Regional concentration of native fuelwood production in Rio Grande do Norte, Brazil (1990–2017)

: This paperexamined the regional concentration of native fuelwood production in Rio Grande do Norte, Brazil, between 1990 – 2017. Information on native fuelwood was gathered fromforestry activitiescollected by the Brazilian Institute of Geography and Statistics (IBGE). This studyanalyzed the current situation and the spatial distribution of the state’s fuelwood production by quartiles. The following indicators were used to measure market concentration: Gini Coefficient (G), Comprehensive Concentration Index (CCI), Herfindahl-Hirschman Index (HHI) and Concentration Ratio [CR(k)]. In Rio Grande do Norte, there was a -2.76% annual decrease in the production of native fuelwood, from 5,280 x10³ m³ (1990) to 777 x10³ m³ (2017). Classification of the municipalities by quartile revealed that most municipalities had low fuelwood production. The G inferred a very strong to absolute inequality for the municipalities and a weak to null inequality for the mesoregions.The CCI demonstrated no market concentration in the municipalities and a regional concentration in the mesoregions. The HHI corroborated the CCI by affirming the presence of a competitive market for the municipalities and microregions and a concentrated market in the mesoregions.The CR(k) of the four largest municipalities indicated a moderately low concentration. This study concluded that there is a competitive market structure for native fuelwood inthe state of Rio Grande do Norte.

Industrial concentration, an economic activity, is one of the most important components of competition between firms. Concentration and competition are related inversely: as concentration intensifies, the competition level in the market declines (POSSAS, 1999). Additionally, concentration indicators provide empirical elements that explain supply and demand, the degree of product differentiation, and market entry conditions, among others (RESENDE, 1994;RESENDE& BOFF, 2002).
Market studies and regional analyses have recommended tests that apply market concentration to the forest sector. From the international scenario, COELHO JUNIOR et al.(2013)  Considering the need to understand the fuelwood market in RN and the state's market structure, this study analyzes the regional concentration of native fuelwood production in RN between1990-2017.

MATERIALS AND METHODS
Information on the production of native fuelwood (m 3 ) in RN is provided in the data on Forestry Activities (PEVS) collected by the IBGE. the data was analyzed for the period between 1990-2017. Observations of the state of RN were based on geopolitical segments: municipalities, microregions, and mesoregions.
the geometric growth rate (GGR) was used to evaluate changes (gains and losses) in thenative fuelwood production of RN in the regional segments: , where V F is the fuelwood production for the final year in t; V 0 refers to the values for the initial year; ∆t is the temporal variation of production (expressed in years) (CUENCA& DOMPIERI, 2017). the following indicators were used to measure concentration: Gini coefficient, Comprehensive Concentration Index, Herfindahl-Hirschman index, and Concentration Ratio.
The Gini Coefficient (G) is a measure of inequality developed by Gini (1912). this coefficient was originally indicated to measure income inequality. However, it can also measure the degree of inequality within an industry or production: , where n = number of fuelwoodproducing regions in RN; S ij = cumulative share of the amount of fuelwood produced in ascending order; S i = market share percentage of region i(municipalities, microregions, and mesoregions) in the fuelwood production of RN. G varies between 0 and 1 and can be classified asnull to weak (0.10 < G ≤ 0.25), weak to medium (0.25 < G ≤ 0.50), medium to strong (0.50 < G ≤ 0.70), strong to very ∑ strong (0.70 < G ≤ 0.90) and very strong to absolute (0.90 < G ≤ 1.00).
Proposed by Horvarth (1970), the Comprehensive Concentration Index (CCI) measures relative and absolute dispersion: where S 1 is the largest market share among fuelwood producers in a region (municipalities, microregions, and mesoregions).
( ) represents the sum of the squares of each region's proportional sizes, and a weighted multiplier was applied to reflect the rest of the state. A CCI equal to 1 indicates a monopolistic condition, indicatinghigh concentration.
The Hirschman-Herfindahl Index (HHI) was originally claimed by HIRSCHMAN (1964); although, the creators Hirschman and Herfindahl developed the indicator independently: , where S i = market share percentage of region i (municipalities, microregions, and mesoregions) in the fuelwood production of RN andn = number of participants in fuelwood production in region i. the index varies between 1/n (no concentration) and 1 (maximum concentration), indicating a monopolistic situation. For intertemporal comparative analyses that contemplate entering and exiting participants, RESENDE (1994) suggested the adjusted Hirschman-Herfindahl Index (HHI'): . the HHI' lies in an interval between 0 and 1 (monopoly); therefore, market concentration increases as the value moves away from zero and is classified as follows

RESULTS AND DISCUSSION
table 1 shows the progress of fuelwood production derived from vegetation extraction in the mesoregions of RN for 1990RN for , 1995RN for , 2000RN for , 2005RN for , 2010RN for , 2015RN for , and 2017. Fuelwood production was 5,280 x10³ m³ in 1990, and it was 777 x10 3 m³ by 2017, representing an average annual decrease of -2.76%, lower than in the northeastern region (-3.82% per year) (MARtINS et al.,2018). this retraction of forest extractivism was attributed to the scarce availability of forest resources due to agricultural and urban expansion and greater inspection by environmental agencies (COELHO JUNIOR et al., 2018). Prior to 2000, the Central Potiguar mesoregion led the state ranking, and the Oeste Potiguar mesoregion assumed hegemony over native fuelwood as of 2000. the Agreste Potiguar mesoregion had the biggest fall in GGR (-12.38% per year), followed by the Oeste Potiguar (-8.76% per year), Central Potiguar (-5.56% per year), and Leste Potiguar (-5.15% per year) mesoregions. Based on the spatial distribution of fuelwood production in northeastern Brazil, COELHO JUNIOR et al. (2018b) observed that the state of RN is among the largest producers of fuelwood from vegetationextraction per km 2 . Coelho Junior, Martins, and Carvalho (2018) quantified the impacts of burningnative fuelwood in northeastern Brazil and reported that RNwas among the highest emitters of carbon dioxide equivalent per area (kg CO 2 -eq./km 2 ). Figure 1 represents the spatial distribution of fuelwoodproduction from vegetation extraction in the microregions and municipalities of RN for 1990RN for , 2000RN for , 2010, and 2017 by quartiles. Figure 1 Figure 2 shows the progress of fuelwood production in RN from 1990-2017 based on the G and the CCI. the mean values for G (Figure 2.a) demonstrated a very strong to absolute inequality (0.9697) for the municipalities (G Munic ), a strong to very strong inequality (0.7809) for the microregions (G Micro ) and a weak to medium inequality (0.3083) for the mesoregions (G Meso ). the inequality of native fuelwood production in RN is more significant  (Figure 2.b) presented a peculiar characteristic at regional levels, resulting in a high concentration (CCI Meso = 0.7007) despite the weak to medium inequality in the mesoregions when associated with G. G indicated a high inequality in the municipalities (CCI Munic = 0.1015) and microregions (CCI Micro = 0.3036). However, the market was not characterized as a concentrated market. Figure 3 shows the progress of fuelwood production in RN from 1990-2017 based on the Herfindahl-Hirschman Index (HHI). Although, the other indicators demonstrated different behaviors between the regions, the municipal HHI (HHI Munic ) and microregional HHI (HHI Micro ) exhibited behaviors similar to those seenin figures 3.c. and 3.b., respectively; thus, demonstrating an unconcentrated market. Figure 3.a. illustrates the mesoregional HHI(HHI Meso ), indicating the concentration trends relative to the lower limit (LL). Since 2000, the HHI Meso has distanced it self from the LL, indicating an increase in market concentration, with a mean HHI Meso of 0.3903 and a LL of 0.25 in the analysis period. For the microregions and municipalities, the HHI approached the LLand revealed a low concentration, resulting in a mean HHI Micro of 0.097 for the microregionsand LL of 0.052 between 1990-2017 (Figure 3.b). The difference between the HHI Micro and the LL was greater in 2013 (0.072). In 2001, the difference was smaller (0.026). At the municipal level, the mean HHI Munic was 0.0206, and the LLwas 0.0064 for the period in question. Figure  3.d depicts the HHI for the three regional segments. the HHI Meso presented an unconcentrated market structure (HHI'<0.15) until 1997. Additionally, there was a moderately concentrated displacement due to increased production in the Oeste Potiguar mesoregion until the end of the analysis period. Nevertheless, the HHI' Munic and HHI' Micro remained very close and presented stable behaviors thanthe HHI Meso , demonstrating a competitive market. COELHO JUNIOR et al. (2018) analyzed the HHI Meso forfuelwood production in Paraíba, and the indicator presented more stability in a moderately concentrated market. Figure 4 shows the CR(k) of fuelwood production in themicroregions and municipalities of RN from 1990-2017. According to BAIN's classification (1959), the mean CR(4) Micro was 50.94%, indicating a moderately high concentration in the state's fuelwood production (Figure 4.a.). the highest concentration was registered in 2013 (63.08%), while the lowest was in 2001 (42.02%). throughout the period in question, the CR(4) Micro presented a moderately low concentration with no changes in the concentration pattern. As reported by COELHO JUNIOR et al. (2018), the behavior of the CR(k) forfuelwood production in Paraíba was similar to that of RN. the microregions of RN that contributed the most to the CR(4) Micro (Figure 4.b.) was 20.02%, indicating a low concentration. the highest CR(4) table 1 -Evolution of the quantity of firewood produced in the mesoregions of Rio Grande do Norte -RN, in thousand cubic meters (x10 3 m 3 ) for 1990, 1995, 2000, 2005, 2010, 2015    Parelhas. the municipalities that contributed at least once to the CR (8) (30) Munic revealed that competition exists between the fuelwood-producing municipalities in RN.

CONCLUSION
Based on the analyses, fuelwood production in RN declined at an annual rate of -2.76%, from 5,280 x10³ m³ in 1990 to 777 x10³ m³ in 2017. Most municipalities in the state have low production of fuelwood derived from vegetation extraction. G inferred a very strong to absolute inequality for the municipalities and a weak to null inequality for the mesoregions. the CCI indicated an unconcentratedmarket in the municipalities and regional concentration in the mesoregions. the HHI corroborated this result by detecting a highly competitive market for the municipalities and microregions and a concentrated market for the mesoregions. the CR(k) of the four largest municipalities indicated a moderately low concentration. therefore, fuelwood production in the state of RN presents an unconcentrated market structure.

DECLARATION OF CONFLICT OF INTEREST
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.