Last week, this post generated a lot of feedback. Erik Bruvold and Vince Vasquez from the San Diego Institute for Policy Research had come up with some interesting stats about how much the county spends to keep its libraries open and how much the city spends.

Take a look at it to refresh your memory of what they said.

I got this response to it from reader Jeffrey Davis:

The San Diego City Library System serves a greater population than the county, as Bruvold himself notes in the comments. Now I’m no mathematician, but using a calculator and some more precise population data I found that the costs to the city per hour open, per person are \$0.000415, and for the county they are \$0.000424. In other words, the Library is inefficient and has misplaced its priorities. But it’s the county, not the city! Bruvold and Vasquez have got the wrong Library!

Note: these figures use 2006 population estimates, but the comparison was true for 2000 data as well.

And here’s Bruvold’s response:

At the fundamental level, Mr. Davis mistakes our argument. We never tried to say who was the more “efficient”. We asked a different and simpler question – what is the ratio of total operating income to hours of operation? We found that the City had a ratio of \$544, the county \$436.

When we then explored possible reasons for this difference we found that the city has 420 FTEs while the County had 290 FTEs. We opined that this problem could be exacerbated because the size of the new central library would seem to require more FTEs for each hour of operation.

To Mr. Davis’s point directly – it is unclear to me what precisely a ratio of operating income/hours/population actually measures. There are several problems with this ratio, one of the biggest is that the marginal cost of serving each additional person in the population and the marginal cost of each hour of operation are likely at very different places on a marginal cost curve. If Mr. Davis wishes the short course in economics, have him contact me directly and we can walk through the analytic challenges of what he is trying to do and why I don’t think he is measuring anything meaningful in his ratio.

I would close with the following observation. The debates about the City’s library system when budget cuts (or more typical the inability to increase budgets as much as the bureaucrats propose) INEVITABLY lead to discussions about cutting operating hours. What this discussion has pointed out is that there could be a different debate – whether hours could be preserved if the system CHANGED the MIX of services that it offered? I, for one, would relish the opportunity to hear that discussed.