As to the rest of what you said, isn't it somewhat obviated by the article, it saying that the Doyle estate has been making money from his works, despite them being written around a hundred years ago? I'm wondering if I misunderstood something.
Yes.
The purpose of US copyright is to "promote Science" (that is, written knowledge"), and to effect that by "securing for limited times to authors ... the exclusive right to their respective writings". Since Doyle was a British subject, he'd have been governed by UK statute and purpose, and I'm less familiar with British legal doctrine in this case. I do understand, though that UK copyright at the time his works were authored didn't extend to 2014 -- that was a subsequent extension.
Which means: at the time Doyle composed his works, the benefits he anticipated could not have extended to the present day. Even if they had, the economic present-value analysis shows that the benefit would have been minuscule.
The fact that the Doyle estate has been benefiting from his writings has no retroactive incentive encouraging his writing them in the first place.
If the work does live on, you won't be charging a constant price for them year after year - the price of a book, for example, will go up to match inflation, so if you sell a constant number of books per year, your "dollar" revenue will also go up with inflation (I'm ignoring technological advances in printing, etc., which are independent of this argument). It is essentially in this way that the Doyle estate continue(s/d) to make money from Arthur's works, albeit through licensing - the point is those things were priced at current market value.
However, I personally don't believe that the creators of copyrightable works take any of this into account when they are producing those works, partly because of the uncertainty involved in future revenues - it is highly likely that any given work will be one of the ones that just dies, and so anyone who might bank on a perpetual revenue stream is probably deluded, and most people are smarter than that.
I'm not sure, but I think your analysis might provide the expected value of a work, but that is essentially meaningless for someone who is only going to produce a relatively small number of works, which are highly unlikely to somehow represent a random sample of all possible works.
Assuming I understood correctly, I agree with everything in the post to which I'm replying, regarding the role of incentives, just not the present-value analysis you refer to.
Prices rising with inflation is only keeping them stable in constant dollars. You'd have to apply an inflation discount to your future revenues as well.
My model isn't trying to argue that you'd value the actual real-world value of a book in terms of a constant, real-value, revenue stream. Reality is far less remunerative than that.
It's that even if that were an accurate model, the distant-future revenues would provide a minimal incentive to a current opportunity-cost analysis of writing for publication and income vs. alternative activities.
Which is to say: copyright terms are far longer than can be justified on an economic basis as incentive to authors.
That they're an incentive to present copyrightholders of aged works with some present value isn't at debate, but that's the only justification for post-hoc copyright term extension.
Also, apologies for not replying sooner, I thought you'd lost interest and had stopped checking.
Notwithstanding which, those numbers actually indicate that even after 70 years there's a significant present value in the return. You wrote: "Assuming a $1000 constant payment stream, the present value of the 70th payment is only $32.86."
I would write that: "Assuming a $1000 constant payment stream, the present value of the 70th payment is still as high as $32.86". And they'll be even better than that since very-long-term compound average discount rates are low, closer to 3% iirc.
Instead, try modelling an annuity (yes, that's as bogus as the perpetuity, but bear with it) for two periods: 45 years and 52 years. At 3%, I make that a 5.5% better deal for the extra seven years of viability. I won't bore everyone with the math.
Note also, I'm not arguing for the current system; merely pointing out that (irrespective of other complications) setting IP rights as coterminous with the originator is inequitable.
Which means that you're looking at a future payment stream that's both decreasing nominally AND is being discounted to an ever increasing amount.
But in order to support the increasingly perpetual duration of copyright, for which only a handful of works benefit, the public is enjoined from having access to _any_ works published in the past century, unless the copyright holder can be found, identified, and persuaded to publish the work.
This has a number of profound effects.
There's a hole in the sale of new editions from Amazon (not "freely available downloadable books", mind you, but sales) from 1920 to 2000. There are more books from the 1840s available than from the 1930s.
Germany's industrial expansion from a series of disjoint states to the powerhouse of Europe in the 19th century is thought to have been greatly promoted by weak copyright.
I explore both here: http://www.reddit.com/r/dredmorbius/comments/23xrkd/copyrigh... (with some bonus entertainment thrown in).
Freakonomics has looked into the question of whether or not copyright makes books disappear: http://www.reddit.com/r/dredmorbius/comments/1wp3o8/freakono...
And noted copyright jurist and author Pamela Samuelson, of UC Berkeley, has stated: "Copyright has become the single most serious impediment to access to knowledge" http://www.reddit.com/r/dredmorbius/comments/1wssas/copyrigh...
What I don't support is for the term to be either indeterminate (as the repeated extensions of the past century have established), or perpetual, or even particularly extended. There are only a small number of cases where a 50-60 year term wouldn't be sufficient, and the concept of an extension means that unvalued works would enter into the public domain quickly.
To achieve the ends, that is, the progress of science and useful arts, the means is provided: exclusive rights for limited times.
Unfortunately, the future value of a 70 year income stream is effectively nil.
You can look at this in terms of the present values of annuities or perpetuities. In the case of a perpetuity (a constant income stream forever), the present value is expressed as: C/r
Where C is the period cash flow, and r is the nominal rate of interest expressed as a decimal fraction, e.g., a 5% interest rate is given as 0.05.
The value for any period of the perpetuity is C/(1+r)^n
Where n is the period.
Assuming a $1000 constant payment stream, the present value of the 70th payment is only $32.86. Double that and you're down to $1.08 as present value of a $1000 future payment.
At 14 years, you're seeing $505 in present value, at 28 years, $255.
This is sensitive to the interest (discount) rate, where the present value falls as interest rises. A 10% nominal interest rate gives you a $263 value for 14 years, $69 at 28, $1.27 at 70, and $0.001 at 140 years. At a 2% interest rate, the values are $758, $574, $250, and $62, respectively.
So while your argument does make a case for a fixed term of copyright, it doesn't pass muster for an extensive duration. Nor, more compellingly, does it allow for the retroactive extension of copyright duration as has been the case for the Doyle estate. Sir Arthur didn't write his works, published between 1887 and 1927, with any reasonable expectation that his heirs or corporate designates would be continuing to profit by them in 2014.
http://www.investopedia.com/terms/p/perpetuity.asp