"The true cost of minimum wage labor" is a nebulous concept because it can only be computed to fall within a range and it differs from one section of the country to another. When applied to minimum wage workers it is essentially the cost of housing, feeding, clothing, transporting and providing medical and dental care for a minimum wage worker. It is higher than the government's poverty income for an adult worker living alone, because that income calculation omits subsidies such as food stamps, public housing and medicaid; consequently the value of those subsidies must be included when computing the true cost of labor. The concept of true cost of labor applies to all wage workers, not just adult workers.
When wages drop below the true cost, someone, or some entity, must making up the difference. For the teenage worker living at home it might be the workers family, for an adult worker it might be the local, State, and Federal government, various welfare organizations,etc.
Currently @ 7.25$/hr the minimum wage is well below the true cost of labor in all sections of the country and places these workers at the government's official poverty level for a one person household. These minimum wage workers are being subsidized. In effect, the tax payer is indirectly subsidizing employers that hire minimum wage workers. To end this subsidy, and create a more honest labor market, the minimum wage must be raised to somewhere between 10 and 11 dollars an hour. Even then, in some sections of the country, employers will find it difficult to hire at the minimum, and the market will require still higher wages. Nowhere in the U.S.A., however, should the wage be below $10/hour to avoid taxpayer subsidy of employers. That's a very safe minimum in the sense that we can be certain that if wages drop below that level extensive subsidies will be involved. However the wage would have to be raised considerably above that level to assure that there are no subsidies.
In the today's dollars, the minimum wage in the mid 1960's was approximately $10.50/hr. That would likely be a reasonable level in many sections of the country today.