RobinZ comments on The Math of When to Self-Improve - Less Wrong

6 Post author: John_Maxwell_IV 15 May 2010 08:35PM

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Comment author: RobinZ 16 May 2010 12:05:15PM *  0 points [-]

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).

Comment author: Dan_Moore 17 May 2010 08:10:07PM 0 points [-]

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.

Comment author: RobinZ 17 May 2010 08:39:26PM 0 points [-]

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.