Obviously, a minimum wage hike is damaging to employees who lose their jobs because of it. Additionally, some economists have made the point that, even for workers who see wage gains because of the minimum wage, these gains are offset by losses in non-wage factors, such as fringe benefits, job flexibility, training, safety, etc. This is the idea I would like to explore here. I think it is optimistic to say that these wage gains are merely offset by losses from these other factors. The marginal worker who receives a wage increase due to an increase in the minimum wage, and remains employed, almost certainly would experience a loss of total utility, even with the higher wage.
Imagine a worker making $8/hour (compared to the current MW of $7.25). First, we can say that this wage level is the product of some balance of market forces. There is some skill or value that the worker in question brings to the table which pulls the wage level up to $8. The wage could have been legally more or less than $8, but some complex balance of value and power between the worker and the employer and other stakeholders in this contract has led to a value of $8/hour.
Whatever effect the MW may have on wages or employment, it is not going to change anything about the underlying balance of these market forces. The total cost incurred by the employer for this worker is a product of these forces, so that the total cost incurred, which includes an $8 cash payment plus many other considerations, will not change, ceteris paribus, if the means exist for the employer to adjust non-cash costs.
Further, the total utility gained for this work can be imagined as a sort of production-possibility frontier. Cash payment will form a large part of the benefits to the worker. But, as mentioned above, there are many factors about any job that can be changed, to the relative cost or benefit to the worker or the employer. If the worker values flexibility more than the employer, an $8 job with more flexibility may be more valuable to both the worker and the employer than an $8.50 job with an unyielding schedule. There are innumerable non-wage factors that we could imagine with any job, and most jobs come with a set of conventions and non-cash benefit equilibria that reflect a complex evolution of the relative values and needs of both workers and employers. Most of the time, we take these factors for granted - some types of workers are home every day at 5, others have to stay late when work is heavy, others have to put time in on the graveyard shift. Some types of workers can show up a couple hours late when their child needs to go to the doctor and make the work up later, others have to find a way to cover their shift. For the most part, these kinds of job-specific demands are the product of a web of competing needs so complicated, they would be impossible to calculate. But, for every individual worker, through conventions, negotiations, and compromise, an equilibrium is reached, and is constantly monitored and tweaked, in conscious and unconscious ways, by both the worker and the employer. (This can be as formal as allowed vacation days, or as informal as a willingness to put up with a co-worker's poor hygiene. The number of variables here is endless.)
The optimal cash/non-cash combination of considerations captured by the worker will be the combination where the marginal cost to the employer of substituting a non-cash consideration for cash is equal to the marginal benefit to the worker. So, the curved line in the figure represents the costs the employer is willing to bear for the employment contract. The total value to the worker is the combined value of cash and non-cash considerations. The diagonal line shows the potential cash/non-cash combinations that would have the same value as they do at the optimal wage. Of course, this line is tangential to the curve of possible combinations, with the total value to the worker decreasing as the wage departs from the optimal wage.
For our hypothetical worker, that equilibrium settled at $8/hour, plus some long list of potentially mutable demands or benefits. We can suppose that while perfection is rare, this contract, and contracts in general, tends toward an optimal equilibrium, where the trade-off between cash and non-cash considerations is optimal. It easy to imagine that employers would be enthusiastic about finding employment contracts that attracted workers with lower cash payments, and that they would utilize non-cash considerations that were valued by potential workers whenever possible.
Now, imagine that the minimum wage was raised to above $8/hour. To imagine that the wage would simply be raised, with no change in non-cash considerations, we would have to believe two things - (1) that the entire universe of non-cash considerations valued by the worker are entirely immutable, and (2) that the firm held some sort of monopoly power that allowed it to sustain a total labor cost at below the competitive rate. Number one is simply unlikely, and number two begs the question. Whatever competitive pressures led to the job settling at $8/hour (plus the original non-cash considerations), those pressures would tend to move the cash/non-cash compensation along the utility frontier. They wouldn't lead to a rise in cash wages with no corresponding change to non-cash compensation (the green line in the figure). The frontier reflecting the total available cash and non-cash considerations doesn't just go away because a wage law was passed.
So, to the extent that the context of the job is mutable, the balance of cash and non-cash considerations available to the worker will settle at the original frontier, but at the new, higher wage. This will not be the optimal balance of cash and non-cash considerations. For the employer to settle at the original total cost, the worker will have less total utility as compensation for this job. The worker will be worse off.
The ironic conclusion to this puzzle is that the impetus for minimum wage legislation is the conception of low-wage employers as powerful taskmasters who have broad power over the level of wages and terms of employment. These happen to be the characteristics that would lead to a long term equilibrium that pinned the total utility at the original frontier of cash/non-cash compensation.
If excess profits exist as the result of some competitive monopolist context that the employer enjoys, but the original low wage was a product of a power mismatch between the worker and the employer, so that the employee was not capturing any of the surplus, then, the same competitive imbalance will be in place with regard to non-cash considerations, and the employee will be denied utility through the denial of non-cash considerations after the wage hike.
If the employee is able to capture all of the surplus resulting from the wage hike, then why would we assume that he wasn't capturing all of the surplus to begin with? So, that, in that case, with no surplus left to share, the firm will be forced to either pin the total cash+non-cash cost back at the original frontier, at the new, sub-optimal balance, or terminate the worker.
The likely outcome, especially in the long run, appears to be a loss of utility for everyone, especially the workers - even the workers that don't lose their jobs.
It may be possible for some firms to experience gains resulting from the exit of weaker competitors after a MW hike, which might allow for some ability for workers at these firms to remain at a higher total consideration, at least temporarily. Here is a previous post where I tried to think through some of the implications of MW hikes among different firms. But, the resulting expected change for the typical worker affected by a MW hike, all else equal, seems tilted to the negative to me.