## 4 Results and Discussion
### Phase 6--Development of Geographical Maps of Economic Benefits
#### 4.6.2 Isoprofit Maps
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Minimum and Maximum Positive Break-Even Incentive Value**} \\ \hline \multirow{3}{*}{**Macro-Area**} & \multicolumn{2}{c}{**Central Area**} & \multicolumn{2}{c}{**Semi-Central Area**} & \multicolumn{2}{c}{**Peripheral Area**} \\ \cline{2-7}  & **Minimum** & **Maximum** & **Minimum** & **Maximum** & **Minimum** & **Maximum** \\  & **Value** & **Value** & **Value** & **Value** & **Value** & **Value** \\ \hline \multirow{3}{*}{North-Western Italy} & La Spezia & Asti & Imperia & Cuneo & \begin{tabular}{c} Monza e \\ Brianza \\ 11\% \\ \end{tabular} & \begin{tabular}{c} Turin \\ 113\% \\ \end{tabular} \\ \hline \multirow{3}{*}{North-East Italy} & Venice & Gorizia & Piacenza & Belluno & Treviso & \begin{tabular}{c} Reggio \\ Emilia \\ 96\% \\ \end{tabular} \\  & 4\% & 65\% & 2\% & 89\% & 26\% & \begin{tabular}{c} Rieti \\ 97\% \\ \end{tabular} \\ \hline \multirow{3}{*}{Central Italy} & Fermo & Ascoli Piceno & Fermo & Ascoli Piceno & ROME & \begin{tabular}{c} Rieti \\ 10\% \\ \end{tabular} \\  & 1\% & 78\% & 4\% & 61\% & 10\% & \begin{tabular}{c} Vibo \\ Valentia \\ 91\% \\ \end{tabular} \\ \hline \multirow{3}{*}{Islands} & Salerno & Catanzaro & Brindisi & Vibo Valentia & Lecce & \
\begin{tabular}{c} Vibo \\ Valentia \\ 91\% \\ \end{tabular} \\  & 7\% & 111\% & 21\% & 90\% & 3\% &
\begin{tabular}{c} Caltanissetta \\ 122\% \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Minimum and maximum positive value of the break-even incentive for each macro-area (private investor’s profit margin = 15%). than 110% [1-110%] able to make the initiative sustainable has been observed; (ii) for a profit margin of 12%, in 52% of the central areas, in 76% of the semi-central areas, and in 89% of the peripheral areas of the Italian provincial capitals, an incentive less than 110% [1-110%] is required for the financial sustainable intervention; (iii) for a profit margin of 15%, in 59% of the central areas, in 82% of the semi-central areas, and in 89% in the peripheral areas of the Italian provincial capitals, an incentive less than 110% [1-110%] is required for the financial sustainable intervention; (iv) for a profit margin of 17%, in 64% of the central areas, in 82% of the semi-central areas, and in 91% of the peripheral areas, a public incentive less than 110% [1-110%] has been found able to ensure the intervention convenience for the private; (v) for a profit margin of 20%, in 67% of the central areas, in 87% of the semi-central areas, and in 93% of the peripheral areas of the Italian provincial capitals analyzed, a percentage incentive less than 110% [1-110%] has been estimated to guarantee the condition of minimum operation convenience. In Figure 5, the sensitivity analysis graph obtained in correspondence of five percentage profit margins considered--10%, 12%, 15%, 17%, and 20%--for the central area of the Italian provincial capitals considered (the same typology of graph for the semi-central and peripheral areas of the provincial capitals considered is included in Supplementary Files in Figures S22 and S23). In particular, in the graphs, a dotted horizontal line corresponding to the current incentive provided for by the legislation equal to 110% and five dotted vertical lines corresponding to the incentive percentage equal to 0% have been included. In this sense, it should be noted that for the central urban area for one provincial capital in correspondence of the profit margin of 10%, for one provincial capital in correspondence of the profit  
Figure 5: Sensitivity analysis obtained in correspondence of five percentage profit margins considered (10%, 12%, 15%, 17%, and 20%) for the central area of the Italian provincial capitals considered. margin of 12%, for two provincial capitals for the profit margin of 15%, for two provincial capitals in correspondence of the profit margin of 17%, and for two cities for the margin equal to 20%, an incentive percentage greater than 110% is required.