A Big Mac costs $$4\mathrm{.}00$ in the United States and $7\mathrm{.}00$ Euros in Germany. $$If the exchange rate is $$1=2,$ then purchasing power parity predicts the U$.$S$.$ dollar is $[$ Select $]["$undervalued$",$ "overvalued"$].$ In the long$-$run, the demand for U$.$S$.$ dollars will $[$ Select $]["$increase$",$ "remain unchanged", "decrease"$]$ and the value of the U$.$S$.$ dollar will $[$ Select $]["$depreciate$",$ "appreciate", "remain unchanged"$].$