The current federal minimum wage for workers in covered sectors is $7.25 an hour. As you suggest, raising the minimum wage to $15 an hour would motivate many workers who were already being paid $15 in the old regime to seek employment in less demanding jobs that would now pay the same rate. To retain workers in more skilled, physically or mentally demanding, dangerous, or unpleasant jobs, employers would need to adjust wages upward to some degree. Still, couriers should not anticipate dramatic increases in their wages following a minimum wage increase. Relatively few couriers would be able to find preferred work in the jobs directly affected by the mandated wage increase.

Much of the public discourse implicitly assumes that cashiers worth at least $7.25 an hour to an employer are also worth $15 an hour. This is a dangerous assumption. There is a tradeoff: while many cashiers would receive a significant raise, others would be let go or have their hours reduced. To justify the higher mandated wages, employers would hire a smaller group of cashiers to individually serve more customers per hour. Some would cut back store hours to serve customers only during the most profitable times. Less profitable owners might simply go out of business if forced to pay $15 per hour.

In your example, it is likely that the number of cashiers would decline dramatically as employers replaced them with automated checkout systems. The relative quality of the remaining grocery store cashiers would rise as store owners started drawing from a larger pool of applicants, and the responsibilities of the remaining cashiers would increase to justify the added expense.

Among other unintended consequences, higher production costs would raise grocery prices for all customers, including those living in poverty. The excess supply of cashiers would also make it easier for employers to be discriminatory in their hiring practices if so inclined.

Historically, the highest federal minimum wage in real terms was $10.69 in 1968, converted to current dollars. If the federal minimum wage were raised to $15 an hour (the rate proposed by Senator Bernie Sanders of Vermont and recently enacted in Seattle, to be phased in over time), it would be 40% higher than it has ever been.

In 1938, the Fair Labor Standards Act established a federal minimum wage of 25¢ an hour, or about $4.20 in current dollars. At the time, the average hourly wage rate in the U.S. was about 63¢ per hour, or about $10.50 in current dollars. Less than 1% of the workforce was directly affected by the 25¢ mandate. But this same 25¢ mandate was also introduced in Puerto Rico, where wages were much lower – e.g., about 12¢ per hour in fruit canning and 18¢ per hour in apparel. According to the New York Times (October 24, 1938), both employers and labor groups in Puerto Rico agreed that the minimum wage law would end employment for about 120,000 workers. It was estimated that the Puerto Rican unemployment rate approached 50% in the first year of the mandate. 1 Even if these numbers are significantly overestimated, they should give pause to the notion that minimum wage hikes do nothing but make life easier for workers: first, they need to stay employed.

In the U.S., prevailing wages tend to be lower in the South and West than in the industrialized Northeast, so minimum wage increases would have the greatest bite in such states. They would also have the greatest bite in industries that have high concentrations of low wage workers, such as in wholesale and retail trade and in the hospitality and leisure industries.
LINK