Just as a comparison, in 1960 the minimum wage was $1/hr, the median family income was $5.6K, and the average detached house cost ~$19K. So 19,000 hours of minimum wage would get you the median house (not the cheapest) and a full-time minimum wage worker earned about 36% of what the median family income was.
If you use those ratios using today's values, you'd get the following:
Median US house price is ~$430K, so 1/19000 of that is $22.50/hr
Median family income is ~$85K, so 36% of that would mean a minimum wage of ~$15/hr.
So yeah, a $15/hr minimum wage is reasonable by historical standards. True, if you apply those ratios to the poorest states, you end up down in the $7-10/hr range, but that disparity existed back then too, but the federal minimum wage was still that high. For instance, in the southern US minimum wage was equivalent to about 50% of the median family income in 1960.
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