The distinction between marginal and average values is a vital point in economics. Critical year i was among a team of researcher who obtained into a robust conflict with some other researchers – play out through a series of journal papers and also letters come the editor – top top matters connected to mean values, marginal values, and total values. 

The conflict was around sharks. We had published a record on the financial value of shark-related tourism in Palau (Vianna et al. 2012) (see PD207). Human being go there specially to dive through sharks, and also they spend a most money in the process. We uncovered that the sharks that communicate with tourist in Palau would certainly generate much less revenue if they were captured by fishers.

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Catlin et al. (2013) subsequently published a record in which castle criticised several files (including ours) for estimating the worths for tourism of separation, personal, instance animals, fairly than bigger aggregations that animals.

They asserted that, ‘‘The basic characteristics of wildlife tourism tasks do not lend us to valuation at the individual animal level.’’ your stated comes to were that: the tourists might have invested the money anyway; that is hard to determine the number of animals in the population; that is simple to confuse yearly values with life time values; the animals that interact with tourists may be atypical of the population, making extrapolation dangerous; and also if comparing tourism to extractive uses, the relevant population sizes can be different.

They didn’t state whether they were pertained to with the median value the a shark, or the marginal value of a shark, or both. They never used the terms “average value”, or “marginal value”, simply the ambiguous term “individual value”.

The simplest, and most amusing, failure in their document was the claim that we presented individual values in our file at all. Every our outcomes were gift at the level the the whole populace of sharks that engage with the Palau travel industry.

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Photo: G. Vianna

In an previously report, which ended up being the subject of an write-up published in the brand-new York Times, we had converted the results into an mean value every shark, based upon high-quality information around the dimension of the population. Ns guess Catlin et al. Must have seen that report and assumed we’d excellent the exact same thing in our newspaper article, without analysis it properly.

Anyway, earlier to average and also marginal values. In a Letter come the Editor, we stated that invidual values could be average or marginal, the average and marginal values space different, the Catlin et al. Had actually not distinguished in between them, that none of the pertains to raised by Catlin et al. Impacted the conclusion of our study, and that, although we hadn’t excellent so in the newspaper article, it would have actually been meaningful and also valid to current the typical value the sharks because that tourism and also compare it v their mean value for fishing.

That last suggest is just demonstrated. If you recognize the dimension of the population, compare tourism and fishing worths for the whole population of sharks is no various to comparing castle on average, per animal. The mean values are just the populace values divided by the populace size. If the question is, ‘should we carry out all one or all the other?’, and you use averages correctly, friend will never be misled around which alternative is an ext valuable.

The other way to obtain an “individual” value would it is in to calculate the marginal worth of a shark: the adjust in value resulting from changing the number of sharks by one. Because that example, if the Palau authorities wanted to recognize the optimal balance in between sharks because that fishing and sharks because that tourism, they would have to estimate the marginal values for each use for different levels that fishing matches tourism. The optimal allocation would be whereby the marginal worth for tourism equaled the marginal value for fishing (because, if the marginal value for one was smaller than the other, you could make more money by relocating towards the other.) If castle were never equal, the optimum would be either every fishing or all tourism. When again, it is meaningful and also valid come look at individual values – in this instance marginal values.

Of course, it would certainly be challenging to accurately estimate the marginal worth of sharks because that tourism, however no more an overwhelming than estimating the aggregate values for different levels the fishing matches tourism. In fact, the marginal value curve is merely the slope of the aggregate value curve, therefore if you know one, you deserve to derive the other. Once again, the difference between individual (marginal) values and accumulation values is a false distinction. They are carefully inter-related.

So, what occurred in the robust debate? Catlin et al. Released a Letter in answer to our Letter, but they just made problem worse, really.

Most outrageously, they said that “Our article is trying to allude out the the two values are frequently confused.” Talk around moving the score posts! it does nothing of the sort. It doesn’t even mention average or marginal values. It just lumps them together as “individual” values.

They claimed that we had compared average worths for tourism with marginal worths for fishing “without explaining that they space not straight comparable”. Since we didn’t existing average values for travel in the paper, that’s clearly not strict correct. However reinterpreting the comment, there is something to it. It suggests that catching much more or fewer sharks might conceivably change the industry price that sharks, and it’s true that us didn’t permit for that. However, in the situation of Palau, there room only about 100 sharks that hang about at tourist spots. If caught and also sold, this sharks would be a small speck in the market. Clearly, market prices for the 100 sharks would certainly hardly vary, if in ~ all, if fewer or much more of them to be caught. That’s why us assumed a continuous price (= a continuous marginal value for fishing), which method that the marginal value amounts to the average value and also can validly be compared with the average value for tourism.

Note the the price that sharks would need to be staggeringly sensitive to the number caught in stimulate to adjust the an outcome that the sharks room worth more alive 보다 dead. Specifics the industry value that a captured shark would need to increase from $100 every shark to, I’d estimate, number of hundred thousands dollars every shark. Over there is no possibility that our assumption of a constant price had any type of material impact on the conclusion.

In any case, the criticism is irregularity to the straightforward question of whether marginal or mean values are valid and also meaningful if used correctly. That is a criticism of making use of marginal and average values incorrectly.

To wrap up their reply, Catlin et al. Recurring their claim that “valuation at an industry, location, or other higher scale is a an ext robust and reliable measure 보다 is the valuing of individual animals.” Clearly, that’s wrong. Separation, personal, instance and aggregate values space too closely inter-related for the statement to make sense. For some management questions, the forced information is marginal values, or, equivalently, accumulation values offered in a means that discover what the marginal values are. For other monitoring questions, the forced information is median values, or, equivalently, accumulation values that are equal to the average values time the population size.

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We chose not to send an additional Letter to the Editor, reasoning they’d be i can not qualify to publish a third letter on the topic. Rather we sent a letter directly to Catlin. He recognized receipt, but that’s all.

Further reading

Catlin, J., Hughes, M., Jones, T., Jones, R. And also Campbell, R. (2013). Valuing individual animals through tourism: science or speculation? Biological Conservation 157, 93–98. Abstract at journal net site

Catlin, J., Jones, T., Campbell, R., Hughes, M. And Jones, R. (2013). Letter to the Editor: keeping perspective on using tourism worths for conservation – answer to Vianna, Biological Conservation 166, 303. Journal web site

Vianna, G.M.S., Meekan, M.G., Pannell, D.J., Marsh, S.P. And also Meeuwig, J.J. (2012). Socio-economic and also community services from shark diving by tourists in Palau: a sustainable usage of reef shark populations, Biological Conservation 145(1), 267-277. Abstract at journal web site

Vianna, G.M.S., Meekan, M.G., Pannell, D.J., Marsh, S.P. And also Meeuwig, J.J. (2013). Letter come the Editor: Valuing individual pets through tourism: science of speculation? – answer to Catlin et al. (2013), Biological Conservation 166, 301-302. Journal web site

Kirillov, S. (1974). Marginal and average values in the concept of price formation, Problems of financial Transition 16, 42-59. Ideas page