re: Paper Tray - Deisgn Q

I agree with your comment as to appearance and economy of wood usage. With a design that expands along the width you will need to figure a way to allow the back rail to move at its ends. Basically anywhere two boards join that have perpendicular grain, there will need to be provisions for movement. This is where you could slot the back rail and glue in the panel at the center. Affix the back rail to the sides and have the slots in the sides deep enough to contain and hide the movement. 
Some method will be needed at the front to keep the panel and sides inline, possibly a dowel pin in through the bottom, through a slotted hole in the panel. Alternatively you also might be able to "hide" a thin cross rail for the front underneath which is attached solidly to the sides, basically a full-frame design.

This project is small enough that you might not need to worry so much, a lot depends on the wood species and the environment where the project will live.