4. Models to optimize the base number of contributors per fiscal regime

#### 4.1. Generic model for ISR

In the following a generic model for ISR is presented. The model is structured in accordance to the official information up to September 31 of 2015 and obtained via a request of public information [33]. The authorities detail that the total number of contributors up to September 3110, registered up to the 2009 exercise, is 11,107,553; however, in order to give an example for the following model, we will take the total number of contributors as 16,752,516. To test the model, constant returns are considered for each contributor, and these can be obtained by

<sup>9</sup> Quantity that corresponds to the sum of incomes for the year 2016 and included in the federal income law (Table 3)

<sup>10</sup>In addition, the authority claims with respect to the requirement of information that "the requested information are not part of the data that the administrative unit makes periodically, however, the transparency agencies provide data relative to the fiscal regime up to September 31, 2015 which corresponds to the contributors of ISR…"

dividing the total collection of ISR in the fiscal year 2015 which is \$1059206.20 (in million pesos) by the total number of contributors which is 16,752,516 and which results in an approximated return per contributor of 0.0632 million pesos11. The objective function will be represented by the returns of each fiscal regime reported by the authority. Restrictions are composed of the total number of contributors (for this case it is greater than the one reported on September 2015 which is 17,000,00012), and consequently a better tax collection is expected than the one that was considered for the base of the returns. The following restrictions (14 in total) will correspond each to the total number of contributors per regime13; the number of residents abroad without a permanent establishment in Mexico is at least 200. Also, the restriction, wages, salaries, and similar regime together with the fiscal incorporation regime are at least 10,600,000 contributors14. In the following, the notation is presented15:

τ þ 1φ þ 1ω ≤ 61:70 τ þ 0φ þ 0ω ≥ 19:90 τ þ 1φ þ 0ω ≥ 29:90 τ þ 0φ þ 1ω ≥ 2:05 τ þ 1φ þ 1ω ≥ 34:43 τ þ 0φ þ 1ω ≥ 22:50

�τ,φ, ω ≥ 0

The results obtained by using the PHP Simplex tool [35] and replicated with MS Excel Solver are the following: τ ¼ 27:27 million contributors, individuals; φ ¼ 29:90 million contributors,

Based on the optimized number of contributors, the next steps are to multiply these variables by the returns, i.e., the maximized result of (9), and to compare it with the total revenues by

Maximize ¼ 40239:19 27 ð Þþ :27 35963:57 29 ð Þþ :90 37000 4ð Þ :53

Maximize <sup>¼</sup> <sup>2340243</sup>:409

The above result represents the total tax collection expected for 2016 for taxes ISR, IVA, and

4. Models to optimize the base number of contributors per fiscal regime

In the following a generic model for ISR is presented. The model is structured in accordance to the official information up to September 31 of 2015 and obtained via a request of public information [33]. The authorities detail that the total number of contributors up to September 3110, registered up to the 2009 exercise, is 11,107,553; however, in order to give an example for the following model, we will take the total number of contributors as 16,752,516. To test the model, constant returns are considered for each contributor, and these can be obtained by

Quantity that corresponds to the sum of incomes for the year 2016 and included in the federal income law (Table 3)

to the fiscal regime up to September 31, 2015 which corresponds to the contributors of ISR…"

In addition, the authority claims with respect to the requirement of information that "the requested information are not part of the data that the administrative unit makes periodically, however, the transparency agencies provide data relative

IEPS. Using exact quantities with all decimals will result in an exact value.

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employees; and ω ¼ 4:53 million contributors, entities.

ISR, IVA, and IEPS for equality.

222 Taxes and Taxation Trends

4.1. Generic model for ISR

9

10

Using the maximized OF, (9) results in

R<sup>θ</sup><sup>n</sup> ¼ Return per restriction variable

θ ¼ Total number of contributors for ISR in accordance to official goals and objectives ð Þ

θ<sup>1</sup> ¼ Wages and salaries regime and wages like incomes official data ð Þ

θ<sup>2</sup> ¼ Fiscal incorporation regime official data ð Þ

θ<sup>3</sup> ¼ Individuals with enterprise and professional activities regime official data ð Þ

θ<sup>4</sup> ¼ General regime for the law of entities official data ð Þ

θ<sup>5</sup> ¼ Ŕegimen de Arrendamiento dato oficial ð Þ

<sup>θ</sup><sup>6</sup> <sup>¼</sup> Incomes by dividends regime partners and shareholders , official data

θ<sup>7</sup> ¼ Agriculture, forestry, livestock and PF and PM fishing regime official data ð Þ

θ<sup>8</sup> ¼ Regime for the rest of incomes official data ð Þ

θ<sup>9</sup> ¼ Incomes by interests regime official data ð Þ

θ<sup>10</sup> ¼ Entities with non � profit purposes official data ð Þ

θ<sup>11</sup> ¼ Producers cooperatives that defer their incomes official data ð Þ

θ<sup>12</sup> ¼ Regime of coordinated official data ð Þ

θ<sup>13</sup> ¼ Corporate groups regime official data ð Þ

<sup>11</sup>For all the proposed models, the returns may be updated with constant quantities for each contributor or with differentiated quantities with respect to each regime and in accordance to the latest information of the fiscal authorities.

<sup>12</sup>The maximum expected number of contributors could be set according to the goals and objectives of the fiscal authorities; the model presented in this work is exemplified.

<sup>13</sup>In accordance to the official number of contributors reported by the authority [33].

<sup>14</sup>These two restrictions represent examples in which additional restrictions may be derived (in accordance to the goals and objectives of the fiscal authorities).

<sup>15</sup>The number of contributors for each regime is found in the inequalities of the presented notation.

θ<sup>14</sup> ¼ Regime of consolidated official data ð Þ

θ<sup>1</sup> þ 1θ<sup>2</sup> þ 1θ<sup>3</sup> þ 1θ<sup>4</sup> þ 1θ<sup>5</sup> þ 1θ<sup>6</sup> þ 1θ<sup>7</sup> þ 1θ<sup>8</sup> þ 1θ<sup>9</sup> þ 1θ<sup>10</sup> þ 1θ<sup>11</sup> þ 1θ<sup>12</sup> þ 1θ<sup>13</sup> þ 1θ<sup>14</sup> ≤ 17000000 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 6155456 θ<sup>1</sup> þ 1θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 4444544 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 1θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 3764639 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 1θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 1496588 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 1θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 547070 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 1θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 324011 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 1θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 187716 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 1θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 45000 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 1θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 18337 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 1θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 5577 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 1θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 5043 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 1θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 3918 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 1θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 1275 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 1θ<sup>14</sup> ≥ 626 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0ϑ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 1θ<sup>14</sup> ≥ 200 θ<sup>1</sup> þ 1θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 10600000

A Model for Estimating the Number of Taxpayer That Fullfill Mexican Income Law

http://dx.doi.org/10.5772/intechopen.74375

225

The generic model of ISR presented above along with their objective function permitted to obtain a tax collection for \$1,074,400. Due to the fact that two restrictions conditioned the increase of certain fiscal regimes below the one expected in the LIF. The optimized number of contributors with the above restrictions are θ1¼6; 155; 456; θ2¼4; 444; 544; θ3¼3; 764; 639; θ4¼1; 349; 998; θ5¼547; 070; θ6¼324; 011; θ7¼187; 716; θ8¼45; 000; θ9¼18; 337; θ10¼5; 577;

As can be noted, the differences are presented in three of the fiscal regimes. In wages, salaries, and similar regime, the official value went from 6,056,971 to 6,155,456; in the leasing regime went from 547,070 to 693,660; and finally in the other incomes, regime went from 42618.00 to 45000. In the individuals residing abroad without a physical establishment, regime went from

The initial model presented as an evidence of their functionality and based on official information up to the fiscal year 2015 permitted to establish a relation between the active number of contributors and the expected collection in the LIF. This meant that the approach may be used

The performance of the prototype model for the first scenario and that complies with LIF of 2016 adds as restrictions to the official number of individuals and employees and two more additional restrictions and sets as a minimum goal to obtain at least 2.05 million entities. The

θ11¼5; 043; θ12¼3; 918; θ13¼1; 275; θ14¼626 ; and θ15¼200.

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173 to 200 contributors.

under other distinct scenarios.

5. Conclusions

δ<sup>1</sup> ¼ Individuals residing abroad without a physical estabishment in Mexico restricted to 200 ð Þ

δ<sup>2</sup> ¼ Wages and salaries regime and fiscal incorporation regimeR restricted to 10 ð Þ ; 600; 000 :

#### Generic model for ISR

Objective function for ISR:

R<sup>θ</sup><sup>1</sup> þ R<sup>θ</sup><sup>2</sup> þ R<sup>θ</sup><sup>3</sup> þ R<sup>θ</sup><sup>4</sup> þ R<sup>θ</sup><sup>5</sup> þ R<sup>θ</sup><sup>6</sup> þ R<sup>θ</sup><sup>7</sup> þ R<sup>θ</sup><sup>8</sup> þ R<sup>θ</sup><sup>9</sup> þ R<sup>θ</sup><sup>10</sup> þ R<sup>θ</sup><sup>11</sup> þ R<sup>θ</sup><sup>12</sup> þ R<sup>θ</sup><sup>13</sup> þ R<sup>θ</sup><sup>14</sup>

with the following restrictions:

$$\begin{aligned} & \left[ \frac{16\_1}{16\_2} + 0\_2 + 16\_3 + 16\_4 + 16\_5 + 16\_6 + 16\_7 + 16\_8 + 16\_9 + 16\_{10} + 16\_{11} + 16\_{12} + 10\_{13} + 10\_{14} \delta\_{14} \\ & \left[ \frac{16\_1}{16\_2} + 0\_2 + 0\_3 + 0\_4 + 0\_5 + 0\_6 + 0\_6 + 0\_7 + 0\_8 + 0\_9 + 0\_{10} + 0\_{10} + 0\_{11} + 0\_{12} + 0\_{13} + 0\_{14} \delta\_{14} \\ & \left[ \frac{16\_1}{16\_2} + 0\_2 + 0\_3 + 0\_4 + 0\_5 + 0\_6 + 0\_6 + 0\_7 + 0\_8 + 0\_{10} + 0\_{10} + 0\_{11} + 0\_{12} + 0\_{13} + 0\_{14} + 0\_{15} + 0\_{16} + 0\_{17} + 0\_{18} + 0\_{19} + 0\_{10} + 0\_{19} + 0\_{10} + 0\_{11} + 0\_{10} + 0\_{13} + 0\_{14} + 0\_{15} + 0\_{16} + 0\_{17} + 0\_{18} + 0\_{19} + 0\_{19} + 0\_{11} + 0\_{10} + 0\_{11} + 0\_{15} + 0\_{16} + 0\_{17} + 0\_{18} + 0\_{19} + 0\_{19} + 0\_{11} + 0\_{11} + 0\_{11} + 0\_{12} + 0\_{13} + 0\_{14} + 0\_{15} + 0\_{16} + 0\_{17} + 0\_{18} + 0\_{19} + 0\_{19$$

#### Generic model for ISR

Objective function for ISR:

R<sup>θ</sup><sup>1</sup> þ R<sup>θ</sup><sup>2</sup> þ R<sup>θ</sup><sup>3</sup> þ R<sup>θ</sup><sup>4</sup> þ R<sup>θ</sup><sup>5</sup> þ R<sup>θ</sup><sup>6</sup> þ R<sup>θ</sup><sup>7</sup> þ R<sup>θ</sup><sup>8</sup> þ R<sup>θ</sup><sup>9</sup> þ R<sup>θ</sup><sup>10</sup> þ R<sup>θ</sup><sup>11</sup> þ R<sup>θ</sup><sup>12</sup> þ R<sup>θ</sup><sup>13</sup> þ R<sup>θ</sup><sup>14</sup>

with the following restrictions:

θ<sup>1</sup> þ 1θ<sup>2</sup> þ 1θ<sup>3</sup> þ 1θ<sup>4</sup> þ 1θ<sup>5</sup> þ 1θ<sup>6</sup> þ 1θ<sup>7</sup> þ 1θ<sup>8</sup> þ 1θ<sup>9</sup> þ 1θ<sup>10</sup> þ 1θ<sup>11</sup> þ 1θ<sup>12</sup> þ 1θ<sup>13</sup> þ 1θ<sup>14</sup> ≤ 17000000 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 6155456 θ<sup>1</sup> þ 1θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 4444544 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 1θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 3764639 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 1θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 1496588 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 1θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 547070 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 1θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 324011 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 1θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 187716 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 1θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 45000 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 1θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 18337 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 1θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 5577 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 1θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 5043 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 1θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 3918 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 1θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 1275 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 1θ<sup>14</sup> ≥ 626 θ<sup>1</sup> þ 0θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0ϑ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 1θ<sup>14</sup> ≥ 200 θ<sup>1</sup> þ 1θ<sup>2</sup> þ 0θ<sup>3</sup> þ 0θ<sup>4</sup> þ 0θ<sup>5</sup> þ 0θ<sup>6</sup> þ 0θ<sup>7</sup> þ 0θ<sup>8</sup> þ 0θ<sup>9</sup> þ 0θ<sup>10</sup> þ 0θ<sup>11</sup> þ 0θ<sup>12</sup> þ 0θ<sup>13</sup> þ 0θ<sup>14</sup> ≥ 10600000

The generic model of ISR presented above along with their objective function permitted to obtain a tax collection for \$1,074,400. Due to the fact that two restrictions conditioned the increase of certain fiscal regimes below the one expected in the LIF. The optimized number of contributors with the above restrictions are θ1¼6; 155; 456; θ2¼4; 444; 544; θ3¼3; 764; 639; θ4¼1; 349; 998; θ5¼547; 070; θ6¼324; 011; θ7¼187; 716; θ8¼45; 000; θ9¼18; 337; θ10¼5; 577; θ11¼5; 043; θ12¼3; 918; θ13¼1; 275; θ14¼626 ; and θ15¼200.

As can be noted, the differences are presented in three of the fiscal regimes. In wages, salaries, and similar regime, the official value went from 6,056,971 to 6,155,456; in the leasing regime went from 547,070 to 693,660; and finally in the other incomes, regime went from 42618.00 to 45000. In the individuals residing abroad without a physical establishment, regime went from 173 to 200 contributors.
