The lightship in economics

Abstract

What role does government play in the provision of public goods? Economists have used the lighthouse as an empirical example to illustrate the extent to which the private provision of public goods is possible. This inquiry, however, has neglected the private provision of lightships. We investigate the private operation of the world’s first modern lightship, established in 1731 on the banks of the Thames estuary going in and out of London. First, we show that the Nore lightship was able to operate profitably and without government enforcement in the collection of payments for lighting services. Second, we show how private efforts to build lightships were crowded out by Trinity House, the public authority responsible for establishing and maintaining lighthouses in England and Wales. By including lightships into the broader lighthouse market, we argue that the provision of lighting services exemplifies not a market failure, but a government failure.

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Fig. 1

Notes

  1. 1.

    Beginning with the 5th edition of Economics: An Introductory Analysis, Samuelson (1961, pp. 192–193) used the lighthouse as an example of pure public good. Even after the publication of Coase (1974), however, Samuelson continued to use the lighthouse as an example of a good that required public provision. The lighthouse still appears as an example of a public good in the 19th edition of his textbook (see Samuelson and Nordhaus 2009, p. 37).

  2. 2.

    As Brubaker (1975, p. 151) puts it, “An essential and neglected fact is that no matter how costly individual exclusion may be after the creation of a collective good, prior to consummation of a contract exclusion of the group, and consequently also of the individual, is always very easily accomplished. The producer simply holds no inventories. He works strictly on the basis of pre-paid orders. Lacking a firm contract with the community there will be no collective good for any of its members”. Leeson (2007b) employs a similar self-enforcing mechanism to explain how the extension of credit by producers increased the costs of theft and raised the benefits of trade among middlemen in late precolonial Africa. In terms with which Brubaker might agree, credit is a pre-contractual mechanism of excludability because credit allowed producers to trade with goods that did not yet exist, minimizing the benefits of theft, and incentivizing future repeated dealings. Thus, credit was a pre-contractual mechanism to produce a public good privately, in this case self-governance, namely by eliciting a demand for trade among the middlemen. Analogous to the case being made herein, pre-payments for the construction of lightships allowed its producers to minimize free riding and incentivized payers to reveal their demands for lightship services.

  3. 3.

    In 1836, an act of Parliament nationalized all remaining privately owned lighthouses in England (Hardy 1895, p. 41); see also Coase (1974).

  4. 4.

    According to Clarke (2016, p. 32), pilotage refers to “the art of taking a vessel from one place to another in sight of land and providing ships with safe passage onto rivers and harbours or through dangerous waters”.

  5. 5.

    Historians argue that since Trinity House was responsible for mariners’ pensions, it was reluctant to bear too much risk. As such, its monopoly power allowed it to shift risks to private parties (Lindberg 2013, p. 546).

  6. 6.

    The 1834 report of the House Select Committee (1834, pp. XXXVII–XXXVIII) reported 55 lighthouses and floating lights operated by Trinity House for 1832 and 14 privately operated lighthouses in England and Wales. Taylor (2001, p. 758) writes that by 1835, the number of private lighthouses had fallen to 10. Ireland and Scotland had their own lighthouse authorities (the Commissioners of Irish Lights and the Commissioners of the Northern Lighthouses), which were separate from Trinity House’s operations in England and Wales.

  7. 7.

    We distinguish between for-profit, private lighthouses and non-profit, private lighthouses specifically to focus our discussion on the former, rather than the latter. Although lighthouses were provided by hermits and religious orders on a voluntary basis, they were operated on a non-profit basis (see Van Zandt 1993, p. 59). Block and Barnett (2009) also argue that purely private production was possible for charitable purposes. Because the main dispute in the literature is on the profitability of lighthouses in the absence of state enforcement of the collection of light dues, we do not focus on non-profit lighthouses.

  8. 8.

    Our argument also builds on a theme that Coase already had developed in his 1961 paper, “The British Post Office and the Messenger Companies,” which illustrates how, in an attempt to preserve its monopoly, the Post Office tried to obstruct the entry of private entrepreneurs into the provision of postal services.

  9. 9.

    We use the term “rivalry” here to mean mutual exclusivity of consumption and/or production; we do not use it interchangeably with “competition” or “contestability”.

  10. 10.

    In any case, patents for lighthouse operation came with a radius of exclusive operation within which no competitor could install itself.

  11. 11.

    In navigational distance, the Nore lightship was 48 miles away from London (Chandler, Diston and Adams 1788, p. 113). The route between the Nore and the Port of London took roughly three hours (House of Commons 1796, p. 46).

  12. 12.

    Modern lightships under the Trinity House system are no longer manned. According to Clarke (2016, p. 150), the majority of manned lightships was decommissioned in the 1970s and 1980s. The last manned lightship in England, the Inner Dowsing, was decommissioned in 1991.

  13. 13.

    Clarke (2016, p. 38) reports that the origins of modern lightships can be traced back to ancient Roman galleys, known as liburnae, used by the Roman navy for raids, but also provided lighted beacons to deter pirates. As he states further, the “vessels carried on their mastheads iron baskets in which fire was built serving as a signal when a friendly vessel was sighted”. However, their functions as lightships were limited because ancient sailors tried not to sail at night. It is unclear whether Avery or Hamblin were aware of their historical provenance.

  14. 14.

    Lightships were very popular for the navigation of Canada’s Saint Lawrence seaway (Cloutier and Charest 2016) and the American eastern coastline (Webster 2000). This is a telling element given that frontier economies like Canada and the United States would be have been blank slates in terms of technologies available to adopt, which may explain their greater relative popularity in North America.

  15. 15.

    Coase (1974, p. 366) excluded “floating lights” from his presentation of the numbers.

  16. 16.

    By 1834, all 13 lightships were owned by Trinity House (House of Commons 1834, p. 344).

  17. 17.

    Most of the secondary sources that discuss the event rely nearly exclusively on the information provided by John Whormby (1746 [1861]). Whormby was the clerk of Trinity House who wrote a history of the Corporation in which he gave his retelling of the Nore lightship episode as he lived it. Most of it is condescending towards Hamblin and Avery.

  18. 18.

    Some secondary sources mention 1732 (e.g., Adams 1870, p. 254; Gattie 1890, p. 156) and some even place it in 1733 (Cotton 1818, p. 77), while others are vague about the date (Adams and Woodman 2013, p. 87). But the advertisements published in the Daily Courant (October 12, 1731), the Universal Spectator and Weekly Journal (October 16, 1731), the Daily Post (October 12, 1731), and the London Journal (September 18, 1731; October 16, 1731) all make it clear that the ship became operational in 1731. Hamblin mentions in an ad submitted on October 10 that he had “this morning moor[e]d a complete ve[ss]el of about 100 tons” (London Journal, October 16, 1731). The only secondary source that gives 1731 as the starting date is Stevenson (1959, p. 139) for whom we have confirmed every assertion. A July 22nd, 1731, article in the Grubb Street Journal mentions a ship placed at the buoy at the Nore on order of Trinity House (this is echoed in the Caledonian Mercury of July 26, 1731). However, the article is unclear about what was occurring, but we know that, given its virulent reaction (see next section) to the Nore lightship, Trinity House could not have ordered the placing of the first 19-ton lightship. The possibility exists of a journalistic error. However, it is true that notice of a first ship was placed by Hamblin for advertising purposes. Secondary sources confirm it. Robert Peirce Cruden (1843, p. 412) pointed out that on the August 9th 1731 (a date that contradicts the July Grubb Street Journal ad), Hamblin moored a 19-ton vessel at the Nore (called the Experiment), which he had replaced by an additional ship (called the Good Intention) of 100 tons on October 10th 1731. The mooring of the Experiment apears to have been meant as a marketing ploy. The elements contained in Cruden’s account are confirmed by the September and October ads placed in the Daily Post, Daily Courant, Universal Spectator and Grubb Street Journal. As such, the 19-ton Experiment operated from either late July 1731 to early October 1731 or from early August 1731 to early October 1731.

  19. 19.

    This is confirmed by the clerk of Trinity House, John Whormby, in his 1746 history of the corporation. He pointed out that Trinity House apprehended, “very justly” in in his opinion, that Avery would go “round the kingdom with lights of that kind, to the danger and confusion of navigation, as well as to the prejudice of fixed lights” (Whormby 1746 [1861], pp. 135–146; emphasis added).

  20. 20.

    The Well refers to Dudgeon Shoals off the coast from Cromer in East Anglia where a lighthouse already existed (Stevenson 1959, p. 136).

  21. 21.

    Few sources provide details about how that was the case. The one exception is a laudatory article in the Newcastle Courant on August 21, 1731. The article refers clearly to the first, smaller, lightship as a “great advantage to Navigation in general, as well a Means to preserve the Lives and Fortune of his Majesty’s Trading and Maritime Subjects from the Dangers of the Nore Sand”. However, that article was a copy of the August 11, 1731 article published in London’s Daily Courant.

  22. 22.

    The voluntary payment component of the lightship at the Nore often is noted in passing (Cruden 1843, p. 412; Pask 1884, pp. 604–605). In fact, Trinity House complained explicitly about the voluntary nature of payments through subscription books.

  23. 23.

    The official historians of Trinity House refer vaguely to expenses of £2,000 on the “project” (Adams and Woodman 2013, p. 87). Many sources mention “fitting out”, but they all represent secondary sources. As we document in Appendix, it is likely that the estimates combine operating costs (i.e., variable costs) and fixed (i.e.,construction) costs. If the secondary sources are correct that the figure of £2,000 concerns only the construction and fitting-out of the Experiment and Good Intention, then the operating cost estimate derived using the number of workers and gallons of fuel consumed is the most accurate (see Appendix).

  24. 24.

    They also were more expensive to build: Chambers’s Encyclopaedia (1891, p. 623) placed the construction cost of a lighthouse between £5,000 and £10,000, while a lightship cost £9,000 during the late 19th century.

  25. 25.

    Revenues from smaller ships are omitted. Moreover, we do not include revenues from the public subscriptions, which were collected ex ante.

  26. 26.

    Including the lightship at the Nore, which had, by that time, passed into the hands of Trinity House. The rate schedules probably were vestiges of Avery and Hamblin’s experiment because the schedules were taken from the last establishment that practiced price discrimination in 1832 (House of Commons 1834, p. 341). The other lighthouses were the Castor and Lowestoft lighthouses (which charged a flat fee of four pence for all ships and then an additional 16 pence for every 100 tons) and the Winterton lighthouse (which charged 6 pence for ships under 100 tons and 12 pence for all ships above 100 tons) (Anonymous 1768, p. 21–22). All other lights had a flat rate per ton or per ship.

  27. 27.

    Lai et al. (2008a, b) are the only contributors to the lighthouse literature who emphasize the importance of the point regarding price discrimination, arguing that it makes private provision more viable–an argument that has not been made elsewhere. However, Koyama (2012) advanced the same argument for the same period of British history, but for prosecution associations (private conflict adjudicators) because it elicited greater participation by poorer individuals. What is more important, is that it is worth emphasizing that free riding can be endogenous. If free riding was to drive the enterprise into losses, the marginal user might free ride less so as to keep the operation afloat. A system of price discrimination would have been able to cater to that marginal user and thus permit sustainable production (we are thankful to Robert Whaples for this insight).

  28. 28.

    Omitting colliers, which were major sources of potential revenues.

  29. 29.

    The secondary sources tend to mention that the patent specified ships’ ability to distinguish light sources based on their colors. That is not the case. Hamblin’s petition makes no clear mention of color (National Archives 1730, SP 36/17/81). It merely speaks of the ability to distinguish one light from another. However, the lightship–being a novelty–would have distinguished itself from lighthouses, making it easier for Avery and Hamblin to differentiate their product and collect fees from users. Moreover, the vague wording of the petition, by not mentioning the lightship, meant that the innovation could be copied by others. Patents define products, not markets.

  30. 30.

    From the Attorney General’s report to the King regarding the petition made by Trinity House to revoke the patent.

  31. 31.

    More details on the legal technicalities raised could not be found. However, by virtue of the petition of Trinity House (National Archives 1731, PC 1/5/3), combined with the report of the Attorney General and Solicitor General (National Archives 1732a, PC 1/5/4), we can see that revocation was argued on two bases. The first was that the invention was not new, the second that public subscriptions with more than five individuals was not permissible under the patent. The former seems to have been the basis that the special committee of the Privy Council (National Archives 1732b, PC 1/5/5) used to justify the revocation. It made no mention of the latter point to justify revocation.

  32. 32.

    The presence of the Customhouse appears strange, as it invokes the possibility that Customs officials collected the revenue. However, in an advertisement in the October 12th edition of the Daily Post, Hamblin specified that payments could be collected in the Long Room of the Customs House. The Long Room was open to the public and merchants frequently would interact on the premises. As such, it acted as a meeting place and was not an indication of state support. The revocation of the patent by the King in May 1732 and the continued existence of the lightship at the Nore thereafter militate against that contention. Why would the King provide his support to collect revenues for the lightship after the patent was revoked?

  33. 33.

    This supports a point made by Mancur Olson (1965 [1971, p. 33, emphasis in original) in The Logic of Collective Action, that “if at any level of purchase of the collective good, the gain to the group exceeds the gain to any individual, then there is a presumption that the collective good will be provided, for then the gain to the individual exceeds the total cost of providing the collective good to the group”.

  34. 34.

    A similar mechanism existed in the United States, where lotteries financed some of the lighthouses of the colonial era (Dolin 2016, p. 60) even if few private lighthouses existed at the beginning of the Republic. Moreover, given that the subscriptions were solicited at coffeehouses, it also worth pointing out that, according to Stringham (2015) and Kingston (2007, 2014), coffeehouses often used ostracism and social norms to enforce complex contractual arrangements that otherwise may have given room for opportunistic behavior. Members who did not honor their arrangements would be blacklisted and, through multilateral punishments, other club members would shun relations with them. Most of the coffeehouses mentioned by Hamblin in his advertisement were merchant houses that could have acted to ostracize non-payers. They also could offer a reputational premium through the discipline of continuous dealings. For example, Lloyds coffeehouse, where individuals involved in the insurance market met, was known for being “a hub for information about… the reputations of market participants” (Kingston 2007, p. 380; see also Kingston 2014).

  35. 35.

    As we document in Appendix, with such economies and with the relaxing of some of upwardly biased operating costs estimates, it is impossible for potential revenues to have been less than costs.

  36. 36.

    The article identified Avery as the proprietor.

  37. 37.

    Hardy (1895, p. 32) argues that there were similar proposals as early as 1623, but he provides few details on these proposals.

  38. 38.

    Later, the Attorney General said that he thought that Hamblin and Avery merely intended to diversiy the colors of the lights by making them burn blue or green (Adams and Woodsman 2013, p. 87).

  39. 39.

    Coyne and Leeson (2004, p. 237) have coined the term “evasive entrepreneurship” to describe such activity. Avery and Hamblin, while engaging in productive entrepreneurship, also were expending effort and resources to evade being excluded from the coastal lighting market by Trinity House.

  40. 40.

    Stevenson (1959, p. 139) makes it clear that the patent they obtained was unusual. The normal patent empowered its holder to collect dues for a term of years from every vessel. The type of patent received by Avery and Hamblin “allowed an individual to exploit an invention for 14 years” (ibid.). One secondary source asserts that once they had obtained their patent, Avery and Hamblin petitioned for the “power of levying payment” (Anonymous 1865, p. 624). However, no other source mentions that aspect of the petition. In fact, other sources highlight the “voluntary” nature of the payment system (Cruden 1843, p. 412; Pask 1884, pp. 604–605). Moreover, one of the key complaints of Trinity House in its November 1731 petition is the system of public subscriptions upon which the financing of the Nore lightship rested (National Archives. PC 1/5/3 1731).

  41. 41.

    The accounts of the reactions can be found in multiple sources. They all offer the same timeline and storyline with varying degrees of detail (see Anonymous 1865, p. 624; Renard 1867, pp. 193–195; Adams 1870, p. 254; Gattie 1890, pp. 156–159; Hardy 1895, pp. 72–75; Stevenson 1959, pp. 138–140).

  42. 42.

    Adams and Woodman (2013, p. 87) mention that Hamblin attempted to open another lightship (date undisclosed) with a Yarmouth pilot at the Cockle Gat, but that Trinity House turned them down, preferring the existing lighthouse.

  43. 43.

    This line of reasoning explains why Avery’s negotiation of a license with Trinity House to keep the lightship operating resulted in private operators of lighthouses joining hands with Trinity House to protest the lightship’s patent.

  44. 44.

    Krause (2015) provides an example lighting provision with buoys in the case of a present-day suburb of Buenos Aires. While we have focused on the case of the lightship as an example, buoys and other seamarks should enter future studies as well.

  45. 45.

    Bertrand’s argument also aligns with the broader portrait of rent seeking between different interest groups that were competing for the rents from the British Crown (see Zahedieh 2010). As such, lighthouse operators can be seen as one of the many groups participating in that wider historical struggle.

  46. 46.

    Of that amount, £11.25 came from superannuated pensions to seamen–an expense that Avery and Hamblin would not have needed to cover (House of Commons 1834, p. 346). To remain conservative, we did not adjust for this minor issue.

  47. 47.

    The same numbers were reported in a House of Commons document (House of Commons 1816, Vol XIX, pp. 149–173). That probably is the source of Cotton’s numbers.

  48. 48.

    The lowest level of expenses was in 1813, at £479.8 and the highest was in in 1808, at £840.6.

  49. 49.

    The lowest level of expenses after removing collection costs was in 1813, at £357.9 and the highest was in in 1808, at £694.3.

  50. 50.

    These numbers refer to large vessels. Willan (1934 [1964], pp. 103–105) points to lower costs, but the numbers therein apply to barges, lighters and trows.

  51. 51.

    Ralph Davis (1962, pp. 373, 378) reports a wide array of prices–few of which include the cost of fitting-out ships with masts, spars, ropes and the critical pieces of equipment for lightships, such as anchors and lanterns. He reports only construction costs. Armstrong (1991, p. 80) argues that fitting out a ship inflated total costs by somewhere between 50% and 100%. Those percentages probably are too low for a lightship, given the special equipment it requires. The lanterns were not inexpensive and the anchors were specifically designed (mushroom anchors) to limit drifting. As such, we used the high bound of the fitting-out cost when using Craig's (1971, p. 129) estimate. 

  52. 52.

    The first sailed at 19 tons and acted as an experiment (the ship was christened Experiment), while the latter weighed at 100 tons (Cruden 1843, p. 412; Grubb Street Journal July 22nd 1731).

  53. 53.

    On another page of the House report (1834, p. 340), oil consumption is given at 193 gallons rather than 199 gallons. The difference would reduce operating costs by £2.4.

  54. 54.

    The quantity of oil to be burned would be roughly constant.

  55. 55.

    Seamen were paid the same wages as construction laborers; the mate was paid the wage of a skilled craftsmen, while the master was paid twice the wage of a skilled craftsmen. Converted to 1832 pounds, those wages are higher than the ones reported by the House of Commons in 1834. As such, we believe that our estimate is upwardly biased. We also should not assume size of the crew in 1832 was the same as in 1731. Hiring only a master and two seamen brings the cost to £256.48.

  56. 56.

    Wherries are excluded.

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Acknowledgements

The authors wish to acknowledge the helpful comments of Elodie Bertrand, Peter Boettke, Laurent Carnis, Tyler Cowen, Christopher Coyne, Daniel D’Amico, Alexandra Foucher, Anton Howes, Mark Koyama, Martín Krause, Erik Lindberg, Adam Martin, Ryan Murphy, Jamie Bologna Pavlik, Ennio Piano, Benjamin Powell, Alexander Salter, David Skarbek, Emily Skarbek, Judy Stephenson, Edward Stringham, Robert Whaples, Robert Wright, and Andrew Young. We also thank the seminar participants at the American Institute for Economic Research and the Free Market Institute at Texas Tech University, where earlier drafts of this paper were presented. Special thanks go to the archivists at the British Library and the Trinity House Corporation. We also extend a special thanks to William Shughart and Peter Leeson for their valuable feedback and suggestions. Any remaining errors are entirely our own.

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Correspondence to Rosolino A. Candela.

Appendix: Estimating the costs and revenues of the lightship at the Nore

Appendix: Estimating the costs and revenues of the lightship at the Nore

In order to properly assess the potential profitability of the lightship and the extent of free riding that its operators could tolerate, it is necessary to estimate operating costs and potential revenues. In the present appendix, we prudently use an array of sources providing different nominal values at different points in time. In order to maintain comparability, we deflated prices. Unless stated otherwise, the prices are reported in 1832 terms. The resulting estimates of profitability are meant to present a conservative scenario as we believe our estimates of potential revenues to be understated while operating costs are overstated.

Costs

The best starting point for operating costs is the 1834 report to the House of Commons. In that report, the lightship at the Nore reported expenditures of £681 for the year 1832 (House of Commons 1834, p.412).Footnote 46 In 1820, that figure stood at £949.8 (House of Commons 1834, p. 412). Joseph Cotton (1818, pp. 186, 196)Footnote 47 provides revenues and net produce of the lightship at the Nore for the period between 1805 and 1815, which allows us to generate expenses of £605.2.Footnote 48 As discussed in the text, Avery and Hamblin relied on voluntary payment mechanisms rather than the mandatory dues collection system of Trinity House, whose agents would collect the fees and keep a share of those fees. In 1820 and 1832, collection costs represent 17.4 and 25.4%, respectively, of all expenditures. If we deduct collection costs (which Avery and Hamblin would have avoided) and apply those proportions to the 1805-1815 estimates, we can arrive at an estimate of operating costs for the lightship at the Nore. In 1820 and 1832, operating costs would have been equal to £784.6 and £508.1. Between 1805 and 1815, those costs would have been between £451.5 and £499.9.Footnote 49 How well do these figures relate to 1731, given that they relate to estimates more than a century later?

One way to answer the question is to consider the cost reported by Avery in 1733 for “fitting out” the lightship. When Avery reported costs incurred at £2,000 (£3,491 in 1832 terms), some sources mention that the expenses were for “fitting out” (Stevenson 195, p. 140). However, other scholars seem to think that Avery’s £2,000 encompasses both operating and building costs (i.e., variable and fixed or sunk costs) because he referred to expenses on the “project” (Adams and Woodman 2013, p. 87). However, it is plausible that Avery meant construction costs only, given the numbers available for the building of later lightships. For example, the Owers Lightship was built in 1788 at a cost of £6,112 (Adams and Woodman 2013, p. 88)–close to twice the figure reported for the lightship at the Nore. In the 1740s, a fully fitted-out ship cost £23.7 per ton (Price 1976, p. 720).Footnote 50 Another estimate from the 1770s, augmented by fitting-out costs, brings the total to £23.6 per ton (Craig 1971, p. 129).Footnote 51 Relying on those estimates, the cost of fitting out the two shipsFootnote 52 launched by Avery and Hamblin stands between £2808.4 and £2820.3. Given that the first lightship (the 19-ton Experiment) was launched in late July 1731 and replaced by the larger 100-ton Good Intention in October 1731, which operated outside of Trinity House’s purview until November 1733, the annual operating costs would be between £298.1 and £303.4. Those estimates are biased upward because they include the legal fees Avery and Hamblin incurred to acquire their patent and to fight Trinity House’s petition to revoke it. We also assume that the lightship was just an ordinary vessel with no special fixtures (like the mushroom anchor and the lanterns) that would have increased fitting-out costs (and thus reduced our estimate of operating costs).

Another way to determine costs would be to estimate operating costs directly. In 1832, the lightship at the Nore consumed 199 gallons of oil and hired three seamen, one mate and one master (House of Commons 1834, p. 332).Footnote 53 If we assume the same oil consumption for 1731Footnote 54 and also assume 365 days of wages being paid for the same crew size, we can use Clark’s (2005) wage and price data to estimate operating costs.Footnote 55 Doing so, we arrive at £345.04 per year in operating costs. We also believe this cost estimate to overstate costs as there is an emerging literature in economic history that asserts that English daily wage rates tend to be overstated. On the one hand, new archival evidence has shown wages to be inferior than previously (Stephenson 2018). Simply shifting from the wage rates reported for unskilled building laborers to wage rates for unskilled farm workers reduces the annual operating cost by £14.8.  On the other hand, daily wage rates are not the most ideal measure as pre-19th century workers tended to sacrifice large shares of the going day-labour wage rate if they could obtain steady employment (Broadberry et al. 2015: 265–266; Humphries and Weisdorf 2015, 2017). Given that the workers on the lightship would have been employed year long, the cost of their labor to the operator was probably inferior to what we estimated. Nevertheless, we believe that this estimate is probably the most accurate of the three we generated here. 

As such, as can be seen in Fig. 1, most of the estimates come in below or equal to £500 per year, with the exception of 1820.

Revenues

The estimation of revenues must be understood as a measure of “potential revenues”. Those potential revenues would have been the same regardless of whether or not collection was voluntary. For our purposes, the goal is to see what share of this potential the Nore lightship had to tap to be profitable, and we interpret this as the room available to tolerate free riders.

The largest complication regarding the calculation of revenues relates to entrances and clearances into the Port of London. From some of the advertisements in 1731, we see mention that the fees are per “voyage”. Based on those advertisements, we do not know if they applied round-trip of for each passage. Navigation dictionaries define a voyage as “a journey by sea out and home” (Russell 1883, p. 156). However, from a later advertisement–when Avery secured his deal with Trinity House–we know that the rates applied to ships “passing and repassing” the Nore lightship (Grubb Street Journal November 1st 1733), meaning that each voyage meant two payments. For larger vessels engaged in transatlantic trade, no problem is posed as such ships did not make large numbers of voyages per year. However, for the Baltic, Mediterranean and coastal trade, ships made numerous visits to the Port of London. That frequency raises questions about how to estimate potential revenues. We base our fees on “voyage”, knowing full well that if dues were assessed on each leg of a trip, our case is only made stronger as potential revenues will be larger.

Using the breakdowns of ship classes provided by Colquhoun (1800, pp. 11–13) and the entries into the Port of London provided by Usher (1928, p. 471), we can arrive at estimates of coastal and foreign trade entries into London. For 1728, Usher (1928, p. 471) estimates that 2,152 British and foreign vessels engaged in foreign trade entered the Port of London. Applying the advertised rates to the categories of ships homeported in London for 1732 provided by Colquhoun (1800, p. 9), we arrive at revenues of £204.7 from international vessels.

For the coastal trade, we interpolated the values provided by Usher (1928, p. 471) for 1700 and 1750 to arrive at 6,079 coastal ships in 1731. The coastal trade includes smaller coasters and larger colliers (i.e., ships engaged in the coal trade, largely out of Newcastle). According to Colquhoun (1800, p. 13), the average coaster weighed 73.1 tons in 1798, while the average collier was much larger at 228 tons. Unfortunately, Colquhoun (1800, p. 13) provides breakdowns only for the smaller coasters (of which 86% were less than 100 tons). Assuming that the breakdown of the coastal trade fleet was the same in 1731 as it was in 1798, and that colliers exceeded on average 200 tons (Hausman 1991, p. 593), we arrive at a conservative revenue estimate, namely that Avery and Hamblin collected revenues of £208.3 from coasters and £262.5 from colliers. The total income from those sources, amounting to £675.4, would have constituted the bulk of potential revenues for the lightship at the Nore.

However, less important revenue sources are harder to estimate. Colquhoun (1800, pp. 14–15) pointed out that in the late 18th century, an additional 2,288 lighters, barges and punts circulated on the River Lea and the upper and lower Thames, plus some 3,000 wherries (small ships of 10–12 tons) and a little more than 300 bumboats, sloops, cutters, hoys and fishing peter boats. Alone, the barges, lighters, punts, boats, sloops, cutters and hoys (with an average weight of 32.2 tons per ship)Footnote 56 “in active service in the Port of London” numbered 3,419 in 1796 (Colquhoun 1800, p. 15), representing 23.1% of the ships entering the port at the time. Converted to 1731 proportions, tat percentage translates into an additional 1,901 ships. As such, those smaller vessels potentially added £47.5, bringing total revenues to £723. Readers should bear in mind that the smaller vessels would have made numerous trips down the Thames and that our estimate assumes that they made only one voyage. Adding the other small ships also would raise the pool of potential earnings. However, we prefer not to include them in the estimates because we know that some smaller ships (less than 20 tons) tended not to be subject to light dues at all. Finally, all our estimates of revenues exclude proceeds that would have come from the subscription period (pre-payments). Taken together, those considerations imply that our estimates of potential lightship revenues are biased downward.

By way of comparison, the lightship at the Nore collected £2553.6 in revenues in 1832 (House of Commons 1834, p. 333). By that time, rates had doubled for all ship categories below 200 tons, with an additional shilling to pay per 100 tons. Given the larger volume of entry into the Port of London (Usher 1928, p. 471), our estimation appears to be reasonable.

Profits and plausibility

Given the cost and the conservative revenue estimates, the surplus of potential income over operating costs varies from £330.4 and £377.3 per year. Stated differently, Avery and Hamblin needed to collect somewhere between at worst 51.1% of our downwardly biased estimate of potential revenues to earn a profit. Using the estimates relating to 1805-1815 and 1832, the lightship kept well within the range of profitability: between £167.3 and £223.9. Only 1820 shows a loss of £109.2. How plausible are those estimates?

To answer that question, it is necessary to consider the deal that Avery reached with Trinity House. To continue operating the lightship at the Nore, Avery agreed to pay £100 per year to Trinity House. For him to have accepted such a deal, his profits must have been greater than that sum. Not only that, but he would have had to pay Trinity House for the right to collect light dues, sums ranging between 17.4 and 25.4% of operating costs in 1820 and 1832. Our estimates suggest that he plausibly could have agreed to bear the extra cost burden (collection costs and lease payments) while continuing to earn a hefty profit.

The foregoing discussion lends credence to our calculations and lead to the conclusion that the operation of the lightship was profitable even if our estimates of operating costs are biased upwardly and our revenue estimates are biased downwardly. Additionally, it is worth pointing out that Avery and Hamblin were about to open two more lightships–at the Scilly Isles off the Cornish coast and at the Well. Avery and Hamblin would not have contemplated expanding their coastal lighting services had they been losing money. Nonetheless, we urge caution and suggest that further efforts be devoted to estimating the profitability of lightships.

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Candela, R.A., Geloso, V.J. The lightship in economics. Public Choice 176, 479–506 (2018). https://doi.org/10.1007/s11127-018-0573-x

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Keywords

  • Government failure
  • Lighthouse
  • Lightship
  • Market failure
  • Public goods

JEL Classification

  • D72
  • H40
  • P48