Utopia, you are standing in it!

What if minimum wage rates could somehow be tied to specific locations as suggested by former White House economist Jared Bernstein puts it in an essay in the New York Times:

When we adjust a national minimum wage of $10.10 for regional differences, these are the amounts you’d need to have the same buying power: $11.94 in Washington, D.C., and $11.40 in California, but only $8.90 in Alabama and $9.08 in Kansas.

And of course, prices vary within states as well. In the New York City area, it would take $12.34 to meet the national buying power of $10.10; upstate around Buffalo, you’d need only $9.47. In the Los Angeles area, it would take $11.94; go up north a bit to Bakersfield, where prices are closer to the national average, and it’s $9.83.

To repeat what George Stigler said on the unsuitability of a nation-wide minimum wage in 1946 when there was monopsony, and therefore a small minimum wage increase is less likely to result in a reduction in employment:

If an employer has a significant degree of control over the wage rate he pays for a given quality of labour, a skilfully-set minimum wage may increase his employment and wage rate and, because the wage is brought closer to the value of the marginal product, at the same time increase aggregate output…

This arithmetic is quite valid but it is not very relevant to the question of a national minimum wage. The minimum wage which achieves these desirable ends has several requisites:

1. It must be chosen correctly… the optimum minimum wage can be set only if the demand and supply schedules are known over a considerable range…

2. The optimum wage varies with occupation (and, within an occupation, with the quality of worker).

3. The optimum wage varies among firms (and plants).

4. The optimum wage varies, often rapidly, through time.

A uniform national minimum wage, infrequently changed, is wholly unsuited to these diversities of conditions

A smarter federal minimum wage is a federal minimum wage of zero. Let each state and city set a minimum wage in accordance with its own economic conditions and the blackboard economics of monopsony and competition in the labour market.

As soon as you concede that there is not one single national labour market, other concessions must be made. This slippery slope includes that the monopsony power of employers might vary from state to state, city to city, and local labour market from local labour market.

Even a state or city minimum wage  regulator  would have to pretend to know an immense amount of information about the labour market with most of this information in a tacit form that cannot be summarised in statistics or other decision aids for regulators. As Hayek reminded in his classic in 1945 on The Use of Knowledge in Society:

the fact that the sort of knowledge with which I have been concerned is knowledge of the kind which by its nature cannot enter into statistics and therefore cannot be conveyed to any central authority in statistical form.

The statistics which such a central authority would have to use would have to be arrived at precisely by abstracting from minor differences between the things, by lumping together, as resources of one kind, items which differ as regards location, quality, and other particulars, in a way which may be very significant for the specific decision.

It follows from this that central planning based on statistical information by its nature cannot take direct account of these circumstances of time and place and that the central planner will have to find some way or other in which the decisions depending on them can be left to the "man on the spot."