A B757-200 flight crew suffered a TCAS RA with a light aircraft while on a dogleg visual approach to Runway 19 at JAC.

Narrative

While on a visual approach to JAC Runway 19 in VFR conditions; we got a TCAS RA to climb due to a small student plane heading directly towards us that was supposed to be on downwind. We were on a 3 mile slight dogleg to final and cleared to land by the Tower. The small plane was instructed to follow us for landing and reported us in sight. We did not see the small plane and notified the Tower that we did not see the plane but we could see the airport. We responded with an immediate go around [in response] to the TCAS Climb RA. The Tower should have given better instructions to the small plane with the inexperienced pilot to stay farther east of the airport while on downwind; in my opinion. The Tower just cleared both planes for a visual and never gave any subsequent instructions to either plane to avert the near midair. While going around we also asked the Tower for a missed approach altitude and the Controller did not provide nor offer any altitude; just an instruction to enter a downwind for another approach.