Problem with taper object on bezier curves

I am attempting to make a hose/pipe object using a pair of bezier curves (as seen in the “Variable Diameter” portion about half-way down here). I created a curve (in the top view so the y axis is consistent), then created another curve that was just a straight line. I applied rot/scale/pos to both, made sure the directions were the same and that the parent vertex was on the left for both.
I gave the curve-that-will-be-my-shape a bevel depth, a smoothing modifier, and then assigned the taper object. The problem is that the generated mesh does not taper in a way that matches the desired shape.
Please help me understand what I am doing wrong as this has been very frustrating. I used the exact same method yesterday with no problems.
Here is my blend file: