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Table 7 Numerical simulation

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