@Xeo In **general** (if it's joining sentences), the tense does carry over. Prices are somewhat stable, so both interpretations make sense.
Consider this example: 働きすぎて、体を壊した. (I harmed my body by working too hard). This makes sense only if the working-too-hard took place in the past as well. Compare with the English "by working too hard", which doesn't contain any tense either.