Hi Neil: I'll just add some statistics for the Commonwealth of Pennsylvania (where "firearms are easily acquired" legally except by convicted felons and those involuntarily admitted to a psychiatric hospital): There were 9030 reported suicides in the state for the five years 2012-2016. Of these, 4522 deaths (51%) involved firearms. Source: https://www.health.pa.gov/topics/HealthStatistics/EDDIE/Pages/EDDIE.aspx. As an aside, firearms are harder to acquire in the adjoining states of NJ, NY, and MD, which also have much lower suicide rates than PA.
Tony, 51% of suicide deaths in PA involved firearms is telling. The data is, of course, correlational, but what a correlation! Comparison to neighboring states having both lower firearm-related suicides and more limited access to firearms is also correlational. There may be demographic or other factors besides firearm availability accounting for at least part of the difference. Still, 51% is an astounding statistic. One wonders how many of those completed suicides would have found another means, but it is certainly the case that firearms represent an immediate and extremely lethal means for individuals considering suicide.