# Maximization problem FOC and Euler equation

Can someone please help me with the Lagragian and the derivation of the following objective function ? Beneath I provide the objective function, the constraint and the Euler equation that results from the maximization. Your help is very much appreciated !!

Thanks !

• The author mentions before the Euler equation that the household takes the public good as given! I would like to know is this a result from the derivation ? I.e. after the derivation we are left only with the private consumption c ? Or it means that from the beginning we consider the public consumption and constant ? – Kamel Ismaël May 8 at 12:49