RDP 2009-01: Currency Misalignments and Optimal Monetary Policy: A Re-examination Equation (B5)

\begin{array}{l} υ_{t} = [{\bar{c}}_{t} + {\bar{c}}_{t}^{*} - {\bar{n}}_{t} - {\bar{n}}_{t}^{*} + \frac{1 - σ}{2} ({\bar{c}}_{t}^{2} + {\bar{c}}_{t}^{* 2}) - \frac{1 + ϕ}{2} ({\bar{n}}_{t}^{2} + {\bar{n}}_{t}^{* 2})] \\ + {\tilde{c}}_{t} + {\tilde{c}}_{t}^{*} - {\tilde{n}}_{t} - {\tilde{n}}_{t}^{*} + \frac{1 - σ}{2} ({\tilde{c}}_{t}^{2} + {\tilde{c}}_{t}^{* 2} + 2 {\bar{c}}_{t} {\bar{c}}_{t} + 2 {\bar{c}}_{t}^{*} {\tilde{c}}_{t}^{*}) \\ - \frac{1 + ϕ}{2} ({\tilde{n}}_{t}^{2} + {\tilde{n}}_{t}^{* 2} + 2 {\bar{n}}_{t} {\tilde{n}}_{t} + 2 {\bar{n}}_{t}^{*} {\tilde{n}}_{t}^{*}) + o (‖ a^{3} ‖) \end{array}