Table 3 Results for devolution with no matching grant
From: Devolution and grant-in-aid design for the provision of impure public goods
“Pure” devolution | |
|---|---|
Subsidy | \(p\left( 1-\nu _{j}^F\right) =\theta z_{j}\), \(j=1,2\) |
Quantities | \(Q_j^{F}=\frac{1}{2} \left( 1-\frac{p}{\theta \beta } +\frac{ z_j}{\beta }\right)\), \(j=1,2\) |
\(Q^{F}=1-\frac{p}{\theta \beta }+\frac{z_{1}+z_{2}}{2\beta }\) | |
Welfare | \(W^{F}=Y-p+\theta \left( \frac{\beta }{2}+\frac{(z_{1}+z_{2})(1+k)}{2}\right) +\frac{p^{2}-(z_{1}+z_{2})(1+k)p\theta }{2\beta \theta } +\theta \, \frac{z_{1}^{2}+4kz_{1}z_{2}+z_{2}^{2}}{4\beta }\) |