Marginal Utility

Before continuing, it seems sensible to define what is implied by a job that pays minimum wage. To do that, we need to consider the reason on would offer only a minimum wage for a job, remembering Samwick’s precondition that the EITC serves as a “safety net” for potential workers.

A minimum-wage job, definitionally, must be one in which the employer either (1) expects a high turnover (since any potential employee can achieve at least the same compensation doing any other job) or (2) is deliberately offering the position to someone at a monetary loss in exchange for some other compensation.

I believe we can safely stipulate that the second is, definitionally, a poor business practice to the extent that it deprives the firm of some assets. (Exception noted for the case of a single employer/owner, who is depriving only him or her self—but even the special case is definitionally not an optimal use of resources.)

That leaves the assumption that the job have a high employee turnover ratio, which may be a significant business expense in itself because the attendant transaction costs, both on a time and a monetary basis. Hiring people costs money, both directly (interviewing, offering, rejection letters) and indirectly (accounting adjustments, withholding and payment of taxes, benefits if any).

For instance, Wal-Mart's employee turnover ratio is significantly higher than that of Costco, which leads to real bottom-line results:

Costco offers far better than average health care and family leave policies as well. The tangible financial results to date include turnover at just one-third of the industry average, 7 percent labor costs versus an industry average of 16 percent, 2003 sales of $34.4 billion across 312 stores against $32.9 billion for Sam's Club's 532 stores, and sales by square foot of $112 million versus $63 million for Sam's Club. Perhaps most telling, Costco's employee theft ratio is a tenth of the industry average—this alone saves it millions of dollars each year.

Again, it is useful to define the margin. Mr. Samwick, for instance, will not see his own compensation at Dartmouth directly affected by a minimum wage increase. The immediate effect will be on those jobs paying between approximately $10,300 and $14,500 per year on an annualised basis. Concurrently, there will be an effect (0<coefficient<1) on the jobs currently paying above $14,500 on a declining basis to a certain point. (For the case of simplicity, let us assume the threshold to be $20,000/year, or $10/hour.) The result would be:

1. Person A currently makes minimum wage. Over the next three years, their compensation would rise to $7.25/hour.
   
2. Person B currently makes $12,000 a year. Their compensation must rise to $14,500, and may be fairly presumed to be higher than that at the end of those three years, if only because the job cannot currently be filled by any warm body.
   
3. Person C currently makes $15,000 per year ($7.50/hour). All things being equal, their compensation will rise because the job will be perceived as more valuable than something that only pays $500 more than minimum wage. (At time(0) [now] it is worth $4,700 more than minimum wage.)
   
4. Person D currently makes $20,000 per year ($10/hour). This is likely the end of any residual effect that would be caused by (as opposed to simply being correlated with) the minimum wage increase; their wage may increase by (guessing) 1-3% because of the increases.
   
5. Person E currently makes $25,000 per year. Any increase would not be caused to any significant extent by the minimum wage increase, as $12.50/hour is well away from the margin.
   

The graphic of the above is left as an exercise to the reader.

Mr. Samwick posits that there will be a negative impact on some businesses that have a large dependence on people who make the minimum wage or an amount tied to the minimum wage (e.g., high-school students who may be paid 80% of the minimum--”sub-min”--for certain jobs.

It is here that he does not take his reasoning far enough. Again, let us make some simplifying assumptions:

1. That Businesses A and B compete for the same market
   
2. That each currently has 50% of the market and the same operating costs (i.e., profits are the same).
   
3. That another company, in another market, announces that its redesigned process produced an increase in revenues without increasing operating expenses.
   
4. In that scenario, if Company B adopts the process and Company A does not, do we then conceptually need to compensate Company A? (Ignore, for the moment, Chapter 11 of NAFTA, which does precisely that.)
   

Why would a minimum wage increase—new information in the market—be any different? It cannot be emphasised enough: new information in the market must be managed, and how that information is managed determines how viable the business is.

If the company is EK—makers of the best photo paper in the world, but whose legacy business (and position as the largest user of silver in the U.S., and probably the world) is exposed to new technologies—then the management actions may not be enough. If instead it is the U. S. steel producers of the late 20th century, then the new business model, to some extent, saved the industry. (I say to some extent because a cui bono analysis of the industry reveals that much of the cost of the restructuring was borne by the government and the workers in broken pension contracts. Still, the smaller, more specialised plants that grew from the one-LARGE-size-fits-all model added some value.

An increase in the Federal minimum wage is the same: new information in the market. Adapt or die.

It is perpetually argued by commenters that increases in minimum wages cost jobs (without, one must note, any empirical evidence of same). If we assume a dynamic system—say, the capitalism Andrew Samwick wishes were practiced—we can easily see why this is so.

Employers do not, as a rule, hire people out of the goodness of their heart. Indeed, the business reason to hire any worker is that you expect that he or she will produce more value for you than they will cost. This is why there is an employment process, and the first person to be interviewed does not always get the job.

Businesses survive—or thrive—based on the decisions of their management, including personnel decisions. Assuming an increase in the minimum wage directly affects the worker's compensation, the employer must make a business decision: is that specific person still worth employing?

Remember, Samwick has claimed that the EITC makes a minimum wage unnecessary. (Let us for the moment ignore that the timing of the cash flows might be problematic at best.) So there is no societal harm (based on Samwick's posit) in eliminating or replacing that person.

But hard reality still intervenes. The work has to be done, which means someone will be paid, or have to forego something else, to do it.

The business at that point has one of two choices: it can either pass the extra cost on to the consumer (notably absent from Mr. Samwick's needs-to-be-compensated identification) or it can absorb the cost and cut its gross profit margin.

Let us assume, for the moment, that the business cannot or does not pass the
additional cost onto the consumer; that is, that the business is actually a price-taker, not a price-maker for its goods. Under such a scenario, the business must evaluate its employees based on the new information in the market:

1. Employee A produces $5.50/hour worth of current value. As a business decision, it is relatively easy to look to replace this person with someone (A') at $7.25/hour who is likely to produce more value.
   
   
   
   1. In such a scenario, Employee A', who can now make an acceptable salary, re-enters the workforce, while Employee A either leaves the workforce (with the EITC still as his or her safety net) or finds employment at another firm that can better leverage his or her skills.
      
   
   
2. Employee B produces $7.25/hour worth of current value. In this case, the employer may well decide that transaction costs make retaining that person worth the effort, in which case the gross profit margin remains the same, while the net profit is marginally redistributed to the existing employee. (The firm's after-tax income declines by [1 minus its marginal tax rate] * the change in the employee's
   compensation, or {[1-T_m]*d[Comp]}.)
   
   
   
   1. Should the employer opt for Employee B', the return from the new employee must be greater than the transaction costs for both terminating the current employee and hiring a replacement. This is essentially an option to the employer with a largely-fixed cost.
      
   
   
3. Employee C produces $8.00/hour worth of current value. Again, the employee is likely to be retained, while the firm's net profit margin is reduced by the formula in (2).
   
   
   
   1. Replacing this employee would require finding someone else who willingly takes a minimum wage job but produces at least 75 cents per hour more in value to the firm. Given the definition of a minimum wage job, this seems unlikely. While the probability is admittedly not zero, the search costs would rise, changing from (hiring cost) to approximately (hiring cost)/(p)
      
   
   

Note that in none of these scenarios does the actual quantity of people employed decline. This is for the simple reason that the decision of the business owner is between a reduction in profit by the formula in (2) above or to reallocate his or her existing resources in a suboptimal manner.

In the simplest decision tree, the owner decides to terminate one of the workers above and does not replace them. In this case, either (1) the remaining workers must work more hours, at not less than the other worker's compensation, (2) the owner must take on those duties and expend their own time doing the job (it is only if one finds this credible that there would be a decrease in total employment—and this would result in the owner either not attending to other, non-fungible duties or devoting more time than he or she had previously committed;
in either case, there is a decline in the return on investment [including sweat equity”] to the owner that is at least equivalent to equation (2) above), or (3) some combination of (1) and (2) must occur.

None of those three scenarios will produce a return greater than the equation laid out for Employee B above. Therefore, the employer who opts for them has made a poor business decision based on the new information in the market.

Distortions Created by the Minimum Wage

It is certainly true that the minimum wage creates distortions in the economy—but those distortions accrue entirely to businesses, and as such they should be viewed as a form of corporate welfare in that they make marginal businesses appear (more) viable.

Assume for the moment that the last (1997) increment in the minimum wage produced a steady state. To the extent that a business subsequently does not raise the compensation of its employees, the business could accurately be seen as accruing excessive profits that
would, in the steady state, have been distributed to the workers. The excess accruals make the firm appear more viable than it is, as the increase in profits that is directly related to the firm's decision to undercompensate its employees should not be credited to management's skill.

This is, presumably, one of the reasons Mr. Samwick is willing to concede that, if a minimum wage is justified, it should be increased on a regular basis by a legitimate level of inflation. This, however, would have to be a tightly managed process, and it seems unlikely that annual increases would not introduce too much uncertainty in the marketplace.

Rather, minimum wage increases should be linked, as k harris suggested at angrybear, to increases in productivity or, better still, average wages:

On principle, inflation indexing of wages is a bad idea, from a monetary policy point of view. I might be convinced that the minimum wage covers too few workers to matter as a conduit for wage inflation, but we would not want the example emulated on a wide scale. Indexing to productivity, as suggested here, would over the past decade mean that the minimum wage would have risen faster than average wages. That is not necessarily a bad thing, but needs to be kept in mind....If we want to avoid a direct tie to inflation, the minimum wage could be indexed to average wages. That would still have meant a substantial increase in minimum wages over the past decade, would avoid the pattern of stagnant minimum wages over long stretches that has been the historic norm, and might give an impression of fairness.

Recalling the definition of a minimum-wage job, I'm more sympathetic to the argument that the minimum wage should be tied to productivity increases or average wages than a determination of the inflation rate (especially one that is quite subject to political maneuvering. After all, as Samwick notes, there is still the EITC.

1. The minimum wage, by setting a standard of value for work, requires that businesses be managed more efficiently than they would have to be without it,
   
2. The minimum wage provides a benchmark against which companies can judge the replacement cost of their least valuable employees—though reducing a firm's employee turnover ratio also presents significant collateral benefits,
   
3. Indexing the minimum wage to inflation is probably a bad idea, though tying it to either average wages or productivity increases, and making the adjustment on a regular but not annual basis would be more reasonable and manageable,
   
4. Failure to adjust wages makes businesses appear more profitable than they would be in a steady state, which is a suboptimal allocation of profits, and, finally,
   
5. There is a psychological effect of employment that should not be dismissed out of hand. Or, as Kevin Kline said in the words of Aaron Sorkin:
   

   If you've ever seen the look on somebody's face the day they finally get a job, I've had some experience with this, they look like they could fly. And its not about the paycheck, it's about respect, it's about looking in the mirror and knowing that you've done something valuable with your day. And if one person could start to feel this way, and then another person, and then another person, soon all these other problems may not seem so impossible. You don't really know how much you can do until you, stand up and decide to try.