Does the Market Underprovide Safety for Workers Who Are Poor?

Not necessarily, says David Henderson.

"In a comment on a recent post of mine on worker safety, in which I highlighted the "Job Safety" entry by W. Kip Viscusi in The Concise Encyclopedia of Economics, MikeDC wrote:

If you've got an impoverished and hungry subsistence or near subsistence level population, you don't have much have to worry about their safety. You just replace them if they get hurt or die.
So I take that as a fairly legitimate moral limitation. Maybe one of the few where a free market doesnt push in the right direction.

I had promised to respond with a further post saying why the market would provide the optimal level of safety even to poor people. This is that post. 

 Throughout the analysis, I assume that workers have good knowledge of risks and I assume that employers want to maximize profits.

I recommend, if you have trouble following the reasoning below, that you go back to the "Job Safety" article."

Start with the employer providing less than the optimal amount of safety to low-income workers. What does it mean to say that the safety is less than optimal? It means that they would value an increment in safety more than it costs to provide. A profit-maximizing employer would see that he can provide that increment and increase his profits. The reason is that he can cut the employees' pay by more than the cost of providing the safety. That's what it means to say that the workers value the increment in safety more than the cost of provision.

So the employer provides that increment in safety. He is better off and the workers are the same off. Now let's say safety is still suboptimal. Then the employer can provide another increment of safety and pay less for it than the amount by which he can reduce workers' wages. This continues until the employer hits the optimal amount of safety.

I should point out that I'm also assuming no income or payroll taxes. If there are income or payroll taxes, which, in the United States, of course, there are, then the amount of safety for all workers will be more than optimal. Why? Because income is taxed and safety is not."