Tragedy of Incentives

One of the Daily Dish's guest authors raises the issue here of America's delusional assumption that Iraq's care about the whole. Part of this may hark back to the negative connotations people have concerning incentives. I am referring to something along the lines of: "Altruism is what good people do, bad people need incentives to achieve the same results". As an example, in high school the founders of the US were never discussed as having benefited from the break from England, but they went from being the second class (below the ruling British) to being the elite as a result. They also got to shape the future of a nation and become one of the few models for democracy the world has ever known. How cool is that?

We should be asking questions like "Does the ruling party in Iraq feel like a stable Iraq is there only option? If not, how do we incentivize them to create a stable Iraq?". But if we are trapped in the 'good people are altruistic' mode, we can't ask those kinds of questions and hope to find an answer.

NPV of user

What is equation for valuating users that incorporates referrals? I haven't found this on the web anywhere and they didn't teach it at Wharton so I thought I should write up what I've managed to stumble through on my own. I probably am just missing the right terminology to do a proper search for it; maybe a reader can help.

1. It costs money to acquire a user. Let's call this the cost per click (CPC)


2. It not all clicks lead to registered users. Let's call this the conversion rate for ads (CONV-ADS)


3. Each registered user is worth money. We can break this out in terms of click through rates etc. but for now lets just stick to average revenue per user (ARPU)


4. Each user refers one or more users (REF)


5. Each referred user has its own conversion rate (CONV-REF)


6. Finally, refers take time. We can break out average time per referral and use a yearly discount rate, but to simplify let's assume you did that and now just have a discount rate per referral iteration (DIS)

The equation starts out like this:

NPV = -CPC + CONV-AD * ARPU

Which is simply chance of getting a registered user times value of that user minus cost of acquisition.

Now to add referrals, we change the value of that user:

NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * ARPU)

This prices in the value of the referrals to the value of the original user. The discount rate leads to:

NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * ARPU)

But of course each referal can refer someone else:

NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * ...

You get a geometric series which converts back down to:

NPV = -CPC + CONV-AD * ARPU / ( 1 - X)

Where X = REF * CONV-REF / ( 1 + DIS)

This converges if X < 1, otherwise you get infinite value per user. Of course this assumes conversion rates, referral rate and ARPU are constant as your user base grows and therefore can't really 'price' infinite iterations of referrals, but I'm finding it useful to do sensitivity analysis on various changes to web sites when I set N in the geometric series to something like 3 rather than infinity as above.

Renaming some of the terms will probably make this equation less web centric, but the web vocabulary is what I'm most familiar with these days.

Money blinders

The Economist comes to the conclusion that the west no longer controls worldwide money supply here. I think they are underestimating money supply growth greatly; what about all the counterfeit currency the North Koreans are printing? That won't show up in official reports. The M0 increase may be concentrated in the west so even their assumption that all the growth is in emerging markets may be wrong.