From: Devolution and grant-in-aid design for the provision of impure public goods
 | \(p^1_u\) | \(p^2_u\) | \(Q_{1}\) | \(Q_{2}\) | Q | t | \(\tau _{1}\) | \(\tau _{2}\) | \(t+\tau _{1}\) | \(t+\tau _{2}\) | W |
---|---|---|---|---|---|---|---|---|---|---|---|
\(Y=100\); \(p=80\); \(\theta =1.1\); \(\beta =80\); \(z_{1}=25\); \(z_{2}=35\); \(k=0.5\); \(z=30\) | |||||||||||
 FB | 33.250 | 27.750 | 0.311 | 0.342 | 0.653 | 0.324 | 0.000 | 0.000 | 0.324 | 0.324 | 118.828 |
 C | 35.000 | 35.000 | 0.301 | 0.301 | 0.602 | 0.271 | 0.000 | 0.000 | 0.271 | 0.271 | 112.656 |
 F | 52.500 | 41.500 | 0.202 | 0.264 | 0.466 | 0.000 | 0.111 | 0.203 | 0.111 | 0.203 | 117.239 |
 Equi | 38.017 | 38.017 | 0.284 | 0.284 | 0.568 | 0.112 | 0.126 | 0.126 | 0.238 | 0.238 | 118.639 |
 FR | 39.667 | 39.667 | 0.275 | 0.275 | 0.549 | 0.091 | 0.131 | 0.131 | 0.222 | 0.222 | 118.614 |
\(Y=100\); \(p=80\); \(\theta =1.1\); \(\beta =80\); \(z_{1}=25\); \(z_{2}=35\); \(k=0.75\); \(z=30\) | |||||||||||
 FB | 23.625 | 20.875 | 0.366 | 0.381 | 0.747 | 0.432 | 0.000 | 0.000 | 0.432 | 0.432 | 124.574 |
 C | 27.500 | 27.500 | 0.344 | 0.344 | 0.688 | 0.361 | 0.000 | 0.000 | 0.361 | 0.361 | 117.227 |
 F | 52.500 | 41.500 | 0.202 | 0.264 | 0.466 | 0.000 | 0.111 | 0.203 | 0.111 | 0.203 | 120.996 |
 Equi | 30.775 | 30.775 | 0.325 | 0.325 | 0.650 | 0.193 | 0.127 | 0.127 | 0.320 | 0.320 | 124.148 |
 FR | 33.250 | 33.250 | 0.311 | 0.311 | 0.622 | 0.154 | 0.137 | 0.137 | 0.291 | 0.291 | 124.090 |
\(Y=100\); \(p=80\); \(\theta =1.01\); \(\beta =80\); \(z_{1}=10\); \(z_{2}=45\); \(k=0.5\); \(z=27.5\) | |||||||||||
 FB | 47.175 | 29.500 | 0.208 | 0.317 | 0.526 | 0.229 | 0.000 | 0.000 | 0.229 | 0.229 | 111.641 |
 C | 38.750 | 38.750 | 0.260 | 0.260 | 0.520 | 0.215 | 0.000 | 0.000 | 0.215 | 0.215 | 110.635 |
 F | 69.900 | 34.550 | 0.067 | 0.286 | 0.354 | 0.000 | 0.014 | 0.260 | 0.014 | 0.260 | 109.964 |
 Equi | 59.884 | 59.884 | 0.129 | 0.129 | 0.259 | 0.043 | 0.009 | 0.009 | 0.052 | 0.052 | 110.595 |
 FR | 61.273 | 61.273 | 0.121 | 0.121 | 0.242 | 0.034 | 0.012 | 0.012 | 0.045 | 0.045 | 110.575 |
\(Y=100\); \(p=80\); \(\theta =1.01\); \(\beta =80\); \(z_{1}=10\); \(z_{2}=45\); \(k=0.75\); \(z=27.5\) | |||||||||||
 FB | 35.813 | 26.975 | 0.278 | 0.333 | 0.611 | 0.300 | 0.000 | 0.000 | 0.300 | 0.300 | 115.226 |
 C | 31.875 | 31.875 | 0.303 | 0.303 | 0.606 | 0.291 | 0.000 | 0.000 | 0.291 | 0.291 | 114.475 |
 F | 69.900 | 34.550 | 0.067 | 0.286 | 0.354 | 0.000 | 0.014 | 0.260 | 0.014 | 0.260 | 111.453 |
 Equi | 54.876 | 54.876 | 0.160 | 0.160 | 0.321 | 0.080 | 0.000 | 0.000 | 0.081 | 0.081 | 112.872 |
 FR | 56.959 | 56.959 | 0.148 | 0.148 | 0.295 | 0.061 | 0.007 | 0.007 | 0.068 | 0.068 | 112.827 |