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CDC injury data: the US in 2009 saw 12,000 gun homicides, and 550 gun accident deaths, which I'll round up to 600. Also 18,000 gun suicides, which I'll ignore. (Though I wonder: are accidents all accidental deaths, or just accidentally shooting someone else, with shooting yourself by accident being a suicide? Ah, I see indication elsewhere of "self-inflicted" accidental deaths.)
Of the homicides, the vast majority are with handguns, many of them a result of flared tempers. However, apparently there's about 160 "mass shooting" deaths every year, incidents where 4 or more people are killed, usually in a planned crime with a semi-automatic weapon. (I'd assume rifle, though semi-auto pistols exist too.) The article doesn't note that population has increased, so the per capita rate of mass shooting deaths has actually gone down by 25% since 1980.
The statistical-actuarial value of an America human life is about $7 million, so you should be willing to spend up to that to save a life. In practice, there are probably much cheaper ways of saving American lives -- traffic safety measures, vaccines for kids, other health care -- that aren't fully funded, so $7 million is too much. (I leave aside the possibility of saving non-American lives for even less; this is clubhouse or social contract utilitarian thinking, not universalist-altruist thinking.)
Costs of gun safety programs, testing or training or licensing or what not, include not just the administrative cost of such programs but the time and inconvenience imposed on gun owners. I'll rate that at about $20/hour. There are roughly 100 million US gun owners, many owning both handguns and long guns. Imposing one hour of annoyance per year on them uses up a budget of $2 billion. Ten hours of a training program, say, would cost $20 billion of citizen's time -- not counting the cost of the trainers and ranges and administration.
So.
Mass shooting deaths: 160*$7m = $1.1 billion/year. So we should be willing to spend up to that to prevent all mass shooting deaths. If a proposed intervention could plausibly only reduce deaths by 10%, say, then we should spend up to only $110 million/year. That'd be about $1 per gun owner, or 3 minutes of their time. If you screened owners once every 10 years you could stack that, for $10 or 30 minutes. AFAIK mass shootings tend to come out of the blue, so I'm not sure we could even reduce deaths by 10% by background checks or profiling, but it might be possible. OTOH, recall that this is saving lives at a full $7 million per life. If we could be saving lives at $500,000 per life, this doesn't seem like a good use.
I think it'd be more effective to tax semi-automatic weapons for the average cost they cause, $10-20/year, and use that to save lives other ways. I've been asked how you'd levy the tax; I'm not sure, I guess either a one-time tax on the gun, $100-200 at time of manufacture or import perhaps, or an annual licensing fee. Or a decadal licensing fee, since collecting $10/year is probably expensive.
What if we just ban the guns, and that reduces the death rate to 0, with killers not displacing to other means? Say there's 100 million guns, and owners get cumulative utility of $1000 from each, for $100 billion. Then the ban would pay for itself in about a century. Not a great recommendation.
Do restricting magazine size, or banning semi-auto rifles in favor of, what, revolving rifles, make sense? Possibly; I don't know enough to put any estimates on the cost/benefit there. But there's only $1 billion of benefit to be gotten from such measures. It sounds callous to call 160 lives a year 'only', but really in a country this size it is. We're in death-by-lightning-strike territory.
Accident deaths: 600*$7m = $4.2 billion, or $42 per gun owner. Bit more promising budget, and we can imagine training programs or mandatory child locks to reduce deaths. Except, well, the accident rate is already really low, and guns are already commonly locked or held unloaded, whether out of safety concerns or actual law. The accident rate has been going down, partly because of NRA training programs. So it's not obvious what you can do that isn't already being done. If you could freely identify the unsafe gun owners you could do a lot, but if you have to screen or train all of them you don't have a lot to work with. $24 per owner, for a goal of reducing deaths by 50% -- and again, that's at actuarial break-even, $7 million spent per life saved. Again, a simple excise tax or license fee is probably simplest.
Homicides: 12,000*$7m = $84 billion/year, or $840/year per owner. That's a significant social cost, and nominal budget. If we aimed to reduce deaths by 10%, and at a cost of $700,000 per life, that'd still be $8.40 per owner. Not a lot, but enough for a background check every few years at least. Though I think we already do that, at least for purchases from licensed dealers. It's less obvious what *else* you can do for that money.
It's worth remembering that homicide risk isn't evenly distributed. The risk of a car owner killing someone isn't exactly even -- teens, old people, SUV drivers all have more -- but it's kind of even, so it makes sense to impose on all drivers for the sake of safety. But rural rifles or shotguns are far less likely to kill someone than an urban handgun, and a lot of gun crimes are by people who are already ex-felons and not supposed to have a gun in the first place. So it's both fairer and more efficient to target the urban handgun supply than long guns, and to put the effort into trying to keep handguns away from criminals. OTOH, we already do that too -- urban gun bans, background checks, buy-backs...
An $840/year tax would probably severely reduce the rate of legal gun ownership. Alternately, we could ask whether simply banning guns would deprive owners of $840/year of benefit. Guns provide benefits of food (hunting), fun (hunting, range shooting), peace of mind and self-defense (including against large animals or to protect livestock); they also increase the household risk of accidents or homicide, though as note the accident rate is pretty small. Long guns provide the food and fun benefits of hunting and shooting, and home defense benefit, while having low social cost in crime. Handguns have less hunting use and more urban or automotive self-defense use, but also provide most of the gun crime risk to be defended from. (But handguns can also chase off muggers with knives or bats.)
(How much self-defense benefit they give, I don't know. Estimates seem to vary by a factor of 100. I'm not going to try to put numbers on 'fun' either.)
For some rural people, the hunting benefit is rather large; getting 1000 pounds of meat is worth $2000 or more. (For rural Alaskans, where everything non-local is expensive, a lot more.)
Worth noting: the US homicide rate by non-gun means, e.g. knives, is higher than the total homicide rate of other developed countries. We are, simply, a more violent country, at least in parts. So it's quite likely that making handguns vanish wouldn't diminish homicides by the full 12,000, with people turning to knives for muggings and passion fights. Getting stabbed can be deadlier than a handgun wound, too. So that kind of reduces the $84 billion "budget"; by how much, I have no idea.
Conclusion
Measures, especially moderate ones, aimed at reducing the rate of mass shootings or accident deaths seem very unlikely to be worth the effort; the risk is too widespread, the maximum potential benefit too small. For general homicide, more aggressive measures aimed at handguns might be worth it; a nation wide ban on handguns, so that there's little supply to leak out into the criminal world, could make even more sense if effective, as you'd be removing much of the threat people want handguns to get a benefit of defense from. I suspect there's a non-linearity, where a politically palatable moderate measure doesn't do much good, while draconian banning nationwide could. Assuming you could peaceably enforce it, which given elements of US gun culture seems open to question.
Long gun owners should probably be left alone, as they don't cause much crime and have a lot of real benefit to much of the population. This is consistent with the experience of other countries; the US isn't that unusual in total gun ownership, but is in handgun ownership. That said, the US is unusually high in homicides, and less so in other crime; the idea that gun ownership deters some crime shouldn't be totally dismissed.
Adverse selection
I realized there's an analogy to lemon cars in gun politics. Buyers can't tell lemons from good used cars, so don't pay full price, which keeps good cars off the market... Some gun advocates might be willing to compromise on reasonable control measures, but feel unable to tell sincere moderates from ones who'll push for further and further controls, and thus feel unsafe in making any deals. Gun control advocates who want to control or get rid of handguns but not all guns might send some costly signal to indicate that, like actually owning a rifle, or donating to some gun organization or training course.
ETA: Of course, guns cause injuries, not just deaths; that should have been factored in as well. Oops. Well, say there's 10x as many injuries. If they cause medical costs of $700,000, that basically doubles the 'budgets' or total social costs If they cause medical costs of $70,000 or less then they add 1% and are kind of irrelevant. I guess there's not just up front medical costs but permanent injuries like lost eyes or fingers. Hard to find recent sources, but late 1990s sources have non-lethal gun injuries as 4x the rate of lethal ones, ignoring suicide[1]. So they'd have to be 'worth' $3.5 million each to double the total cost of guns.
[1] About 80% of gun suicide attempts were fatal. 25% of attacks, and less than 10% of accidents.
Of the homicides, the vast majority are with handguns, many of them a result of flared tempers. However, apparently there's about 160 "mass shooting" deaths every year, incidents where 4 or more people are killed, usually in a planned crime with a semi-automatic weapon. (I'd assume rifle, though semi-auto pistols exist too.) The article doesn't note that population has increased, so the per capita rate of mass shooting deaths has actually gone down by 25% since 1980.
The statistical-actuarial value of an America human life is about $7 million, so you should be willing to spend up to that to save a life. In practice, there are probably much cheaper ways of saving American lives -- traffic safety measures, vaccines for kids, other health care -- that aren't fully funded, so $7 million is too much. (I leave aside the possibility of saving non-American lives for even less; this is clubhouse or social contract utilitarian thinking, not universalist-altruist thinking.)
Costs of gun safety programs, testing or training or licensing or what not, include not just the administrative cost of such programs but the time and inconvenience imposed on gun owners. I'll rate that at about $20/hour. There are roughly 100 million US gun owners, many owning both handguns and long guns. Imposing one hour of annoyance per year on them uses up a budget of $2 billion. Ten hours of a training program, say, would cost $20 billion of citizen's time -- not counting the cost of the trainers and ranges and administration.
So.
Mass shooting deaths: 160*$7m = $1.1 billion/year. So we should be willing to spend up to that to prevent all mass shooting deaths. If a proposed intervention could plausibly only reduce deaths by 10%, say, then we should spend up to only $110 million/year. That'd be about $1 per gun owner, or 3 minutes of their time. If you screened owners once every 10 years you could stack that, for $10 or 30 minutes. AFAIK mass shootings tend to come out of the blue, so I'm not sure we could even reduce deaths by 10% by background checks or profiling, but it might be possible. OTOH, recall that this is saving lives at a full $7 million per life. If we could be saving lives at $500,000 per life, this doesn't seem like a good use.
I think it'd be more effective to tax semi-automatic weapons for the average cost they cause, $10-20/year, and use that to save lives other ways. I've been asked how you'd levy the tax; I'm not sure, I guess either a one-time tax on the gun, $100-200 at time of manufacture or import perhaps, or an annual licensing fee. Or a decadal licensing fee, since collecting $10/year is probably expensive.
What if we just ban the guns, and that reduces the death rate to 0, with killers not displacing to other means? Say there's 100 million guns, and owners get cumulative utility of $1000 from each, for $100 billion. Then the ban would pay for itself in about a century. Not a great recommendation.
Do restricting magazine size, or banning semi-auto rifles in favor of, what, revolving rifles, make sense? Possibly; I don't know enough to put any estimates on the cost/benefit there. But there's only $1 billion of benefit to be gotten from such measures. It sounds callous to call 160 lives a year 'only', but really in a country this size it is. We're in death-by-lightning-strike territory.
Accident deaths: 600*$7m = $4.2 billion, or $42 per gun owner. Bit more promising budget, and we can imagine training programs or mandatory child locks to reduce deaths. Except, well, the accident rate is already really low, and guns are already commonly locked or held unloaded, whether out of safety concerns or actual law. The accident rate has been going down, partly because of NRA training programs. So it's not obvious what you can do that isn't already being done. If you could freely identify the unsafe gun owners you could do a lot, but if you have to screen or train all of them you don't have a lot to work with. $24 per owner, for a goal of reducing deaths by 50% -- and again, that's at actuarial break-even, $7 million spent per life saved. Again, a simple excise tax or license fee is probably simplest.
Homicides: 12,000*$7m = $84 billion/year, or $840/year per owner. That's a significant social cost, and nominal budget. If we aimed to reduce deaths by 10%, and at a cost of $700,000 per life, that'd still be $8.40 per owner. Not a lot, but enough for a background check every few years at least. Though I think we already do that, at least for purchases from licensed dealers. It's less obvious what *else* you can do for that money.
It's worth remembering that homicide risk isn't evenly distributed. The risk of a car owner killing someone isn't exactly even -- teens, old people, SUV drivers all have more -- but it's kind of even, so it makes sense to impose on all drivers for the sake of safety. But rural rifles or shotguns are far less likely to kill someone than an urban handgun, and a lot of gun crimes are by people who are already ex-felons and not supposed to have a gun in the first place. So it's both fairer and more efficient to target the urban handgun supply than long guns, and to put the effort into trying to keep handguns away from criminals. OTOH, we already do that too -- urban gun bans, background checks, buy-backs...
An $840/year tax would probably severely reduce the rate of legal gun ownership. Alternately, we could ask whether simply banning guns would deprive owners of $840/year of benefit. Guns provide benefits of food (hunting), fun (hunting, range shooting), peace of mind and self-defense (including against large animals or to protect livestock); they also increase the household risk of accidents or homicide, though as note the accident rate is pretty small. Long guns provide the food and fun benefits of hunting and shooting, and home defense benefit, while having low social cost in crime. Handguns have less hunting use and more urban or automotive self-defense use, but also provide most of the gun crime risk to be defended from. (But handguns can also chase off muggers with knives or bats.)
(How much self-defense benefit they give, I don't know. Estimates seem to vary by a factor of 100. I'm not going to try to put numbers on 'fun' either.)
For some rural people, the hunting benefit is rather large; getting 1000 pounds of meat is worth $2000 or more. (For rural Alaskans, where everything non-local is expensive, a lot more.)
Worth noting: the US homicide rate by non-gun means, e.g. knives, is higher than the total homicide rate of other developed countries. We are, simply, a more violent country, at least in parts. So it's quite likely that making handguns vanish wouldn't diminish homicides by the full 12,000, with people turning to knives for muggings and passion fights. Getting stabbed can be deadlier than a handgun wound, too. So that kind of reduces the $84 billion "budget"; by how much, I have no idea.
Conclusion
Measures, especially moderate ones, aimed at reducing the rate of mass shootings or accident deaths seem very unlikely to be worth the effort; the risk is too widespread, the maximum potential benefit too small. For general homicide, more aggressive measures aimed at handguns might be worth it; a nation wide ban on handguns, so that there's little supply to leak out into the criminal world, could make even more sense if effective, as you'd be removing much of the threat people want handguns to get a benefit of defense from. I suspect there's a non-linearity, where a politically palatable moderate measure doesn't do much good, while draconian banning nationwide could. Assuming you could peaceably enforce it, which given elements of US gun culture seems open to question.
Long gun owners should probably be left alone, as they don't cause much crime and have a lot of real benefit to much of the population. This is consistent with the experience of other countries; the US isn't that unusual in total gun ownership, but is in handgun ownership. That said, the US is unusually high in homicides, and less so in other crime; the idea that gun ownership deters some crime shouldn't be totally dismissed.
Adverse selection
I realized there's an analogy to lemon cars in gun politics. Buyers can't tell lemons from good used cars, so don't pay full price, which keeps good cars off the market... Some gun advocates might be willing to compromise on reasonable control measures, but feel unable to tell sincere moderates from ones who'll push for further and further controls, and thus feel unsafe in making any deals. Gun control advocates who want to control or get rid of handguns but not all guns might send some costly signal to indicate that, like actually owning a rifle, or donating to some gun organization or training course.
ETA: Of course, guns cause injuries, not just deaths; that should have been factored in as well. Oops. Well, say there's 10x as many injuries. If they cause medical costs of $700,000, that basically doubles the 'budgets' or total social costs If they cause medical costs of $70,000 or less then they add 1% and are kind of irrelevant. I guess there's not just up front medical costs but permanent injuries like lost eyes or fingers. Hard to find recent sources, but late 1990s sources have non-lethal gun injuries as 4x the rate of lethal ones, ignoring suicide[1]. So they'd have to be 'worth' $3.5 million each to double the total cost of guns.
[1] About 80% of gun suicide attempts were fatal. 25% of attacks, and less than 10% of accidents.