In Australia the legal concept is assigned to "The Sunshine Harvester Case" of 1907. (Ex parte H.V.McKay, Commonwealth Court of Conciliation and Arbitration 1907)
The Sunshine Harvester factories were major employers in Victoria (and in Australia) where they built a range of agricultural machinery. In 1907, H.V.Mckay, the owner, applied to the Arbitration Court for exemption on tariffs on his machinery under the Excise Tariff Act 1906, which allowed an exemption from tariffs for Australian companies which paid their workers "fair and reasonable wages". There was at that time no legal definition for a "fair and reasonable wage" The Agricultural Implements Society (a union representing McKay's workers,) opposed McKay's application on the basis that the wages he paid for an unskilled labourer of 36 shillings a week were not a reasonable wage.
There being no definition of a reasonable wage, Justice H.B.Higgins took the view that it must mean a wage, not linked to the profits earned by the employer, on which a worker could provide for the frugal necessities of life for himself, a wife, and three children. That is, a "living" or "family" wage. He took evidence from individual landlords, butchers, etc. and the wives of working men to ascertain the minimum frugal costs of maintaining a family. He set this at 42 shillings a week or 7 shillings a day and in Australia this formed the basis of the calculation of later "minimum wage" requirements.
It should be noted that in Australia "minimum wage" legislation targeted the concept of a "family wage" for a long time. For instance a junior wage could be paid which was less than the minimum wage. For instance single men under 21 tears old and women could be paid trainee wages, which typically would increase each year until the full wage would be paid at maturity (or if a man married before turning 21) and the Australian Defence Force still pays a "Trainee Dependant Allowance", formerly "Married Trainee's Allowance" which increases the trainee soldier rate of pay to the base rate if the soldier has a spouse or children.