RDP 2009-01: Currency Misalignments and Optimal Monetary Policy: A Re-examination Equation (B34)

\begin{matrix} υ_{t} - υ_{t}^{\max} = [Ω + (1 - σ) (c_{y}^{2} - c_{y})] {({\tilde{y}}_{t} - {\tilde{y}}_{t}^{*})}^{2} - (\frac{σ + ϕ}{2}) ({\tilde{y}}_{t}^{2} + y_{t}^{* 2}) \\ - \frac{ξ}{2} (σ_{p t}^{2} + σ_{p * t}^{2}) + 2 Ω ({\bar{y}}_{t} - {\bar{y}}_{t}^{*}) ({\tilde{y}}_{t} - {\tilde{y}}_{t}^{*}) \\ + (1 - σ) (2 (c_{y}^{2} - c_{y}) - (ν - 1) c_{y} + \frac{ν}{2}) ({\bar{y}}_{t} - {\bar{y}}_{t}^{*}) ({\tilde{y}}_{t} - {\tilde{y}}_{t}^{*}) + o (‖ a^{3} ‖) . \end{matrix}