$$% \text{\$} \text{€} \text{₩} \text{￥} % \Delta \left( \right) \dfrac{}{} \dfrac{\dot{E}}{E} = \pi^{US}_t - \pi^{EU}_t$$ $$\dfrac{\left(\dfrac{\dot{M_{US}}}{M_{US}}\right)}{\left(\dfrac{\dot{L_{EU}}}{L_{EU}}\right)-\left(\dfrac{\dot{Y_{US}}}{Y_{US}}\right)}-\dfrac{\left( \dfrac{\dot{M_{EU}}}{M_{EU}} \right)}{\left(\dfrac{\dot{L_{EU}}}{L_{EU}}\right)-\left(\dfrac{\dot{Y_{EU}}}{Y_{EU}}\right)} \\\ \left( \dfrac {\dot{M_{US}}} {M_{US}} \right) - \left( \dfrac {\dot{Y_{US}}} {Y_{US}} \right) - \left[ \left( \dfrac {\dot{M_{EU}}} {M_{EU}} \right) - \left( \dfrac {\dot{Y_{EU}}} {Y_{EU}} \right) \right] \\\ \left(\dfrac{\dot{M_{US}}}{M_{US}}\right)-\left(\dfrac{\dot{M_{EU}}}{M_{EU}}\right)-\left[\left(\dfrac{\dot{Y_{US}}}{Y_{US}}\right)-\left(\dfrac{\dot{Y_{EU}}}{Y_{EU}}\right)\right]$$ $$\left( \mu_{US} - \mu_{EU} \right) - \left( g_{US} - g_{EU} \right) \left(\mu_{US}-\mu_{EU}\right)-\left(g_{US}-g_{EU}\right)$$ $$E_{\text{\$/€}} = c \times \dfrac { \dfrac {M_{US}} {M_{EU}} } { \dfrac {L\left(R_\text{€}, Y_{US} \right)} {L\left(R_\text{€}, Y_{US} \right)} }$$ $$E_{\text{\$/€}}=c\times\dfrac{\dfrac{M_{US}}{M_{EU}}}{\dfrac{L\left(R_\text{€},Y_{US}\right)}{L\left(R_\text{€},Y_{US}\right)}}$$ $$E_{\text{\$/€}}=c\times \left( \dfrac{\dfrac{M_{US}}{\bar{M_{EU}}}}{\dfrac{L\left(R_\$ (\Uparrow),\bar{Y_{US}}\right) (\Downarrow)}{L\left(\bar{R_\text{€}},\bar{Y_{EU}}\right)}} \right)(\Uparrow)$$