## 4 Results and Discussion
### Phase 6--Development of Geographical Maps of Economic Benefits
#### 4.6.2 Isoprofit Maps
In addition, assuming a profit margin of 10%, for no intervention carried out in the central areas of the provincial capitals a higher incentive compared to that currently used is needed. With reference to the number of Italian provincial capitals in which the financial convenience of the energy efficiency intervention in the central area is ensured, on the left of the vertical lines the graph shows the number of cities for which no public incentive is required to ensure the condition of minimum convenience for an investor, and on the right, the number of provincial capitals for which it is necessary to introduce a fiscal measure in terms of gradually increasing subsidy from 1% to 139%, i.e., the maximum percentage found. With reference to the central area, the number of Italian provincial capitals for which a situation of convenience has been verified without the need for the Superbonus mechanism for all ordinary profit margins of the investor from 10% to 20% is equal to two hundred and sixty out of total of five hundred (by taking into account five margin profits for 110 provincial capitals). In particular, for the defined isoprofit percentage of 10% for 59 provincial capitals, of 12% for 52 provincial capitals, of 15% for 43 provincial capitals, of 17% for 38 provincial capitals, of 20% for 34 provincial capitals, the convenience of the intervention for the private operator has been ensured. Exclusively for eight provincial capitals (by considering five margin profits for 110 provincial capitals), the financial threshold capable of guaranteeing the condition of minimum convenience higher than 110% has been detected. For the semi-central area, the sustainability condition of the energy efficiency investment compared to the different profit margins of an ordinary entrepreneur without the need to the 110% incentive has been verified in 105 provincial capitals (with reference to five margin profits for 110 provincial capitals). In particular, in the semi-central areas of nine provincial capitals, a lack of need for any incentive (<0%) for all ordinary profit margins of the investor from 10% to 20% has been recorded, whereas the limit of 110% being exceeded has been attested to in nine cases for which it is necessary to provide a percentage of the incentive higher than that currently implemented. For 436 out of total 500 cities, the sustainability with the use of a public funds between 1% and 110% has been obtained, and for 11 provincial capitals, a higher than 110% incentive need has been determined. Finally, for the peripheral areas of five provincial capitals, there is a financial feasibility condition to invest in an energy improvement intervention without Superbonus: specifically, the convenience has been certified even without any tax incentive (<0%) for 47 cities. Moreover, for 492 provincial capitals, the sustainability with the use of a public funds between 1% and 110% has been verified, and for 11, a higher than 110% incentive need has been determined. Furthermore, with reference to the three urban areas considered (central, semi-central, and peripheral), the results obtained in terms of the number of provincial capitals found in correspondence of the different percentage profit margins are grouped. Therefore, seven fiscal incentive clusters necessary to guarantee the financial feasibility of the initiative (<0%, 0%, 1-24%, 25-49%, 50-74%, 75-110%, and >110%) have been considered, and, for each profit margin selected, the number of provincial capitals is reported. In particular, it should be noted that for the central area, a significant presence of cities in the cluster < 0% for which no tax incentive would be activated has been defined. The graphs developed for the central areas (Figure 6), for the semi-central areas (Figure 7), and for the peripheral ones (Figure 8) of the provincial capitals analyzed have been reported below.