Although an increase of the minimum wage cannot be directly passed on to consumers, it certainly will have indirect effects that reduce consumer welfare.
First, since fewer laborers are now employed, aggregate production will be reduced and overall prices rise, driving down real wages and incomes of consumers.
Second, and perhaps more importantly, the allocation of resources will be distorted and production diverted from most efficient service to consumer demands by what Walter calls “the costs of rearranging things.”
Thus, for example, my favorite Chicago economist Yale Brozen tells the story of visiting middle-income in-laws in Tennessee after a 50% increase in the minimum wage in the mid 1950s and finding that they suddenly had hired a maid and gardener. The reason was that the increased minimum wage made the local shellfish cannery unprofitable causing it to close down and lay off its mainly black and female labor force, many of whom then shifted to the domestic help sector,which was uncovered by the minimum wage, driving down wage rates in this already low-paying sector even further to the point where they became affordable to middle-income consumers. From the viewpoint of consumer welfare, the minimum wage increase resulted in a more abundant supply of lower-valued domestic services at the expense of greater scarcity of higher-valued canned seafood products.
Distortions of the allocation of capital goods from higher to lower valued uses were also visible in the postwar years when increases in the minimum wage drove urban real estate owners to (prematurely) fire elevator operators and replace manually operated elevators with automatic elevators built, installed and serviced by skilled union laborers and to fire movie ushers and replace them with automatic lighting, again installed and serviced by union workers. Consumers suffered because the scarce capital required for this automation was prematurely and uneconomically withdrawn from higher-valued uses.