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.
Sorry, the concrete example. Take
%20=%201%20+%200.001%20t)and point future income functions
;%20F_2%20=%20\$100%20\times%20\delta(t-20))which (using the Dirac delta function) correspond to instantaneous incomes at times t = 10 and 20. That is, 2010 and 2020.
Using these functions,
=\$100\times\exp\left(%20\int_0%5E{10}-\log(1+0.001t)dt\right)\approx\$95.14)and
=\$100\times\exp\left(%20\int_0%5E{20}-\log(1+0.001t)dt\right)\approx\$81.98)Note that to find (say) the value of F_2 in 2010, you would write
=\$100\times\exp\left(%20\int_{10}%5E{20}-\log(1+0.001t)dt\right)\approx\$86.17)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.