics in economic growth[END_REF]Quah ( , 1996a,b;,b;1997) has repeatedly pointed out, not only does this approach raise a number of econometric problems, it also fails to capture a series of potentially interesting issues relating to the dynamics of the distribution in question. In particular, this type of analysis provides only a partial view of the observed distribution, since it neglects to consider, for example, the fact that the various regions may shift their relative positions over the study period; thus it completely ignores the possibility of intra-distribution mobility. The standard convergence approach also ignores the fact that a reduction in dispersion in the distribution under consideration may be compatible with a process of polarization into several internally homogeneous regional clusters [START_REF] Esteban | On the Measurement of Polarization[END_REF].

In order to overcome the limitations of conventional convergence analysis, we have opted in this paper to use the non-parametric approach proposed by Quah (1996a,b;1997) to examine the dynamics of a distribution over time. In addition, we have applied a set of techniques adopted from spatial econometrics in order to examine the role played by the spatial dimension in this context. The paper is based on data drawn from the Cambridge Econometrics regional database. Specifically, the agricultural productivity of 194 NUTS-2 regions for the period 1980-2001 has been calculated from data on gross value added at market prices and agricultural employment figures 6 . The data provided by Cambridge Econometrics are based mainly on the information supplied by Eurostat. Eurostat information on the agricultural sector, however, is seriously lacking in some respects, especially when it comes to data relating to the early 1980s [START_REF] Shucksmith | The CAP and the Regions: the Territorial Impact of the Common Agricultural Policy[END_REF].

For this reason, Cambridge Econometrics has opted to complete Eurostat data with alternative national statistics 7 .

The content of the paper is organized as follows. Following on from this introduction, section 2 presents an exploratory analysis of the spatial distribution of productivity in the agricultural sector in the European Union. Section 3 examines the evolution of regional disparities in gross value added per worker per worker in European agriculture between 1980 and 2001. Then, in section 4, we explore the dynamics of the distribution that concerns us, paying particular attention to polarization and regional mobility. This done, and in order to complete the results obtained, in section 5 we investigate the role played by a range of variables in explaining existing territorial imbalances in the European farming sector. We finish by presenting the main conclusions in section 6.

6 NUTS is the French acronym for 'Nomenclature of Territorial Units for Statistics', a hierarchical classification of subnational spatial units established by Eurostat. In this classification, NUTS-0 corresponds to country level and increasing numbers indicate increasing levels of subnational disaggregation. 7 In any event, lack of information for the whole of the time interval considered has obliged us to omit from our analysis the countries newly incorporated into the European Union in May 2004, as well as the former East German Länder and the French Overseas departments. We also decided not to include data for Brussels or Inner London, two regions with practically negligible levels of agricultural sector employment, but which, nevertheless, over time, register major fluctuations in the variable of interest, thus affecting the interpretation of our results.

An exploratory spatial data analysis

We will commence our study by carrying out an analysis of the spatial distribution of agricultural productivity in the European Union at the beginning and at the end of the time interval considered. To do so, and in order to avoid the possible influence of fluctuations in agricultural gross value added, due to climatic factors, for example, we have calculated the average productivity of the various regions between 1980 and 1983, and between 1998 and 2001 (four year averages). As can be observed, Figures 1 and2 both reveal the presence of an apparent spatial non-stationarity in the distribution that concerns us. Indeed the presence of some degree of spatial heterogeneity and spatial dependence in this context is quite evident. Thus, notwithstanding the changes that have taken place over time, the regions with the highest levels of gross value added per worker in the agricultural sector are mainly those of the northern and central areas of the Union, while the lowest values, save for a few exceptions, are to be found in regions situated in the southern periphery. This spatial distribution to some extent matches the pattern of regional specialization. That is, the northern and central regions of Europe tend to be oriented towards animal farming, with a relatively large share of cereal and forage crops. The southern regions, meanwhile, concentrate more on the production of vegetables, especially permanent crops such as (fruits and vegetables, vines and olive groves) horticultural crops [START_REF] Dg Regio | Study on the impact of community agricultural policies on economic and social cohesion[END_REF]. In any event, it is worth mentioning that the pattern depicted in Figures 1 and2 is consistent with the dualized view of European agriculture reported by, among others, [START_REF] Kearney | Rural society -disparities in incomes and alternative policies[END_REF] and [START_REF] Gutierrez | Convergence in US and EU agriculture[END_REF]. This initial analysis, therefore, suggests that agricultural productivity is not ran- domly distributed across the European space. By contrast, there appears to be positive spatial association between adjacent areas, in so far as neighboring regions tend to register similar levels of gross value added per worker in the agricultural sector. It is necessary to exercise caution when interpreting the information supplied by Figures 1 and2, however, because any conclusion drawn from them will be highly sensitive to the number of intervals selected to represent the variable in question. It is therefore advisable to complete these initial results with the information obtained by means of Exploratory Spatial Data Analysis techniques [START_REF] Anselin | Exploratory spatial data analysis in a geocomputational environment[END_REF]. This will allow us to gain a deeper understanding of the characteristics of the distribution under consideration, and check for the possible presence of different patterns of spatial association and spatial heterogeneity [START_REF] Haining | Spatial data analysis in the social and environmental sciences[END_REF][START_REF] Bailey | Interactive Spatial Data Analysis[END_REF].

[INSERT FIGURE 1 AROUND HERE] [INSERT FIGURE 2 AROUND HERE]

Following this approach, we began by checking formally for the presence of spatial autocorrelation in the regional distribution of productivity in agricultural sector in the European Union. In this respect, it is worth mentioning that spatial autocorrelation can be defined as the coincidence of value similarity with locational similarity [START_REF] Anselin | Spatial Econometrics[END_REF]. In order to study this issue, we calculated for each year of the study period the Moran's I global test, which can be written as follows (Cliff andOrd, 1973, 1981;[START_REF] Haining | Spatial data analysis in the social and environmental sciences[END_REF]: As can be seen from ( 1), before performing this test, it is first necessary to construct a spatial weight matrix to capture the strength of spatial interdependence between each pair of regions i and j. To do so, a first option is to use the concept of first order contiguity, according to which w ij = 1 if regions i and j are physically adjacent and 0 otherwise8 . However, the use of this type of matrix may raise problems in the European context, where the presence of islands means that W will include rows and columns containing only zeros. This implies that the observations in question are not considered in the analysis, which in turn has an effect on the interpretation of the results obtained.

I = n n i=1 n j=1 w ij (y i -y)(y j -y) S 0 n i=1 (y i -y) 2 (1)
For this reason, in this paper we opted to use a spatial weight matrix that takes into account interactions beyond adjacent regions. In particular, following the proposal made by Le [START_REF] Gallo | Exploratory spatial data analysis of the distribution of regional per capita GDP in Europe, 1980-1995[END_REF], we have considered a row-standardized matrix W based on the ten nearest neighbors, calculated using the geographical distance between the corresponding regional centroids [START_REF] Pace | Quick computation of spatial autoregressive estimators[END_REF][START_REF] Pinkse | Contracting in space: an application of spatial statistics to discrete-choice models[END_REF] checked, the values of the statistic are in all cases positive and statistically significant with p = 0.0001. This reveals the presence of a clear pattern of positive spatial association, which in turn supports the first impression drawn from observation of Figures 1 and2 and supports the decision to apply spatial econometric techniques in this context 10 . We are able to conclude, therefore, that, within the European Union, spatially adjacent regions tend to be characterized by similar levels of agricultural productivity 11 . This is only to be expected, bearing in mind that physically adjacent regions tend to be similar in climate and geography and also, therefore, in their agricultural production structure. It must not be overlooked, however, that efficiency in resource use varies across different agricultural activities, giving rise to productivity disparities among regions with different patterns of specialization [START_REF] Helfand | Farm size and the determinants of productive efficiency in the Brazilian Center-West[END_REF]. Likewise, the existence of spatial autocorrelation would also be consistent with the results obtained for several geographical settings in a series of studies that highlight the presence of important R&D spillover effects in the agricultural sector [START_REF] Johnson | R&D Spillovers to Agriculture Measurement and Application[END_REF][START_REF] Schimmelpfenning | The internationalization of farm technology: patents, R&D spillovers, and their effects on productivity in the European Union and United States[END_REF][START_REF] Mccunn | Convergence in U.S. Productivity Growth for Agriculture: Implications of Interstate Research Spillovers for Funding Agricultural Research[END_REF]. In any event, it is worth noting that Table 1 suggests that spatial factors have decreased in importance in the European setting over the course of the twenty-two years considered in our study. 10 In fact, this result would be of particular importance if, following the approach adopted by [START_REF] Paci | More similar and less equal: Economic growth in the European regions[END_REF], [START_REF] Colino | Patrones estructurales y convergencia interregional en la agricultura europea[END_REF] or [START_REF] Gil | Structural change, infrastructure and convergence in the regions of the European Union[END_REF], the aim of the analysis were to examine regional disparities in European agriculture through the estimation of convergence equations. Indeed, the information supplied by Table 1 raises serious doubts as to the consistency, unbiasedness and/or efficiency of estimations obtained without taking into account the existence of spatial dependence. A more detailed analysis of this issue can be found in [START_REF] Anselin | Spatial Econometrics: Methods and Models[END_REF].

11 To further confirm this finding, we also constructed the Moran's scatterplots for the distribution under analysis. This is a graph on which the standardized values of the variable to be analyzed are plotted on the horizontal axis and the spatial lag of the same variable on the vertical axis. Thus each of the quadrants represents a different type of spatial association. According to Figures A1 andA2 which appear in the Appendix there is a noticeable concentration of regions in quadrants I and III, both at the beginning and end of the study period, thus confirming a predominating tendency in European agriculture toward spatial clustering involving regions with similar values of farm productivity, while there are relatively few cases of major disparity between the agricultural productivity of any given region and the average of its neighbors. It is important to keep in mind, however, that Moran's I is calculated on a global basis for the entire sample. Hence, we do not know whether, irrespective of the overall dependence pattern, there exist clusters of regions in which the concentration of high or low agricultural productivity levels is significantly greater than would be predicted in a spatially homogeneous distribution. In addition, it is not possible with these tests to detect the existence of groups of regions with dissimilar values of the study variable, that is, areas in which gross value added per worker in the agricultural sector is significantly lower or higher than in the adjacent areas. To overcome both these shortcomings, we calculated the local Moran's I, I i , by means of the following expression [START_REF] Anselin | Local indicators of spatial association-LISA[END_REF]:

I i = n(y i -y) n i=1 (y i -y) 2 j∈J i w ij (y j -y) (2)
where J i denotes the set of neighboring regions of i 12 . After standardization, a significant positive (negative) value of I i will indicate clustering around region i of regions with similar (dissimilar) values of the study variable.

It is worth mentioning that the usual practice in the case of I i is to assume a normal asymptotic distribution. [START_REF] Anselin | Local indicators of spatial association-LISA[END_REF], however, has shown that the first and second order moments used in the standardization of the statistic I i are obtained under the null hypothesis of no global spatial autocorrelation. For this reason, and following the proposal of this author, in this paper we calculated the pseudo-significance levels obtained by means of an empirical distribution derived from 10,000 random permutations.

n i=1 I i S 0 , given that n i=1 Ii = n n i=1 n j=1 w ij (y i -y)(y j -y) n i=1 (y i -y) 2
. to be statistically significant. Nevertheless, it must be borne in mind that at the end of the study period there emerge two new regional clusters. The first of these is made up of various Swedish regions with high agricultural productivity surrounded by other regions with high values of the study variable, while the second cluster is formed by the whole of Greece, grouping in this case regions with a lower level of gross value added per worker in the farm sector than those adjacent to them.

[INSERT FIGURE 3 AROUND HERE] [INSERT FIGURE 4 AROUND HERE] F o r P e e r R e v i e

w

It is also worth mentioning the fact that the various regional clusters detected in the above analysis are comprised mainly by regions with similar levels of agricultural productivity. In any event, it is interesting to observe the slight increase that has taken place in the number of regions with significant and negative values of the local Moran's I statistic during the period 1980-2001. However, it must be borne in mind that, of the ten regions that in 1980-2001 presented a value of the variable of interest that was significantly distinct from that of their neighbors, only Luxembourg and Auvergne remain in the same situation at the end of the study period.

3 Regional disparities in the European agriculture

Following this preliminary analysis of the spatial distribution of the variable of interest, we continue our study by examining the evolution of regional disparities in gross value added per worker in the European Union agricultural sector. To this end, we consider the information supplied by the two dispersion measures commonly used to capture the concept of sigma convergence (Barro andSala-i-Martin, 1991, 1992): the standard deviation of the logs (SDlog) and the coefficient of variation (CV ) 13 .

First of all, it should be noted that the magnitude of the territorial imbalances observed in European agriculture is considerable greater than in the secondary and tertiary sectors (Table 2) 14 . In any case, as Figure 5 shows, inequality in the regional distribution of agricultural productivity within the European setting registered few relevant changes 13 Dalgaard and Vastrup (2001) have demonstrated that the joint use of the standard deviation of the logs and the coefficient of variation does not prove redundant in this setting, since these two dispersion statistics could yield different conclusions.

14 A similar result is found by [START_REF] Paci | More similar and less equal: Economic growth in the European regions[END_REF] in a more limited geographical and temporal setting than that covered in the present study. Indeed, similar conclusions have been reached in national analyses. For the Spanish case, see, for example, [START_REF] Mas | Disparidades regionales y convergencia en las Comunidades Autónomas[END_REF], [START_REF] Raymond | Las disparidades en el PIB per cápita y la hipótesis de convergencia[END_REF] or [START_REF] Salinas-Jiménez | Technological change, efficiency gains and capital accu-32 Page 33 of[END_REF]. between 1980 and 2001. In fact, the variation in the values of SDlog and CV did not exceed 2 per cent during the whole of the twenty-two years contemplated. However, the degree of dispersion in the distribution that concerns us did not remain constant throughout that period. In fact, it is possible to identify three distinct stages, each with its own distinguishing features. Thus, during the eighties there was an increase in inequality, reaching its maximum level in 1990. However, in the early 1990s it is possible to detect a process of productivity convergence in European regional agriculture. This situation changes in 1997, when inequality again starts to increase.

[INSERT TABLE 2 AROUND HERE] [INSERT FIGURE 5 AROUND HERE]

When assessing the implications of these findings, it is important to bear in mind that there exist various possible explanations for the lack of convergence in gross value added per worker in European agriculture throughout the entire period of analysis. Thus, it should be remembered that, in spite of the major structural reform that has taken place in the farm sector over the last few decades, agricultural productivity continues to be closely linked to the natural setting and climatic conditions of the various regions. This, in turn, helps to account for the heterogeneity of farming systems and the differences in their remunerative capacity, which constitute a considerable hindrance when it comes to reducing regional inequality over time [START_REF] Jollivet | L´Europe et ses campagnes[END_REF][START_REF] Limouzin | Les agricultures de l'Union Européenne[END_REF].

Having reached this point, we might naturally ask how much impact the Common Agricultural Policy (CAP) has had on regional disparities in European agriculture. Such an analysis is far from easy, however (Shucksmith, Thomson and Roberts,2005), mainly due to the lack of available data for the level of territorial disaggregation and the time horizon considered in our study. Despite this limitation, however, it is worth pointing out that during the 1980s the European agricultural support system was fundamentally based on the implementation of agricultural support prices which are regulated by various common market organizations [START_REF] Fennell | The Common Agricultural Policy: Continuity and Change[END_REF]Ackrill, 2000). In fact, in 1985, the budget of the European Agricultural Guidance and Guarantee Fund (EAGGF) stood at 19,843.4 million Ecus, which was 71 per cent of the total EU budget. That same year, the highest level of support went to dairy products, which took up 30 per cent of EAGGF expenditure, followed by beef production (14 per cent), cereals (12 per cent), sugar (9 per cent) and oil-seed crops (6 per cent). The production of all of these products takes place mainly in the northern and central regions of the Union, in countries such as France, Germany, the Netherlands, the United Kingdom and Denmark. The Mediterranean produce of the southern regions, such as fruits, horticultural products, wine and olive oil, meanwhile, jointly received only 14 per cent of EAGGF expenditure(Commission of the European Communities, 1988). Thus, prices in the northern and central regions of the Union, which specialize in the most heavily subsidized products, have been higher than they would have been without such intervention, and their levels of gross value added and productivity have benefited as a result. Thus,it could be argued that the CAP may have contributed to agricultural productivity disparities among the European regions, in so much as Community intervention has tended to benefit the more productive areas of the Union, to the detriment of regions with lower values of this variable.

Since the CAP reform of 1992, support for agriculture has taken the form of direct farm payments. In theory, these payments are intended to be neutral in distributive terms, since they are meant as compensation for loss of income resulting from the drop in intervention prices resulting from the reform. In 1996, with the reform complete, the EAGGF budget stood at 39,107.8 million Ecus, which was 49 per cent of the overall budget of the EU. The highest amounts that year went to herbaceous crops (cereals, rice, oil-seed and protein crops, which absorbed 42 per cent of EAGGF spending; sugar (4 per cent); dairy products (9 per cent); and beef (17 per cent). Together, these continental products concentrated 73 per cent of EAGGF spending. Mediterranean products (fruits, horticultural products, wine and olive oil), meanwhile, received 11 per cent (European Commission, 1998). These figures are a reflection of how the imbalance in CAP aid for these two groups of products has deepened over the years. The related empirical evidence presented by [START_REF] Shucksmith | The CAP and the Regions: the Territorial Impact of the Common Agricultural Policy[END_REF] shows that CAP aid is spatially concentrated in the central and northern regions of the EU. Indeed, by the end of our period of analysis, the CAP could be said to be having an even more negative effect on agricultural productivity in the European regions than it was during the 1980s.

In their assessment, [START_REF] Altomonte | Economics and Policies of an Enlarged Europe[END_REF] insist once more on the unfairness of the CAP at the farm level, since, in the year 2000, 50 per cent of the direct payments went to 5 per cent of the farms.

Leaving all other considerations aside, however, these remarks are still to be taken with a degree of caution. It is important to bear in mind that these figures do not allow us to establish a direct relationship between the evolution of the CAP over time and the trend in regional disparities in European agriculture as shown in Figure 5.

It should not be overlooked, moreover, that the evolutionary pattern of agricultural productivity is ultimately a consequence of changes in gross value added and/or employment in the different regions. Following the approach adopted by several authors within the framework of the literature on territorial imbalances in per capita income, to explore the role of each of these variables in the evolution of regional disparities in European agriculture, a first option is to characterize the spatial distribution of gross value added and employment by applying some concentration measure [START_REF] Villaverde | Regional convergence, polarisation and mobility in the European Union[END_REF]. For obvious reasons, however, it is risky to relate the results of an analysis of this nature to the evolution of regional disparities in gross value added per worker in the agricultural sector. For a better understanding of this idea, let us consider a hypothetical situation in which two regions, each with a very different level of gross value added, exchange their respective employment levels. In such a context, none of the concentration measures proposed in the literature will register any variation over time, despite the obvious fact that changes in the spatial distribution of employment have an effect on observed inequality.

To overcome this problem, therefore, we perform an alternative analysis, in which we estimate the degree of dispersion in two virtual distributions. In the first, regional gross value added is kept constant at the level for the start of the period and only employment levels are allowed to vary. On the contrary, in the second virtual distribution employment is kept constant and only regional gross value added is allowed to vary over time. The results of this exercise are reported in Figure 6, where it can be checked that dispersion in the first virtual distribution remained practically constant throughout the period 1980 to 2001, while in the second it can be seen to increase. This shows that changes in the distribution of employment prevented an increase in regional disparities in the agricultural sector during the twenty-two years considered. Specifically, the empirical evidence provided in this respect suggests that the higher growth in gross value added registered by the regions located at the upper end of the distribution has in turn been offset by a greater loss of employment in regions with low agricultural productivity levels in 1977. This conclusion is in fact consistent with the findings of [START_REF] Paci | More similar and less equal: Economic growth in the European regions[END_REF] or [START_REF] Gil | Structural change, infrastructure and convergence in the regions of the European Union[END_REF] with respect to the process of structural change that has taken place in the European Union over the last few decades.

[ INSERT FIGURE 6 AROUND HERE] 4 The dynamics of the regional distribution of productivity in the agricultural sector

In the section above we examined regional disparities in gross value added per worker in European agriculture. It is obvious, however, that the various dispersion measures calculated so far do not give a precise picture of the regional distribution of agricultural productivity in the European context (Quah, 1996a,b;1997). For this reason, we will now estimate the density functions of the distribution analyzed. Following common practice in the literature, we will use non-parametric estimation techniques, thus avoiding the need to specify any particular functional form beforehand. This kind of approach undoubtedly offers major advantages in the present context, given the lack of generality and flexibility associated with parametric approximations.

Figure 7 shows the density functions of the regional distribution of gross value added per worker in the European agricultural sector estimated for various years of the study period. As is usual in the literature, in order to facilitate comparisons, normalized productivity levels are plotted on the horizontal axis (sample average equal to 100), while the associated density estimates are plotted on the vertical axis15 . According to Figure 7, the unimodality of the distribution analyzed is a constant throughout the time interval examined. Nevertheless, the results reveal certain differences in the shape of the estimated density during the twenty-two years considered, allowing us to conclude that the initial situation did not remain stable during the period. Thus, the density concentrated around the average increased between 1980-1983 and 1998-2001, largely due to weight loss at both ends of the distribution over the nineties. It is important to note that these results allow us to complete the findings obtained earlier in relation to the evolution of regional inequality in agricultural productivity throughout the study period.

[INSERT FIGURE 7 AROUND HERE]

There is a major limitation to the non-parametric approach used in this section so far, however, since it does not permit us to obtain a precise quantification of the variations in the degree of polarization that have taken place over time. To address this problem, we applied the methodology proposed by [START_REF] Esteban | On the Measurement of Polarization[END_REF], along with the extension by [START_REF] Esteban | Extension of a Measure of Polarization with an application to the income distributions of five OECD countries[END_REF].

According to [START_REF] Esteban | On the Measurement of Polarization[END_REF], it is possible to measure the degree of polarization of a distribution f partitioned into a number of groups exogenously determined by means of the following expression: where, for the purposes of the present study, µ j and p j denote, respectively, the average level of productivity in the agricultural sector and the population share of group j.

P ER (f, α, ρ) = m j=1 m k=1 p 1+α j p k |µ j -µ k | (
Likewise, α ∈ [1, 1.6] is a parameter that captures the degree of sensitivity of P ER to polarization. Nevertheless, before applying this measure, it is necessary to define a simplified representation of the original distribution in a series of exhaustive and mutually exclusive groups, ρ = (z 0 , z 1 , . . . , z m , µ 1 , . . . , µ m , p 1 , , . . . , p m ), the boundaries of which are given by intervals of the form [z j-1 , z j ], for j = 1, . . . , m. This will involve some degree of error, however, as this grouping will generate some loss of information, depending on the degree of dispersion within each of the groups considered. Taking into account this idea, the measure of generalized polarization proposed by Esteban, Gradín and Ray (1999) is obtained after correcting the P ER index applied to the simplified representation of the original distribution with a measure of the grouping error, ε(f, ρ).

It is important to bear in mind, meanwhile, that there are no unanimous criteria for establishing the precise demarcation between the various groups. To address this problem, Esteban, Gradín and Ray (1999) use the methodology proposed by [START_REF] Aghevli | Optimal Grouping of Income Distribution Data[END_REF] and [START_REF] Davies | Optimal Grouping of Income and Wealth 28 Page 29 of 47[END_REF] in order to find the optimal partition of the original distribution, ρ * . This means selecting the partition that minimizes the Gini index value attributable to within-group inequality, G (f ) -G (ρ * )16 . The measure of generalized polarization proposed by Esteban, Gradín and Ray (1999), therefore, is given by:

P EGR (f, α, ρ * , β) = P ER (f, α, ρ * ) -β [G (f ) -G (ρ * )] (4)
where β ≥ 0 is a parameter that informs about the weight assigned to the error term in We proceeded by applying this methodology to the study of the evolution of polarization in the regional distribution of agricultural productivity in the European Union for the two-group case (bipolarization). In order to check the robustness of the results of our analysis, we consider different values of the parameter of sensitivity to polarization.

Specifically, α = 1, 1.3, 1.6. Likewise, as in Esteban, Gradín and Ray (1999), β = 1 in all cases.

As shown in Figure 8, the results obtained reveal a reduction in generalized bipolarization over the period analyzed, which was particularly intense between 1985 and 1995.

Indeed, the value of P EGR decreased by between 12 and 22 per cent, depending on the degree of sensitivity to polarization considered in each case 17 .

[INSERT FIGURE 8 AROUND HERE]

Nevertheless, expression (4) highlights the fact that the evolution of P EGR depends on two factors: the polarization observed in the simplified representation of the original distribution and the degree of internal dispersion within each of the various groups. Figure 9, therefore, provides additional information regarding these two components of the generalized polarization measure. Thus, it is possible to observe a decrease in bipolarization in the simplified representation during the time interval considered. Specifically, the value of P ER fell by 4 per cent for the various levels of sensitivity to polarization considered in the analysis. With respect to the evolution of the error term, Figure 9 17 The optimal partitioning for the two-group case is characterized by the fact that the productivity level that separates the two groups coincides with the sample average. By adopting this criterion for the classification of the various regions considered, it is possible to explain an average of 71 per cent of total inequality, measured in terms of the Gini index. Thus, the within-group inequality left unexplained by this partition is about 29 per cent.

[INSERT FIGURE 9 AROUND HERE]

The analysis carried out so far is based exclusively on the information obtained from a series of cross-sectional observations of the distribution under study. Therefore, it does not take into account that, over time, the different economies may modify their relative positions in terms of agricultural gross value added per worker (see [START_REF] Mora | Role of mobility in evolution of disparities: European regions evidence[END_REF] or [START_REF] Ezcurra | Regional mobility in the European Union[END_REF] for further details about the importance of this issue). To address this shortcoming and to complete the results obtained so far, we examined the degree of mobility in the regional distribution of agricultural productivity within the European Union during the period 1980-2001.

Most of the studies that have addressed this issue are based on the information provided by discrete transition matrices, obtained by dividing the distribution into a series of exhaustive and mutually exclusive classes18 . This approach entails a problem, however, since the results it yields are sensitive to the discretization used to define the various classes [START_REF] Bulli | Distribution dynamics and cross-country convergence: a new approach[END_REF][START_REF] Kremer | Searching for prosperity[END_REF]. To address this problem, Quah (1996a[START_REF] Quah | Empirics for Growth and Distribution: Stratification, Polarization and Convergence Clubs[END_REF] classes, reducing their size infinitesimally (see [START_REF] Durlauf | The new empirics of economic growth[END_REF] for a formal definition). The stochastic kernel can be reached by estimating the density function of the distribution over a given period, t + k, conditioned on the values corresponding to a previous period, t. In other words, the joint density function at moments t and t + k is estimated and then divided by the implicit marginal distribution in order to obtain the corresponding conditional probabilities.

Figure 10 shows the stochastic kernel and the corresponding contour-plot estimated for five-year transitions [START_REF] Fingleton | Explaining the distribution of manufacturing 29 Page 30 of 47[END_REF] 19 . The three-dimensional graph shows how the cross-sectional distribution at t evolves into that observed at t + 5. In fact, the stochastic kernel gives us the probability distribution of agricultural productivity at t + 5 for a region with a given value at t. Thus, if the probability mass is concentrated around the main diagonal, the intra-distribution dynamics are characterized by a high level of persistence in the relative positions of the regions over time and, therefore, low mobility. If, on the other hand, the density is located mainly on the diagonal opposite the main diagonal, this would indicate a switching of the relative positions of the regions situated at each end of the distribution. Finally, the probability mass could, in theory, accumulate parallel to the t axis. This would reflect the convergence of regional gross value added per worker in the agricultural sector throughout the study period around a certain value of productivity. In order to aid interpretation of the graph, Figure 10 also includes contour plots on which the lines connect points at the same height on the three-dimensional kernel.

[INSERT FIGURE 10 AROUND HERE]

19 Gaussian kernel functions were used in all cases, while the smoothing parameter was selected following Silverman (1986, p. 86). As can be observed, Figure 10 reveals that the probability mass is basically concentrated around the main diagonal. This illustrates the limited degree of mobility in the regional distribution of gross value added per worker in the agricultural sector over the study period. The European regions, therefore, tended on the whole to maintain their relative positions in this context over the twenty-two years contemplated. The bumps in the tails of the distribution shown in Figure 10 are worth noting, however, since they help to reveal the role played by the regions situated at the upper and lower ends of the distribution in explaining the above-mentioned reduction in polarization during the sample period20 .

We then estimated the corresponding ergodic distribution by iteration of the stochastic kernel to reach the convergence of the process [START_REF] Johnson | A nonparametric analysis of income convergence across the US[END_REF]. Given that this is, by definition, a continuous distribution, it can be represented graphically (Figure 11).

As shown, the ergodic distribution obtained is characterized by a single local maximum located around the sample average, which is, in turn, consistent with the information yielded by the density functions estimated in Figure 7 for various years of the period 1980-200121 . This indicates that the existing territorial imbalances in European agriculture will persist into the future. Nevertheless, it is interesting to note that there is no evidence to suggest that the long term outcome might be a fragmentation of the distribution under study into various separate groups of regions. In order to complete the results obtained so far, in this section we will examine the role played by a series of variables in the dynamics of the regional distribution of gross value added per worker in the European agricultural sector. We will tackle this issue using a series of instruments proposed by Quah (1996a[START_REF] Quah | Empirics for Growth and Distribution: Stratification, Polarization and Convergence Clubs[END_REF] and already presented in the preceding pages. These will enable us to obtain a fairly accurate assessment of how far the distribution varies when factors relating to issues other than agricultural productivity are introduced into the analysis.

Ever since the pioneer work by [START_REF] Molle | Regional Disparity and Economic Development in the Euroepan Community[END_REF], authors dealing with spatial disparities in per capita income or aggregate productivity within the European setting have placed repeated emphasis on the importance of country-specific factors in regional growth processes (Quah, 1996c;[START_REF] Rodríguez-Pose | Convergence or Divergence? Types of Regional Responses to Socio-economic Change in Western Europe[END_REF]Ezcurra et al., 2005). It will be of interest, therefore, to explore the role played by the national component in the evolution of the regional distribution of gross value added per worker in European agriculture throughout the period considered. With this idea in mind, we constructed a conditioned distribution by normalizing each region's agricultural productivity according to the average in the rest of the country to which it belongs, excluding the region in question.

Leaving aside any political and administrative factors, we also considered the possible influence on the regional distribution of agricultural productivity of variables such as investment per worker in agriculture, regional per capita income, or the role of industries directly related with farming activity22 . For our purposes, we classified the various regions by deciles, taking as reference the average values of the different variables over the whole of the sample period. We then constructed three more conditioned distributions, this time normalizing each region's agricultural gross value added per worker according to the average agricultural productivity level of those regions in the same decile.

The various conditioned distributions just defined can be intuitively interpreted as that part of the original distribution that remains unexplained by the set of variables considered. For a better understanding of this idea, let us imagine a situation in which the "country effect" had no influence whatsoever on the evolution of the distribution under analysis, such that regions with a below (above) the sample average agricultural gross value added per worker would also be less (more) productive than the rest of the regions in the country to which they belong. In this hypothetical situation, the original distribution would coincide with the conditioned distribution. If, on the other hand, the national component were to play a relevant role, it would be reasonable to expect that productivity in the less (more) productive regions to be closer to the average of the group to which they belong, defined, this time, from a political-administrative point of view.

To overcome the problems involved in using discrete transition matrices in this context, we have opted in this paper to employ a non-parametric approach based on the estimation of stochastic kernels and contour plots23 . Before going on to discuss the outcomes obtained, it might be worth clarifying a few points relating to the interpretation Figures 12, 13, 14 and 15 present the results obtained when this methodology is used to examine the role of the country to which a region belongs, investment in the agricultural sector, regional per capita income, and the size of the agrifood sector, in explaining the dynamics of the regional distribution of gross value added per worker in the European agriculture. The empirical evidence provided by the various graphs clearly shows that, unlike the rest of the variables analyzed, the national component and investment per worker in agriculture play an important role in this context. Thus, the analysis carried out reveals considerable differences between the regional distribution Close observation of the graphs in Figure 12, however, allow us to qualify this finding, at least in part. The "country effect" does indeed appear to be more significant among regions with low or medium values of the variable analyzed. At the same time, however, the probability mass at the upper end of the distribution appears to be approaching the main diagonal. This suggests that agricultural productivity is closer to the national average in regions where gross value added per worker in agriculture is relatively low.

Figure 13, meanwhile, highlights the predominant role played by agricultural investment in this context. Unlike the national component, however, this variable proves more relevant in regions located at the upper end of the distribution that concerns us, given that, generally speaking, agricultural productivity in these regions tends to be on a par with that of other regions making a similar level of investment in the sector.

Conclusions

Throughout the preceding pages, we have examined territorial imbalances in European agriculture between 1980 and 2001. In order to overcome the limitations of conventional convergence analysis, in this paper we have combined the non-parametric approach proposed by Quah (1996a,b;1997) with a set of techniques adopted from spatial econometrics.

The results obtained show the presence of positive spatial dependence in agricultural productivity. This reveals that, with a few specific exceptions, spatially adjacent regions in the European setting register similar values of the variable analyzed, which contributes to highlight the relevance of geographical location in this context. In particular, we have detected the existence of several clusters of regions with levels of gross value added per The level of spatial dispersion in agricultural productivity is also found to have remained practically constant between 1980 and 2001. This is due to the fact that the higher growth in gross value added registered by the regions at the upper end of the distribution was offset by a greater loss of employment in the less productive regions.

At the same time, the various density functions estimated show that the probability mass concentrated around the sample average increased over the course of the twentytwo years considered, largely due to loss of weight at both ends of the distribution that concerns us. As a consequence, regional bipolarization decreased during the time interval considered, irrespective of the value adopted in the analysis by the parameter of sensitivity to polarization.

We also examined the level of mobility in the distribution under study. The results obtained in this respect suggest a low degree of intra-distribution mobility. Therefore, save for a few exceptions, the European regions tend to have maintained their relative positions in terms of agricultural productivity between 1980 and 2001.

Finally, we explored the role played in the dynamics of the regional distribution of gross value added per worker in the sector considered by variables such as the country to which a region belongs, investment per worker in agriculture, regional per capita income, or the impact of industries directly related to agricultural activity. The empirical evidence provided in this respect reveals the importance in this context of the national Notes: Inference is based on the permutation approach with 10,000 permutations [START_REF] Anselin | Local indicators of spatial association-LISA[END_REF]. All statistics calculated are significant at p = 0.0001.

2

  The regional distribution of agricultural productivity:

w

  y i denotes the agricultural productivity in region i, while y is the sample average. Likewise, w ij denotes the corresponding element of the spatial weight matrix, W , with ij = S 0 . As far as interpretation is concerned, it should be noted that after standardization, a significant and positive value of Moran's I will indicate the presence of positive spatial autocorrelation, while a significant and negative value of the statistic will indicate the existence of a pattern of spatial association between dissimilar values.

  Figures3 and 4show the significant regional clusterings detected at the beginning

  degree of internal cohesion in both groups decreased, since the value of ε increased by 8 per cent throughout the twenty-two years contemplated. In any event, this evolution of the error term contributes to explain the reduction in generalized bipolarization observed between 1980 and 2001, since the level of bipolarization predicted in the simplified representation of the original distribution worsens in absolute terms.

  suggests substituting the transition matrix with a stochastic kernel to reflect the probabilities of transition between a hypothetically infinite number of

[5

  Determinants of the dynamics of the regional distribution of agricultural productivity

  and contour plots in this context. Within this framework, these instruments provide information concerning the probabilities of transition between the initial distribution and the conditioned distribution, and not between two moments of time as in the previous case. Thus, if the factors considered do not contribute to explain the distribution dynamics, the probability mass should cluster around the main diagonal. If, on the other hand, the variables selected are determinant in explaining the evolution of the distribution analyzed, the density will tend to accumulate parallel to the axis corresponding to the initial distribution and around the average.[INSERT FIGURE 12 AROUND HERE] [INSERT FIGURE 13 AROUND HERE] [INSERT FIGURE 14 AROUND HERE][INSERT FIGURE 15 AROUND HERE]

  in any member State and in the European Union as a whole.

  similar to each other but different from those of adjacent zones. These clusters are not randomly distributed across the whole of Europe, however. They are in fact located in specific areas of the North, Centre and South of the European Union. It should not be overlooked, in relation to this, that agricultural productivity is closely linked to the natural setting and climatic conditions of the various regions.

  in agriculture. The analysis carried out shows, in particular, that agricultural productivity appears to be closer to the national average in regions with relatively low levels of the variable under study. Investment in agriculture, meanwhile, is more relevant at the upper end of the distribution, where regions with matching levels of investment in the agricultural sector also tend to share similar productivity levels. productivity growth and convergence: an application to Spanish regions", Applied Economics 35, pp. 1839-1851.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Spatial distribution of agricultural productivity, 1980-1983 (four year averages).

Figure 4 :Figure 6 :

 46 Figure 4: Spatial distribution of local Moran's I, 1998-2001 (four year averages).

Figure 7 :Figure 8 :

 78 Figure 7: Density functions of the regional distribution of agricultural productivity.

Figure 9 :Figure 10 :

 910 Figure 9: Bipolarization of the simplified representation and internal dispersion.

Figure 11 :Figure 12 :

 1112 Figure11: Ergodic distribution of regional agricultural productivity.

Figure 13 :Figure 14 :

 1314 Figure13: Investment per worker in the sector and the dynamics of the regional distribution of agricultural productivity.

Figure 15 :

 15 Figure15: The agrifood industry and the dynamics of the regional distribution of agricultural productivity.

Figure A3 :Figure A4 :

 A3A4 Figure A3: Significance of local Moran's I test, 1980-1983 (four year averages).

  9 .

	F o r
	P
	e
	e r
	R e v
	i e
	w
	Table 1 displays the results of the Moran's I global test of agricultural productiv-
	ity for the 194 European regions of the sample over the 1980-2001 period. As can be

Table 1 :

 1 Moran's I statistics for the regional distribution of agricultural productivity.

	Year	Moran's I	Mean	Standard deviation Standardized value
	1980	0.4628	-0.0050	0.0290	16.1085
	1981	0.5462	-0.0050	0.0290	19.0294
	1982	0.5758	-0.0050	0.0289	20.1274
	1983	0.5740	-0.0050	0.0290	19.9376
	1984	0.5760	-0.0050	0.0289	20.1043
	1985	0.5563	-0.0050	0.0292	19.2484
	1986	0.5781	-0.0050	0.0287	20.3454
	1987	0.5833	-0.0050	0.0290	20.2974
	1988	0.5469	-0.0050	0.0290	19.0557
	1989	0.5203	-0.0050	0.0289	18.1998
	1990	0.4596	-0.0050	0.0288	16.1091
	1991	0.4180	-0.0050	0.0289	14.6513
	1992	0.5029	-0.0050	0.0289	17.5649
	1993	0.5076	-0.0050	0.0289	17.7592
	1994	0.5034	-0.0050	0.0287	17.6949
	1995	0.5223	-0.0050	0.0287	18.3618
	1996	0.4800	-0.0050	0.0286	16.9641
	1997	0.4401	-0.0050	0.0288	15.4520
	1998	0.4153	-0.0050	0.0287	14.6361
	1999	0.4112	-0.0050	0.0287	14.4754
	2000	0.4161	-0.0050	0.0289	14.5588
	2001	0.3671	-0.0050	0.0289	12.8605

Table 2 :

 2 Regional disparities in the various sectors.

	Sector	SDlog	CV
	Agriculture 0.5403	0.4619
	Industry	0.3796	0.4290
	Services	0.2987	0.2846
	Total	0.3281	0.3005
	Note: Average for the period 1980-2001.

This is in fact the option taken, for example, by[START_REF] López-Bazo | Regional Economic Dynamics and Convergence in the European Union[END_REF] or[START_REF] Rey | US Regional Income Convergence: A Spatial Econometric Perspective[END_REF].

In order to check the robustness of the conclusions obtained, we considered various spatial weight matrices. In particular, we constructed two more matrices W based on the fifteen and twenty nearest neighbours. Nevertheless, the results are in all cases very similar to those reported in the text.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

All estimates were based on Gaussian kernel functions, while the smoothing parameter was determined in each case followingSilverman (1986, p. 47). It is worth mentioning that the results obtained are robust to the kernel function used.

Note that in this case there is no overlapping between the various groups, since the decomposition of the Gini index into between-group and within-group inequality is exact[START_REF] Pyatt | On the interpretation and disaggregation of Gini coefficient[END_REF].

For example, for the European case[START_REF] López-Bazo | Regional Economic Dynamics and Convergence in the European Union[END_REF] and Le[START_REF] Gallo | Space-time analysis of GDP disparities among European regions: A Markov chain approach[END_REF] estimate various transition matrices to analyze regional mobility in terms of per capita income and aggregate productivity.

Though estimations were repeated for different transition periods, the results in all cases proved very similar to those just discussed. They are not reported here for lack of space, but are available from the authors upon request.

Having reached this point, however, it should be noted that any comparison of Figures 7 and 11 must be based exclusively on the shape of the distributions, since there is no point in comparing the density levels that appear on the vertical axes.

This last variable was proxied by the contribution to regional gross value added made by the food, beverages and tobacco industry (sectoral classification NACE-CLIO R17). It should be noted in this respect that, despite our best efforts, we were unable to obtain data at a higher level of sectoral disaggregation to cover the entire geographical and temporal scope of the present study.

 23 This type of methodology has been used, for example, byEzcurra, Gil and Pascual (2005) to investigate the causes of regional disparities in welfare in the European Union.

Q1 -Agriculture < Q -Agricultural and Natural Resource Economics, R12 -Size and Spatial Distributions of Regional Economic Activity < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics, R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Hasret Benar
email: hasretbenar@hotmail.com

Ph D Candidate

Glenn P Jenkins
email: jenkins@qed.econ.queensu.ca

The Economics of Casino Taxation

Keywords: Casino, taxation, gambling, tourism, economic benefit JEL Codes: H21, H32, H27

In this paper, a model of the costs of a casino is developed that focuses on the implications for economic welfare of different taxation schemes for casinos. The situation being considered is in a country where casinos cater exclusively to foreign tourists. The goal of the country is to determine the maximum amount of taxes that can be extracted from the activities of this sector under different systems of taxation. When the price of gambling is set by regulation above its competitive level, the economic losses created by excessive investment in the sector can be reduced by taxation. A turnover tax on the amount gambled can maximize both tax revenue and the economic welfare of the country. Due administrative constraints, a number of countries rely on the taxation of the casinos' fixed assets or a combination of a turnover tax and a tax on fixed costs. The model is applied to the situation in North Cyprus. The annual economic efficiency loss from its poorly designed tax policies on casino gambling is estimated to be about 0.5 percent of GDP.

I. Introduction

Casinos have had a long history as a source of entertainment, excitement and heartbreak. Because of the incidence of the compulsive gambling and associated crime, most states have tried to regulate the spread of casinos and in some instances have tried to control who is allowed to gamble in the casinos. Taxation has often been one of the tools used for the regulation of this sector.

While casinos have been a feature of entertainment in well-known holiday centers such as Las Vegas, Monaco and Macau for decades, since the 1980's casinos have spread rapidly elsewhere. In some countries, such as Canada and Chile, they have been used as a source of revenue for financing municipal and charitable activities. In particular, a rapid expansion of the casino industry has taken place in those countries where they are a part of the entertainment package used to attract tourists. Many of the Caribbean Islands such as Bahamas, Puerto Rico, Belize and the Dominican Republic are using casinos in this way. In the Mediterranean region, Northern Cyprus has built a substantial casino sector to complement their other tourist facilities. Many of the clients are weekend tourists, who come from nearby Turkey and South Cyprus. These are places where casinos are not allowed to operate.

There is a considerable economic literature on the operation and taxation of lotteries [START_REF] Fink | Lotto nothing? The budgetary impact of sate lotteries[END_REF][START_REF] Glickman | Do Tax and Expenditure Limits Lead To State Lotteries? Evidence From The United States: 1970-1992[END_REF][START_REF] Paton | Taxation and the Demand for Gambling: New Evidence from the United Kingdom[END_REF][START_REF] Clotfelter | The Peculiar Scale Economies of Lotto[END_REF][START_REF] Clotfelter | On the Economics of State Lotteries[END_REF], but the economic literature on the economics of casinos is very limited. Most of the literature has been institutional in nature focusing on the potential of casinos to generate economic development in a region [START_REF] Eadington | The Economics of Casino Gambling[END_REF]; [START_REF] Fink | The Importance of Self-Selection in Casino Cannibalization of State Lotteries[END_REF][START_REF] Henrikson | Hardly a Quick Fix: Casino Gambling in Canada[END_REF]; [START_REF] Gazel | The Economic Impacts of Casino Gambling at the State and Local Levels[END_REF]); alternative methods of taxation [START_REF] Smith | Gambling Taxation: Public Equity in the Gambling Business[END_REF]; Siegel andWilliams, 2001: 2002b); and the control of money laundering (Financial Transaction Reports Act 1988;[START_REF] Roach | The Mob in Casinos, Gambling Research Information and Education Foundation[END_REF], and [START_REF] Nicaso | Mob Launders Money at Ontario Casinos; Loophole in Rules Lets Drug Profits Filter Through[END_REF]). An exception to the above literature is the paper by [START_REF] Thalheimer | The demand for casino gaming[END_REF] In this paper they specifically examine the determinants of demand for casino gambling including its price elasticity. In this paper, we wish to examine a number of regulatory and taxation issues while incorporating the special characteristics of the casino industry.

An important characteristic of casinos is that the "price" of gambling, defined here as the percentage of the amount gambled that is retained on average by the casino, is usually not determined competitively by the interaction of the casinos in the market and the demand for casino gambling. Except for slot machines, the table games and roulette have a specific minimum expected take by the house that is set by the rules of the game [START_REF] Eadington | The Economics of Casino Gambling[END_REF]. There is no reason that these minimum prices are anywhere near to the prices that would be set in a perfectly competitive market. Second, in many jurisdictions the price of gambling is set through government regulation or by state gambling boards. In many cases the "price" is set at several multiples of what might be a competitive price 1 . In such a circumstance, the regulatory question is both one of determining the optimal "price" to set as well as the number of casinos allowed to supply the market. This characteristic is reflected in the efforts of casino operators to try to obtain additional casino licenses. The recent experience of Canada and the UK 1 In North Cyprus the house take is set at 10 percent based on a previous regulation made by Turkey prior to their abolishing casinos. In Belize, the casino operators association has set the house take as 15 percent. In contrast, in the USA the house take is in the order of 3.5 percent of the amount gambled at website:www.bestpayoutcasinos.net/ In this paper, a model of the costs of a casino is built that allows us to focus on the implications for economic welfare of different schemes for taxing casinos.

Several assumptions are made in order to highlight the taxation issues. First, we set aside the issue of the negative externality of the social costs arising from the incidence of compulsive gambling and increased crime that accompanies casino gambling when the local population is allowed to participate in casino gambling. This is done by focusing on tourist destinations where most, if not all, the customers of the casinos are tourists. This is typical of such places as the Caribbean Islands, Belize and North Cyprus. North Cyprus goes so far as to ban the local residents from entering a casino to gamble. 3 Second, any positive externalities that are created in the other sectors of the economy are excluded. These are items such as the increased sales tax revenues from a higher level of hotel occupancy and from the purchase of goods and services.

Third, the effects on the incomes of local factors of production are ignored.

Competitive supplies of factor inputs are assumed. In such tourist destinations the slot machines, gambling tables along with much of the labor employed by the casinos are often sourced from abroad.

In this situation, the economic benefits of casinos in the economy will be through the tax revenues obtained by the government from this activity. Any To develop the parameters for the most efficient supply of casino gambling services, we start by assuming a casino sector that is characterized by perfect competition where, contrary to real life, the "price" of gambling services is determined in a competitive market. Given the total cost function of such a casino and the total demand function facing the country for casino gambling, we obtain the equilibrium conditions for the situation when competition leads to a zero economic profit outcome. Expressions are derived for the optimal size of each casino, q 0 , the competitive price for gambling, P, the total amount of gambling undertaken, D Q 0 , and the equilibrium number of casinos, n 0 , when free entry is allowed into the sector.

Expressions for these variables are then developed for the case where the price of gambling is set above its competitive level by either government regulation or by the rules of the games. At the same time, free entry of casinos is allowed into the sector. 4 It is assumed that the casinos are all identical and compete with each other for the business until their average costs are equal to the price of gambling, hence, a zero profit situation5 . This is a fair description of the casino sector in either Casinos are typically taxed either on the turnover of money gambled or by annual taxes on their fixed costs (or both). To evaluate the potential role of taxation of casinos to raise revenues and regulate the sector, the tax rate on gross turnover is found that would minimize the total economic costs of supplying the casino services now demanded at the non-competitive price. This revenue maximizing rate of tax is exactly equal to the difference between what would be the competitive price and the actual regulated non-competitive price.

An expression is also derived for the revenue-maximizing combinations of turnover taxes and taxes on annual fixed costs. With a tax on fixed costs and free entry, each casino will operate where the average cost of the casino becomes equal to the non-competitive price "s", that is set above the casino's minimum average costs.

The maximum revenue raising combination of taxes therefore be set so that for each casino the average combined tax rate expressed as a rate of q is exactly equal to the After estimating the values of the fixed cost items for a typical casino in North Cyprus, we found that the average total annual value of the fixed costs per casino, K, is approximately US$ 572,000 per year.7 Some illustrative estimations are made of the economic efficiency and losses from the present tax and regulation policies for casinos in North Cyprus. The findings are that the current tax system is far from its welfare maximizing or revenue maximizing levels. There is an incentive for overinvestment in the sector that causes highly wasteful investments to be made. This amount of wasteful overinvestment represents approximately 50 percent of the annual total fixed costs incurred by the sector. The magnitude of the annual economic efficiency losses is equal to approximately 0.5 percent of GDP.

II. The Price of Gambling is Set Competitively

As indicated above, it is assumed that the casino sector only services the foreign tourist population. Given that the country whose economic welfare was being maximized is not concerned with the economic welfare of the tourists, but only with In order to develop an economic efficient base case that can be used to compare with the less efficient situations, the analysis begins by assuming that the casino sector is a perfectly competitive industry with free entry of casinos. The market price of gambling, P, is determined by the minimum average costs of a typical casino. Casinos can enter or exit the industry freely until the quantity of gambling services supplied is equal to the quantity demanded at that price.

Let us assume each casino has a cost function of the following form,

(1) TC = K+bq+cq 2 , where q is the volume of gambling done in each casino per period. K is the amount of fixed costs per period for the typical casino, and bq+cq 2 describes how total variable costs of the casinos change with the volume of gambling undertaken in the casinos per period.

A simple constant elasticity of demand function describes the market's demand for casino gambling 9 .

(2)

Q D 0 = a P e
where the price, P, is the proportion of the turnover of the amount gambled that is retained on average by the casino. The own price elasticity of demand for casino gambling is denoted as "e", and the constant term "a" reflects the effects of all the other variables affecting the size of the market for casino gambling. It follows from

(1) that average cost and marginal cost of a typical casino are,

(3) AC = cq b q K + + 9 For casino gambling on riverboats in the U.S. the value of the price elasticity of demand for casino gambling, was found by [START_REF] Thalheimer | The demand for casino gaming[END_REF] to be approximately -1.0. In a competitive market, each casino would be operating at a level where, P c =MC=AC.

With free entry into the market for casino gambling, the market price (P) will be determined by the minimum average cost of the last casino entering this market.

Hence, as all the casinos are assumed to be identical, the quantity of gambling done by each casino, q, will be where AC = MC. Equating equations ( 3) and ( 4) we have, ( 5)

cq b q K + + = b+2cq c K q = 0 ,
where q 0 denotes the volume of gambling done in each casino when the price of gambling is determined competitively. The competitive price for casino gambling in the market is determined by substituting the expression (5) for q 0 into the marginal cost function of the casino. Because all casinos are identical, then the market price will be,

(6) P c = cK b 2 + .
This competitive equilibrium is shown in Figure 1 for a typical casino with all equilibrium price of P c and a volume of turnover of q 0 . By substituting equation ( 6) for the competitive price into the market demand equation ( 2), the total quantity of gambling demanded by the market is given as,

(7) Q D 0 = a( ) 2 cK b + e .
With free entry and the market price determined competitively, the number of casinos operating in the market, n 0 , will be given by ( 8)

n 0 = a( ) 2 cK b + e / c K . F o r P e e r R e v i e w
10 Taken together, equations ( 5), ( 6), ( 7) and ( 8) yield the competitive solution for q 0 , P c , Q D 0 , and n 0 .

(Insert Figure 1 here)

III. Price of Gambling Set by Regulation

Suppose that instead of the price of casino gambling being set competitively, it is set either by the government through regulation, or set by the odds of the games at a level "s" above the competitive price. We now wish to examine the implications for the volume of gambling, q, and the number of casinos operating in the market, n, if free entry into the casino sector is allowed. When casinos are allowed to freely enter into the market, they will continue to enter until there are zero economic profits being earned by each casino. At this point, each casino will be operating where its average cost is just equal to s, (9) AC = s Now, the casinos will not be operating at the level of output where their average costs are minimized. If we assume all casinos are identical with the same cost function given by (1), then

(10) AC = s cq b q K = + +
The equilibrium quantity of turnover for each casino denoted by q = q 1 will now be:

(11) q 1 = c cK s bs b c b s 2 4 2 2 2 2

+

Comparing equations ( 5) and ( 11), when the regulated price is set so that s>P, the turnover, q 1 , of a casino will be smaller than in the perfect competitive case, q 0 . In order to solve for the number of casinos that will enter the market, we first need to determine the quantity of the gambling services demanded in the market at the fixed price of (s). From (2) and setting P = s then, Using equations ( 11) and ( 12), the number of casinos, n 1 , supplying the market is found as

1 ' 1 q Q n d = , or (13)

+

.

Each casino will be operating a smaller volume of business than in the competitive case. For a given quantity of such services demanded, i.e.

' d Q , there will be more casinos entering the market than there would be if each casino were operating at a level of output where its average cost was minimized.

Economic Welfare Costs of Excess Capacity

With free entry, in equilibrium the average cost of each casino operating at a level of q 1 will be equal to s as in equation ( 10). Under perfect competition, each casino would be operating at a level of q 0 , and its minimum average costs will be equal to the competitive price, P c , as given by equation ( 6). The difference between these two average costs times the quantity of gambling done in the market, measures the economic loss of allowing free entry with a non-competitive price set at s. The welfare cost, WC, is given by

(14) WC = ( cK b s 2 +
)as e .

When the price of gambling is set by regulation higher than P c , the loss in consumer surplus is not considered part of the welfare cost because of our assumption that all the gamblers are non-residents.

IV. Regulation by Taxation

A common form of control over the size and number of casinos is to impose taxation on the activities of casinos. The two types of taxation will be considered here: a tax levied on the turnover or the amount of money gambled in a casino, and an annual tax levied on the fixed costs of the casinos.

Many countries, such as North Cyprus, tax their casinos with some combination of a turnover tax (t*) on the amount gambled and a set of annual taxes (T*), on various components of the fixed costs of the casino. In such a situation, the total cost function for our typical casino is now written as,

(15) TC'= *) 1 ( * 2 T K q t bq cq + + + + ,
with average costs inclusive of taxes, AC',

(16) AC'= *) 1 ( * T q K t b cq + + + + .
In equilibrium with free entry and zero profits, (17) AC'= s.

In these circumstance level of gambling carried out in each casino, q = q 2 will be determined by,

(18) = 2 q c 2 * t b s - c 2 *) T 1 ( cK 4 ) s * t b ( 2 + + .
The volume of turnover of each casino, q 2 , will be a function of the variables s, t* and T*. This equilibrium for a typical casino is shown in Figure 1 with s=AC' and the quantity of turnover of each casino equal to q 2 .

The number of casinos that will enter the market, n = n 2, is found by dividing the total quantity demanded in the market, Q ' d , by q 2 , giving us, The total tax revenue raised from a typical casino is shown as the area sbav in Figure 1.

Economic Welfare Cost of Combination of Turnover tax t* and Annual Tax on Fixed Costs T*

The welfare cost of such a tax system (WC) will be equal to the total costs incurred by the casinos (TC') in the sector less total costs (TC) that would be incurred if the same quantity of services had been supplied by casinos operating at a competitive level of output. Again, because tax revenues do not represent economic costs, we subtract out the revenues collected via the tax on fixed costs. In market equilibrium, it must hold that 2 'n TC = AC'q 2 n 2 = s ' d Q . This value is compared to the total combined costs of all the casinos, AC( ' d Q ), if each is operating at its most efficient level of q 0 , and where Q ' d is the total quantity of casino services demanded at a market price of s. Given these relationships, the expression for the welfare cost of a combination of a turnover tax t* and an asset tax of T* can be written as,

(21) WC = (s-AC)Q d -TR T* -TR t* .

Estimation of the WC of the Existing Price Regulation Tax System in North

Cyprus (At the present time in North Cyprus the price of gambling is set at 10 percent by regulation.)

The taxation system in North Cyprus consists of a set of taxes on the annual fixed costs which includes the annual rental of the machines, and tables, plus an annual license fee of US$ 125,000 per year. For our hypothetical casino, this amounts to US$ 226,050 per year or a rate of T* on fixed costs equal to 0.395. In For the competitive case, from (5), the total turnover of the amount gambled in a casino per year would have been 82 . 37 $ 0 US q = million and from (8), there would have been only n 0 =234.08/37.82=6.2 casinos operating 10 .

From (3), the minimum AC would be equal to 0.036, which would also be equal to, the competitive price, P c , for gambling in the North Cyprus casinos 11 . Substituting the above values for s, AC, Q ' d , TR T* and TR t* into (21), the annual welfare cost of the existing taxation system for casinos in North Cyprus is estimated to be US$ 6.44 million per year. This is a very substantial economic loss for a very small economy, representing approximately 0.5 percent of GDP per year.

Tax Policy Options

Given the relatively large economic losses resulting from the existing tax system for casinos in North Cyprus, further tax policy options should be considered.

Four possible options will be considered below. They are:

A. The existing tax on fixed costs of 0.395 could be abolished and a single revenue maximizing turnover tax, t, could be applied. A rate would be selected that would maximize the revenue collected by the government, given the regulated price s=0.10.

B. The existing tax on fixed costs, T*, at a rate of 0.395 of annual could be retained but also a turnover tax could be levied at a rate that will maximize total tax revenues. 10 In the real world a partial number of casinos such as 6.2 will not exist. However, for the purpose of this illustrative example we have allowed for a fractional number of casinos to exist in order to make the computations easier for the reader to follow. D. Only a tax on fixed costs of, T, is levied at a rate that will maximize tax revenues from the sector.

(a) Revenue Maximizing Turnover Tax

In this case, a turnover tax is imposed at a rate t. The total cost function inclusive of taxes, TC', then becomes, ( 22) TC' = K+bq+cq 2 TC' = cq 2 + bq+tq+K.

Average costs are, (23) AC' = cq+b+t+ q K , and marginal costs inclusive of tax MC' are, [START_REF] Mankiw | Free Entry and Social Inefficiency[END_REF] MC' = 2cq+b+t.

The tax rate that will cause casinos to meet the market demand efficiently needs to be set at a level so that each casino will operate at the level q 0 , as in equation ( 5), where its average costs are minimized. To bring this about it must be set so that MC' = AC' = s. Now, setting marginal costs inclusive of the tax ( 24) equal to the regulated price of (s), we have,

(25) MC' = 2cq+b+t = s b cq s t = 2 .
Now substituting c K for q=q 3 in (25) in order that each casino will operate at its minimum average costs, one can solve for the value of (t) that will bring this about, The tax rate will be exactly the difference between the regulated price (s) and the competitive price given by equation ( 6). This situation is illustrated in Figure 2 where MC'=AC'=s and t=AC'-AC and the equilibrium quantity produced by each casino is q 0 .

In this case, with a regulated price of (s), and a tax rate of (t) set by ( 26), the number of casinos entering the sector will be,

(27) n 3 = c K as e .
Total Revenue from Turnover Tax

The total tax revenue, TR t, from the turnover tax is calculated as TR t = t(as e ).

Substituting equation ( 26) for (t) in the expression for TR t , (28

) TR t = e as cK b s ) 2 ( .
This tax will capture an amount of revenues equal to the entire surplus between the regulated price s and the net of tax minimum average costs of the casinos, times the total volume of gambling. The total tax revenue raised from a typical casino is shown in Figure 2 as the area sfcP c .

(Insert Figure 2 here)

Economic Welfare Cost of Turnover Tax

The welfare cost of the tax can therefore be estimated as the difference between the total financial costs of the casinos' operations with the turnover tax, less the total costs incurred by the casinos in servicing the same quantity demanded, if every casino operated at its perfectly competitive level of output. From this difference we need to subtract the amount of tax revenues that the government This can be written

t e t TR as AC AC WC = ) )( ' (
. Substituting (23) for AC',

(3) for AC, (28) for TR t and setting c K q =

, we find that WC t = 0. In this case, the turnover tax set at a level (t) as in equation ( 26) will have a zero economic welfare cost.

Estimation of Revenue from Revenue Maximizing Turnover Tax:

In this case, the rate for the revenue maximizing turnover tax is derived using equation ( 26). The rate of tax (t) is equal to 0.064. Substituting this tax and the amount of turnover of US$ 234.08 million/year into equation ( 28), we find that the total tax revenue would be equal to US$ 14.92 million/year. The single rate of turnover tax at its revenue maximizing level will result in the same number of casinos entering the sector as in the competitive case. Hence, the welfare cost of this tax will be equal to zero. In fact, by imposing this tax, the economic efficiency in the casino sector will be improved by US$ 6.44 million.

The chief difficulty with levying a single turnover tax on the casino sector is one of tax administration. A number of countries have experienced a high degree of tax evasion and fraud when they attempted to levy a significant tax rate on the purchase of the chips used in gambling. Hence, other designs for the taxation of casinos need to be considered.

Estimation of Tax Revenue from Revenue Maximizing Level of t, given that T* and s are known

One way of reducing the rate of the revenue maximizing tax on turnover for casinos in North Cyprus would be to retain the current asset tax of 0.395 on annual fixed costs and then to solve for the revenue maximizing turnover tax. Using (32), we find that the revenue maximizing turnover tax, t, would be equal to t=0.058 when T*=0.395. From (33) we find that the equilibrium number of casinos would be n 4 =234.08/37.82=6.19. The tax revenue in this case has two components. First, the revenue from the turnover tax is calculated using (28) to be TR t =US$ 13.523 million/year and second, the revenue from the tax on fixed costs is calculated using (34) to be TR T* =0.395(0.572)(6.19)=US$ 1.399 million/year. The total tax revenue estimated is therefore approximately equal to US$ 14.922 million per year.

Substituting these values into (21), the annual welfare cost of the concerned tax policy is zero per year.

(c) Revenue Maximizing Level of T given that t* and s are Already known

In this case, we assume that the rate of tax on the turnover is given as t*, now we want to find the rate of tax, T, on the fixed costs that would maximize overall tax revenues from the sector. This approach to taxation may be necessitated when it is not possible for the authorities to administer a substantial rate of turnover tax, but it is possible to tax the physical assets of the casinos such as the number of slot To have a least cost equilibrium, given the existence of t*, we need to find the rate of T that will maximize revenue with each casino operating where, (37) AC' = s

Using equation ( 37) and setting q 5 =q 0 , the revenue maximizing rate of asset tax T, is found to be

(38) T = c K K t b s ) * ( -2.
Using q 0 and the total quantity of demand in the market, Q ' d , we can now solve for the number of casinos n=n 5 entering the market, (39) n 5 = c K as e .

In this situation, the total revenue paid by the sector in a year can be expressed as, 21), the annual welfare cost of the concerned tax policy is also calculated as being equal to zero.

(d) Revenue Maximizing Tax on Fixed Costs T is levied with no Turnover Tax

A decision to levy a tax only on fixed costs might occur if the degree of tax evasion with respect to a turnover or income tax is very high. In recent years the Dominican Republic has had to revert to such a tax system due to uncontrollable tax evasion with other forms of taxation. In this case firms will enter until AC'=s. In this situation the revenue maximizing rate of tax must be so that AC'=s at a level of output of q 0 so each casino is operating in an economically efficient manner.

The expression for the revenue maximizing rate of tax T can be found directly from (38) by setting t*=0. This gives us, ( 41)

cK cK b s T 2 =
This case is illustrated by Figure 3. The final equilibrium is at point h for each casino with it operating at an output level of q 0 . The tax on fixed costs has shifted the average costs to AC'. The maximum tax revenue for a typical casino is is shown at the area shgP c . With the asset tax, T, set so that each casino will produce 0 6 q q = , the number of casinos, n=n 6 , that will enter the market will be the same as in (39), ( 42) n 6 = c K as e .

In this situation, the total revenue paid by the sector in a year can be expressed as, ( 43) TR = TKn 6.

(Insert Figure 3 here)

Estimation of Tax Rate and Revenue from Revenue Maximizing Level of T

In this case, we estimate the revenue maximizing rate of asset tax, T, given t*=0 and s=0.10. From (41) we find that the revenue maximizing annual asset tax, T, is equal to 4.215. With T=4.215 and Q ' d = US$ 234.08 million per year, the number of casinos will be n 6 =234.08/37.82=6.19. The revenue from the tax on fixed costs is calculated using (43) to be TR T = US$ 14.922 million/year. Substituting the above values into (21), the annual welfare cost of the concerned tax policy is also calculated as being equal to zero.

V. Conclusions

In Table 1, we have summarized the results of the analysis. The magnitude of the efficiency losses from levying too low a set of tax rates while allowing free entry into the casino sector is reported for each case. At the present time, the economic efficiency cost on average is equal to 80% of the revenue collected. From tax policy case (a), we find that if a single turnover tax could be enforced, the additional revenue would be approximately US$ 6.44 million with the welfare cost falling by (Insert Table 1 here)

This paper has shown that in jurisdictions where the price of gambling is set by regulation above its competitive price, and where entry into the sector can not be effectively controlled, then a serious resource miscalculation will occur if the countries do not tax away the potential economic rents accruing to the sector.

It is found that a tax on the turnover of funds gambled is an equally efficient to one that taxes the annual fixed costs of the casinos. However, because of the ease of taxing fixed costs in contrast to taxing turnover, it might be welfare improving to maintain a low turnover tax, and use a tax on the annual fixed costs of the casinos to tax away the rest of the economic rents. In all cases the economic welfare of the country will be improved as the level of taxation is increased on the casinos up to the point where tax revenue is maximized.

F

  by casino operators to expand and the willingness of the casinos to pay heavily to obtain their licenses 2 .

  arising from the creation of excess capacity in the sector will reduce the amount of tax revenues that the government could potentially collect.

  competitive price and the regulated price of s. This condition is satisfied at the same level of output that would exist if the casino market were perfectly competitive.An Evaluation of the Welfare Costs of Regulation and Taxation in the Casino Sector in North CyprusThe assumptions used in the development of the theoretical models below are broadly descriptive of the casino sector in North Cyprus. With a total population of 200,000 souls, it is home to 22 casinos. The market for the casino services is focused exclusively on the tourists visiting the state, primarily from Turkey, the UK and recently South Cyprus. Information through interviews was obtained from three casinos and from the government regulators on the amount of investment made for gambling tables, slot machines, rental cost for the facilities, the structure of variable costs, and the turnover of casinos operating in North Cyprus. The illustrative parameter values used in the estimations of the revenue and welfare implications of current policies are based on the information obtained from these sources.6

  associated with the volume of gambling carried out in a casino in North Cyprus are primarily associated with the marketing efforts undertaken to attract gamblers, including the subsidization of the transportation costs from Turkey to North Cyprus, the cost of food, drinks and entertainment provided by the casino, and some variable labor costs needed to run the casino at a higher level of utilization. The pattern of marketing costs incurred to attract gambling to the casinos from Turkey also provides an empirical basis for the form of the total cost function that is assumed. Marginal costs eventually rise as the volume of gambling increases in a casino because of the declining marginal effectiveness of the promotional expenditures made to attract gamblers to the casino.8

  our goal is to determine the maximum amount of taxes that can be extracted from the activities of this sector under different systems of taxation.

  is a tax on the gross revenues of the casino that translates into a rate of t* on turnover of 1.5 percent.If approximately US$ 10 million is gambled each year in a typical casino, then the parameter values of 0.006 for b and 0.0004 for c results in a total variable cost of about US$ 100,000, an amount that is approximately what is observed. In summary, the parameter values of the variables used in the model used to illustrate the situation for North Cyprus are: K = US$ 572,000, c = 0.0004, b = 0.006, T* = 0.395, t* = 0.015 Substituting these parameter values into equation (15), the total cost function becomes, TC' = 0.0004q 2 + 0.021q+0.798. If s = 0.10, and free entry occurs until zero profits are being earned, then using equation (18), the equilibrium quantity of turnover for each casino will now be US$ 10.64 million. At the present time there are 22 casinos in North Cyprus. Hence, the total quantity of the gambling services demanded from the 22 casinos in the market must be approximately US$ 234.08 million. With this volume of gambling the total annual tax revenue from the 1.5 percent tax on turnover, (TR t* ), (equation 21) is therefore TR t* = (0.015)*234.08 = US$ 3.51 million/year. The total annual tax revenue (equation 27) from the tax on fixed costs, TR T* = T*(K)n 2 = 0.395(0.572)(22)=US$ 4.97 million/year. The total tax revenue estimated by this model is therefore approximately US$ 8.48 million per year. This estimate is close to the actual revenues collected from casino sector in North Cyprus in 2004 of US$ 8.13.

  are simply financial transfers, not economic costs of the casinos' operations.

  TR = tQ d +T*Kn 4.

(

  40) TR = t*Q d +TKn 5.

  .Case (b) where the tax on fixed costs is retained and a revenue raising turnover tax is added and case (c) where the turnover tax is retained and a revenue maximizing tax on fixed costs is added, the results are exactly the same in terms of revenue and economic efficiency as if there was a single revenue maximizing rate of turnover tax case (a), or a single revenue maximizing tax on fixed costs, case (d).

  Fig. 1. Existing System in North Cyprus

Estimation of Tax Rate and Revenue from Revenue Maximizing Level of T given that t* and s are Known

	t*=0.015 and T=3.223. With Q ' d = US$ 234.08 million per year, the number of
	casinos will be n 5 =234.08/37.82=6.19. The tax revenue in this case has two
	components as well. First, the revenue from the turnover tax is calculated using (28)
	to be TR t *=US$ 3.511 million/year. Second, the revenue from the tax on fixed costs
	is calculated using (34) to be TR T = US$ 11.411 million/year. The total tax revenue is
	again estimated to be approximately equal to US$ 14.922 million/year. Substituting
	the above values into (
	F o r
	P
	e
	e r
	R e v
	i e
	w
	Due to difficulty of taxing the turnover of casinos, countries such as the
	Dominican Republic have had to rely more on the taxation of the casinos' fixed
	costs. In the following illustrative estimations, we assume that it is not possible to
	raise the rate of turnover tax in North Cyprus above its current rate of 0.015. To
	complement this tax, we now estimate what would be the revenue maximizing rate of
	tax on fixed costs, T, given t*=0.015 and s=0.10. From (38) we find that the revenue
	maximizing annual tax, T, is equal to 3.223 times the annual fixed costs. With
	22

Table 1 . Tax Policy Options -Annual Revenue and Welfare Cost

 1

	o r
	P
	e
	e r
	R e v
	i e
	w

The condition of free entry of casinos into the sector is critical for the subsequent findings in the paper. As many tourist destinations allow free entry or actively recruit firms to set up casinos in their regions, we feel that it is important that the economic losses inflicted as a consequence of such policies be clearly understood.

This is similar to the situation discussed by[START_REF] Mankiw | Free Entry and Social Inefficiency[END_REF] Free Entry and Social Inefficiency, The Rand Journal ofEconomics, 17, 1,[48][49][50][51][52][53][54][55][56][57][58]

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

In this paper we make the simplifying assumption that there is only one size of casino in terms of the fixed costs incurred by casinos in this market. If there are economies of scale in casinos, then if the size of the casino were increased due to greater investment and greater fixed costs, the conclusion of this paper would be further strenghtened. There would be a larger welfare gain if there were fewer casinos but each having a larger volume of business and operating more efficiently.

It is estimated that the investment costs for the equipment in a typical casino with 4 roulette tables, 5 gaming tables and

slot machines is approximately US$ 520,000. Casino decorations, kitchen, equipment and vehicles bring the total investment costs (excluding the buildings) for such a casino averages US$ 832,000. If an annual user cost of capital of 15 percent of the value of these assets is assumed, the annual cost of these assets would be US$ 124,800. The rental cost of the building is estimated to be approximately US$ 52,000 per year. The annual cost of the utilities amounts to approximately US$ 31,200 per year, and the fixed labor cost associated with the operation of such a casino is approximately US$ 364,000 per year. The user cost of 15 percent is based on a real opportunity cost of funds of 10 percent plus an annual rate economic depreciation of the fixed assets of 5 percent of their market.

Casino operators report that as they increase their promotions offering "free" airfares to potential tourists from Turkey to gamble in the casinos of North Cyprus, the proportion of people who accept their offer but spend large amounts of time on the beach increases.

Acknowledgements

The comments and suggestions of Eric Li greatly improved the analysis. In addition Hasan Ulas Altiok provided very helpful assistance in securing the some of the data used in this paper.

(b) Revenue Maximizing Level of t, given that T* and s are known

In this case, we assume that the rate of tax on the fixed costs is given as T*, now we want to see what would be the rate of turnover tax, t that would maximize the overall revenue yield from the sector. 12 The total cost function for the casinos is now written as, (29) TC ' = cq 2 +bq+tq+K(1+T*), with average costs equal to

To have a least cost equilibrium given the existence of T* we need to find the value of t so that the competitive level of output, q 0 , will exist and every casino will be operating where AC'=s.

From ( 30),

By substituting for the quantity q = q 4 =q 0 into equation (31), we find the revenue maximizing rate of turnover tax t, given T=T* is,

Using q 4 =q 0 and the market demand of Q d , we can now solve for the number of casinos n = n 4 that will now supply the market as, (33) n 4 = ( e as )/ c K .

In this situation, the total tax revenues paid by the sector in a year can be expressed as, 12 This tax policy question might arise when either a state or province levies a tax of T* on the fixed costs of casinos (perhaps through its licensing authority), while central government has the authority to levy taxes on the turnover of the casinos.