Is there a need to display arrows in the drop-down fields in the mobile application?

We build a simple mobile app form with 2 drop-down fields and one text input field for iOS and Android platform.

My question is should we definitely use a small arrow icon at the end of field that designed as drop-down for use one of several values for better UX scenario? Seems that this arrow eats up some space for placeholder of value that can be choose.

Is there any useful use at all for using the arrow for the drop-down fields in a mobile application, given the small screen size of some devices?