Equilibrium, Efficiency, and Asymmetric Information
I
TAXI!
You have just landed at the airport in a city that you are visiting for the first time.
You hail a cab to take you to your hotel. How can you be sure that the driver
chooses the quickest and cheapest route to your destination? You can't, unless
you make an investment beforehand; an investment of money to purchase a
map and of time to compute the shortest route between your departure point
and your destination. Even then, you will not know which streets are normally
congested, so it would be very costly to discover the cheapest route. Assuming
that you are not prepared to incur that cost, is there any way of ensuring that
the taxi driver will not take you out of your way to enhance his or her income
at your expense? We need to find a way of providing the driver with an incen-
tive to choose the least-cost route, so that even though you don't know what
that route is you will be sure that the driver has chosen
it
because that choice
maximizes the
driver's
return from operating the cab. This is the purpose of the
fixed part of the nonlinear pricing schedule for taxi rides. The fare is
F
+ cD
where D is the distance to your destination in miles, c is the charge per mile,
and
F
is the fixed initial fee which is independent of the length of the ride. (In
fact, you will be charged for time spent idling in traffic, but let's keep things
simple.)
If
F
is zero, and hence the fare is
cD,
then the driver has a strong incentive to
make each trip as long as possible. That's a consequence of the fact that when
passengers are dropped off at their destinations,
it
takes the taxi driver time to
find a new passenger. On one hand, from the driver's standpoint, it would be
better to keep the meter running by keeping the original passenger in the cab,
and that requires taking a much longer route than necessary. On the other hand,
if the fixed fee is relatively large-say $3.00 when the average variable cost per
ride is $6.00-then the driver has a strong incentive to maximize the number of
trips per day. But maximizing the number of trips per day can be accomplished
only by making each trip as short as possible.
Example 2.1: The linear fare induces shirking
F
=
0 and
c
=
1. Hence the fare is equal to D, the distance of the trip. To simplify,
each trip is 5 miles long when the taxi driver takes the short route, and the long
route is 10 miles long. The driver can make 30 trips a day of 10 miles each or 55
trips a day of 5 miles each. (Remember, time is lost between trips.) When the
driver works efficiently her revenue is 55 x $1 x 5 = $275. But when the driver
shirks, and takes the long route, her daily revenue is 30 x $1 x ] 0
=
$300: She
makes more money by shirking.
The linear fare schedule (with