Dollar pens are so called because they cost $1.00 in their time.  Dollar pens are distinguished by their two hole clip and flat top and barrel appearance.  Correctly termed, models consisted of B (full sized), A (slender), and H (demi) and ran from 1934 through 1942.

This is a very rare model B demonstrator. They don't come much harder to find than this. The black on the cap is the inner cap.

These are uncommon solid plastic dollar pens ca. 1934.  These have the earliest of the two hole clip design where the clips tapers in towards the very top of the cap.  Also, note the cap band is extremely close to the cap lip like in Hard Rubber pens and V clips of the period.  The levers are of the early spear style.  These plastics do not fare well when exposed to water and have a tendency to warp.  This inferior plastic was only used for a short period of time until better plastics were developed.  The Blue pen actually has a round sticker on the end of the barrel marking it as a model BTL.  These pens also came with later 1938 style clips as can be seen below.

This is a BHR model B dollar set with the 1934 clip. This one has the earlier spear type lever.  The pencil is the first model Esterbrook ever made, the model P in BHR, ca. 1934. Sometimes harder to find than the pens of the era.

This is a model A with a 1938 clip, a thinner sized pen.  While most BHR pens of this period sport the earlier spear type lever, this has the later flat ended lever as seen on its plastic cousins.

This set has a ca. 1938 clip and higher placed cap band.