For 4.6 billion years, the Sun has provided free energy, light, and warmth to Earth, and no one ever realized what a huge moneymaking opportunity is going to waste. Well, at long last, the Sun is finally under new ownership.
Angeles Duran, a woman from the Spanish region of Galicia, is the new proud owner of the Sun. She says she got the idea in September when she read about an American man registering his ownership of the Moon and most of the planets in the Solar System – in other words, all the celestial bodies that don’t actually do anything for us.
Duran, on the other hand, snapped up the solar system’s powerhouse, and all it cost her was a trip down to the local notary public to register her claim. She says that she has every right do this within international law, which only forbids countries from claiming planets or stars, not individuals:
“There was no snag, I backed my claim legally, I am not stupid, I know the law. I did it but anyone else could have done it, it simply occurred to me first.”
She will soon begin charging for use. I advise her to hire a good consultant because pricing The Sun is not your run-of-the-mill profit maximization exercise. First of all, The Sun is a public good. No individual Earthling’s willingness to pay incorporates the total social value created by his purchase. So it’s going to be hard to capitalize on the true market value of your product even if you could get 100% market share.
Even worse, its a non-excludable public good. Which means you have to cope with a massive free-rider problem. As long as one of us pays for it, you turn it on, we all get to use it. So if you just set a price for The Sun, forget about market share, at most your gonna sell to just one of us.
You have to use a more sophisticated mechanism. Essentially you make the people of Earth play a game in which they all pledge individual contributions and you commit not to turn on The Sun unless the total pledge exceeds some minimum level. You are trying to make each individual feel as if his pledge has a chance of being pivotal: if he doesn’t contribute today then The Sun doesn’t rise tomorrow.
A mechanism like that will do better than just hanging a simple price tag on The Sun but don’t expect a windfall even from the best possible mechanism. Mailath and Postlewaite showed, essentially, that the maximum per-capita revenue you can earn from selling The Sun converges to zero as the population increases due to the ever-worsening free-rider problem.
You might want to start looking around for other planets in need of a yellow dwarf and try to generate a little more competition.
(Actual research comment: Mailath and Postlewaite consider efficient public good provision. I am not aware of any characterization of the profit-maximizing mechanism for a fixed population size and zero marginal production cost.)
[drawing: Move Mountains from http://www.f1me.net]


10 comments
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December 6, 2010 at 4:43 pm
Donald A. Coffin
The real problem is that threats to turn the sun off aren’t credible…
December 7, 2010 at 11:30 am
Simon Board
The firm’s profits should equal
Pi=E[[\sum_i MR(v_i)-c(n)]P(v)]
where MR(v_i)=v_i-f(v_i)/[1-F(v_i)] and P(.) is the allocation function. If P=1 then, as n->\infty, this becomes
\Pi=n[v_0-c(n)/n]
where v_0 is the lower bound of the support of values and E[MR(v_i)]=v_0. Hence profits are zero if lim c(n)/n > v_0 and the sun will never shine (we can be more formal by using Chebyshev). With zero marginal production cost, profits will eventually be positive if v_0>0.
If we allow individual exclusion (compulsory blindfolds) then replace MR(v_i) with max{MR(v_i),0}. (See Peter Norman, 2004, ReStud)
December 7, 2010 at 4:02 pm
jeff
simon thanks. don’t we next want to optimize P(.)? Which I guess means setting P(v) = 1 if and only if \sum_i MR(v_i)-c(n) \geq 0 (and hoping that this gives a monotone P(.) )
December 8, 2010 at 12:52 am
Simon Board
I agree – the profit maximizing mechanism sets P=1 if \sum_i MR(v_i)-c(n)>0. I was just trying to show that as ‘n’ gets large then if
v_0 c) 0
Looking at the original M&P paper, their Theorem 2 is actually much stronger – it says that any mechanism that satisfies BB, IC and IR will never provide the public good. Hence this applies to both the efficient and profit-maximizing allocations.
December 8, 2010 at 12:57 am
Simon Board
Hmmm… WordPress seems to hate equations. It was supposed to read:
I agree – the profit maximizing mechanism sets P=1 if \sum_i MR(v_i)-c(n)>0. I was just trying to show that as ‘n’ gets large then if v_0 > lim c(n)/n =:c, the sun never shines. To see this, apply Chebyshev: Pr(|\sum_i MR_i-v_0|>c) 0.
Looking at the original M&P paper, their Theorem 2 is actually much stronger – it says that any mechanism that satisfies BB, IC and IR will never provide the public good. Hence this applies to both the efficient and profit-maximizing allocations.
December 8, 2010 at 12:59 am
Simon Board
I can take a hint: I give up.
December 8, 2010 at 8:40 am
jeff
Simon, yes if c(n) is (asymptotically) linear in n (which is what MP assumed.) so, in other words, per-capita revenue shrinks to zero. but if per-capita costs shrink to zero faster (for example if there is a fixed cost but no variable costs) then there can be positive profits even asymptotically.
December 7, 2010 at 2:44 pm
AS
Can we sue her for giving us skin cancer, sun burn, heat strokes?
October 12, 2011 at 9:10 pm
Anonymous
How about the forest fires, drought. And we might sue her for daylight
saving time since it hasn’t saved anything and most of us have suffered because we had to get to early.
July 11, 2017 at 10:51 am
Earl
Skype has opened its internet-dependent consumer beta for the entire world, following
launching it broadly within the Usa and You.K. previously this month.
Skype for Website also now works with Linux and Chromebook for immediate text messaging interaction (no video and voice yet,
those call for a plug-in installment).
The increase of the beta provides support for an extended set of different languages to assist strengthen that international functionality