Markets and autorickshaws, or why I walk a lot!

Walking on a wet road covered with muck, and observing all autorickshaw drivers refusing pedestrians with disdain, I wondered what makes them tick. One day, between seething in anger and puzzling over some complex issues at work, I realized that the autorickshaw driver's propensity to take me from the station to home is driven by his expectations on the following:
a) Condition of the roads or rc
b) Condition of the autorickshaw or ac
c) Rickshaw meter reading or rr
d) Traffic conditions or tc
e) Population density or pd
f) Number of other rickshaws plying at that point of time or nr

Now, the rickshaw fare is driven by the meter, which is driven, most likely, by the motor rpm and time since it was engaged. It must therefore be correlated to the condition of the road and the traffic conditions.
The road condition is dependent on traffic conditions over a large period of time.
The autorickshaw condition is dependent on the usage of the rickshaw, which is reflected in the rickshaw meter reading, and the condition of the road.
Number of other rickshaws plying at that point of time is dependent on the popululation density in the neighbouring areas, and not so much vice-versa.

Now, under ideal situations, the condition of the road is perfect, the rickshaw runs on a four-stroke engine, rickshaw meter reading is electronically driven and there is no traffic. Let us assume the fare to be 'Base fare'.
Then, the actual fare is a factor of 'base fare' (or bf) and the variations of the conditions from the ideal situation.

The rickshaw driver will think to himself,"How much more than the base fare will I need to make at the minimum? That depends on how much do I make in a day, (or R). So, I will need to make some amount more than (R - bf)."

Now, let us assume that how much more (or less) the rickshaw driver expects to make is:
a) A linear function of the base fare and average fare, and takes the form of y = mx + c
b) Changes in the values of rc, ac, rr and tc are normally distributed around their average values

Then, let me construct a hypothetical variables called Alpha and Beta which are defined as
Alpha = var(pd)*var(nr)/covar(population density, number of other rickshaws)
Beta = var(rc)*var(ac)*var(rr)*var(tc)/covar(rc,ac,rr,tc)
Let us combine the two variables with Gamma = Alpha * Beta
Then, the minimum expected fare must be bf + Gamma*(R-bf)

All who have looked at coroporate finance will know that this is a shameless rip-off of Harry Markowitz' hypothesis of 'Capital Asset Pricing MOdel'. (Well, I am shameless and I do tend to rip-off). But coming back to my autorickshaw driver, he should in a glance think of making at least bf + Gamma*(R-bf).

If road conditions worsen, then the meter reading will have to increase for him to breakeven, since he also has to spend on maintaining the rickshaw condition. In other words, they move in opposite directions and hence, Gamma must be negative. The only way he can be compensated is plying longer distances to increase base fare, for a constant daily income R.

Since I stay close by, and the roads are bad, he figures, in a moment after spitting out paan, that it's not worth the effort, and he continues to stare at the road ahead. The only other question he has to figure out is whether to compete for the high-margin, long distance traveller or not ply at all. I marvel at his quick-witted intelligence, give him a tongue-lashing, and move on. But at least I know that he made the right decision.

As my unnecessarily elaborate theory explains
a) Repair the road and the autorickshaw driver will be motivated to take passengers to their destination
b) Regulate the rickshaw routes by making them pay differential prices for different routes, like a telecom spectrum auction
c) Enforce every autorickshaw driver to take a passenger, regardless of where the passenger wants to go
d) If all theory fails, take a commission from the rickshaw drivers and let chaos prevail.
e) If my theory does not explain reality, then the solution is to complicate it further by assuming that expected payoff is not a linear combination of multiple factors, and the multiple factors are not normally distributed but follow a power law. In mathematical terms, that's confessing,"What, me worry?"

Statistically speaking, this city lacks traffic sense; I trudge on through the slush.