In electrochemical reaction of $Cu + Mg^{2+}$, the metal displacement will not take place.
Displacement reactions occurs when a metal from the electrochemical series is mixed with the ions of metal lower down in the series. In the electrochemical series $Mg$ is placed above $Cu$. Hence, metal displacement reaction won’t occur in $Cu + Mg^{2+}$. In $Pb + Ag^+$ and $Zn + Cu^{2+}$, lead and zinc are more reactive than silver and copper, hence they can displace silver and copper respectively from their salt solution