# RDP 9502: Price Stickiness and Inflation Equation (7)

$\begin{array}{l}\Delta p\left(SDS\right)=\mathit{0}.5\left[\underset{{\theta }_{\mathit{0}}=\underset{_}{\theta }}{\overset{\overline{\theta }}{\int }}\underset{{\theta }_{\mathit{1}}=-\infty }{\overset{\infty }{\int }}\left(2\pi +{\theta }_{\mathit{0}}+{\theta }_{\mathit{1}}\right)d\Phi \left({\theta }_{\mathit{1}},SDS\right)dF\left({\theta }_{\mathit{0}}\right)\\ +\left(\mathit{1}-F\left(\overline{\theta }\right)+F\left(\underset{_}{\theta }\right)\right)\underset{{\theta }_{\mathit{1}}=-\infty }{\overset{\infty }{\int }}\left(x+\pi +{\theta }_{\mathit{1}}\right)d\Phi \left({\theta }_{\mathit{1}},SDS\right)\\ +\underset{{\theta }_{\mathit{1}}=-\infty }{\overset{\underset{_}{\theta }}{\int }}\left(\pi +{\theta }_{\mathit{1}}-x\right)d\Phi \left({\theta }_{\mathit{1}},SDS\right)+\underset{{\theta }_{\mathit{1}}=\overline{\theta }}{\overset{\infty }{\int }}\left(\pi +{\theta }_{\mathit{1}}-x\right)d\Phi \left({\theta }_{\mathit{1}},SDS\right)\right].\end{array}$