Interesting question! According to The First Fleet Piano (Geoffrey Lancaster, 2015), the usual cost of a new, plain square piano made in London on the English market in the 1780s ranged from 15 to 20 guineas, which Lancaster calls "1/15 of an annual middle-class income"; according to the British National Archive currency converter, this would be $1435-1914. (MeasuringWorth.com puts it somewhat higher, at $2612-3482, although this is the lower end of their estimate - the site is run by professors of economic history who are aware that a simple calculation doesn't take into account the fact that objects and services also change in relative value.) However, a similar piano that was secondhand could be priced between 6 guineas ($573/$1043, respectively) and 10 pounds ($911/$1659), which Lancaster estimates as 1/10 to 1/17 of a lower middle-class income. Meanwhile, higher-end pianos with extensive inlaid decoration could go for about 25 guineas ($2393/$4353).
Last year, the median household income in the United States was estimated at $54,462 by the Census Bureau. The "new, plain square piano" at 1/15 of that annual income would be $3630.80. According to the Pew Research Center, the lower end of the middle class is at 2/3 of the median household income, so $36,308 - the similar used piano would come in at $2135 up to the cost of the new piano, $3630.80.
Just using the Gist Piano Center as a middle-of-the-road retailer, I find that a used upright piano - not the same as a square piano, but similar in the sense that both were space-saving downgrades from the grand piano - in good condition generally ranges from $2999 to $3599 (with very nice used pianos up to $5999). Affordable new pianos today cost around $4000-$7000. So it seems that used pianos represent roughly the same share of the income, while new pianos are a rather larger proportion.
To expand on chocolatepot's answer, pianos today are getting close to valueless (particularly used pianos). With the number of people learning to play piano steadily declining, and the increasing number of people living in smaller and smaller houses, seniors downsizing, and so on, pianos are being given away in North America for nothing. There are entire websites offering free pianos. I work in a music school, and get an offer of a free piano every week. We have more pianos than we need, and turn them all away. This is definitely a newer phenomenon, as pianos have previously been a marker of having more money, but today, people don't put their kids in piano lessons, and with a family of 4 living in a small apartment, it's a big waste of space that a lot of people don't want now.
EDIT Recent article in the New York Times about this: http://www.nytimes.com/2012/07/30/arts/music/for-more-pianos-last-note-is-thud-in-the-dump.html
Which people? When? Where? I'd love to see someone try to tackle this question, but this is an incredible can of worms to open, OP.