Table 2 Results for the centralised solution
From: Devolution and grant-in-aid design for the provision of impure public goods
| Â | Centralised allocation |
|---|---|
Subsidy | \(p\left( 1-\rho _{j}^{C}\right) =z(1+k)\), \(j=1,2\) |
Quantities | \(Q_j^{C} = \frac{1}{2} \left( 1-\frac{p}{\beta } +\frac{(1+k)z}{\beta } \right)\), \(j=1,2\) |
| Â | \(Q^{C}=1-\frac{p}{\beta }+\frac{(1+k)z}{\beta }\) |
Welfare | \(W^{C}=Y-p+\frac{\beta +\left( z_{1}+z_{2}\right) (1+k)}{2} +\left( z-\frac{z_{1}+z_{2}}{2}\right) \frac{p(1+k)-z(1+k)^{2}}{\beta } +\frac{1}{2}\frac{(p-z(1+k))^{2}}{\beta }\) |