Public Goods and Spending on lighthouses in Antebellum America

I have been working the last two weeks on a revise and resubmit for a journal article regarding the provision of lighthouses in antebellum America (1790-1860). This is in relation with other works I am doing or have already done (see here, here, here, and here) with respect to the provision of public goods by states or markets (i.e., remember that lighthouses were/are a frequent textbook example of public goods). In the process of doing the revisions, I assembled data on all expenditures by the Lighthouse Establishment and Lighthouse Board to 1860. This includes appropriations for new constructions, salaries of keepers, provisions for operation and maintenance expenditures. I divided these expenditures by GDP to yield the graph below.

There is not a ton to say about this here on this blog except the following three interrelated comments. First notice that the scale means that lighthouse spending to GDP is always less than 0.05% of GDP. That is small. Second, notice that the trend is up over time. It goes from 0.01% to a bit than 0.05% in peak years. These first two comments matter because you would expect the small share to grow smaller over time. Why? Remember the definition of public goods — non-rivalrous and non-excludable. The first part of that definition implies that you take the sum of marginal benefits at any quantity for everyone in a society to arrive at the societal benefit of an extra unit of public goods. If the marginal cost of providing the public good is zero, is constant or is only increasing at a slow pace, this means that adding an extra person would add more to the benefits than the cost. Phrased differently, this means that we should expect lighthouse spending to fall or stay constant as a share of GDP. This is because GDP goes up when more people are added (and the benefits of the public good scale up with extra people) while costs do not increase as much. Ergo, the trend in the graph below should fall.

Figure 1: Lighthouse Spending in America Divided by GDP, 1791 to 1860

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