Given that food and medicine make up a large portion of spending, I think we'll see something more like, "some prices go up and others go down."
Another big chunk is housing, which as far as I know, shouldn't expect much difference in supply or demand in the short term, though demand may increase (at least as measured by square footage) if people are staying home for a long enough time. That may be countered by the reduction in demand for real estate by businesses, though zoning will probably limit the short term effects that has on housing.