Low oil pressure

I own a 1988 VW Rabbit Cabriolet convertible. Lately my low pressure oil
warning light has been flashing after the car has been driven a few miles
and the oil thins out. The oil pressure gage on the center console verifies
that the oil pressure is low, because when the oil is still cold the
pressure is normal at idle (around 1 on the gage), but after it warms up the
pressure gage reads less than 0.5 at idle and the warning light begins
flashing. While driving along with the oil cold, the gage reads almost 5,
but after warm-up it is less than 2 while driving and the warning light does
not flash until I come to a stop.

I tried using a thicker oil (SAE 40), but it made no difference.

The car has over 270,000 miles on it, but it still has plenty of pep and
there is no unusual engine noises (I can easily get it up past 70 MPH and
there is no visible smoke coming out the exhaust pipe). This makes me think
that the problem may just be a bad oil pump rather than bad crankshaft
bearings. What do you think?

Anyway, I am having a new oil pump installed today, along with new oil
pressure sensors. Hopefully that will fix the problem. I'll post the
results.