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RobinZ comments on The Math of When to Self-Improve - Less Wrong
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I am sad because my attempt to teach you about preference reversals has almost certainly failed.
ADDED. For reference, here is the whole dialog on preference reversals.
ADDED. On most subjects, I would have let my esteemed interlocutor have the last word so as to keep the peace and so as not to appear as a self-aggrandizing jerk who cannot stop trying to get one up on the person I am disagreeing with. I humbly suggest however that in subjects like math where there often is an objectively-correct fact of the matter, everyone benefits a lot from writers not being too afraid to be confrontational. One of those benefits is "clarity" (something concrete for the reader's mind to latch onto), something easily lost in the abstractions in conversations about math. In other words, I humbly suggest that a competent writer involved in a dialog about math will appear to observers who are not used to good dialogs about math to be unnecessarily domineering, rude, dogmatic or otherwise socially inept even if he is not.
ADDED. In other words, in internet discussions on math (or programming languages), if you care too much about not insulting or embarrassing your interlocutor, my experience has been that the whole discussion tends to become a hazy fog.
ADDED. I am open to learning from others here how to improve the social side of my communications in dialogs like this.
Sorry, the concrete example. Take
and point future income functions
which (using the Dirac delta function) correspond to instantaneous incomes at times t = 10 and 20. That is, 2010 and 2020.
Using these functions,
and
Note that to find (say) the value of F_2 in 2010, you would write
which is not equal to P(F_1).
The OP gives two examples of market pricing - the market price for a website, and a perhaps more subjective price of acquiring a marketable skill set. The question of how to value cashflows to determine a market price has been pretty well studied. The fundamental theorem of arbitrage-free pricing basically boils down to saying that to avoid arbitrage possibilities in pricing, risk-adjusted cashflows must be discounted at a risk-free rate.
The scope of this theorem is continuously traded securities; it seems reasonable to apply inductive logic to extend this result to any commodity well modeled by a Walrasian auction. This would include, I think, a marketable skill set.
When the OP talks about 'my discount rate', he must be referring to his personal preferences - i.e., his utility function.
I don't know much economics, but I think the point I was making was that other utility functions were possible. I don't have any comment on pricing risk.