Applied economists are "detectives". We know that we do not know your preferences. If we could learn about your willingness to pay for market goods such as cell phones or for non-market goods such as clean air and safe streets, then both businesses and governments will demand our services. Economists look for clues and design experiments to learn about people. For example, if a person buys a $5 Starbucks drink then we immediately learn that a lower bound on how much she is willing to pay for such a drink is $5. If a week later, when the price is now $7 if she no longer buys it then, we now have learned that we can bound her willingness to pay for this product between $5 and $7 dollars. This book applies this revealed preference logic to dozens of problems to teach you how economists learn about people by watching what they choose under different circumstances.
If the following revealed preference problem interests you, you can buy my Amazon book; "An Introduction to Empirical Microeconomics" for $1 on Amazon.
In the typical intermediate microeconomics class, the teacher tells you the consumer's utility function and the consumer's budget constraint and tells you to solve for the consumer's optimal behavior.
My entire book studies the inverse of this problem. I tell you what the consumer chose and what her budget constraint was. As the budget constraint shifts (because of changes in the economy), I ask you to solve for what you have learned about the consumer's utility function.
This is an important exercise because in this age of Big Data, this is what applied economists actually do for a living.
Here is one example from my book. When I revise this example, I will include a utility function and ask the reader to put bounds on the consumer's marginal rate of substitution at various points of the domain of the function in pizza, cell phone minutes consumption space.
New Problem
Maurice
gains utility from eating pizza and talking on his cell phone (measured in
minutes talking). He has an income of
$300. The market price of pizza is
$1. Maurice does not own a cell
phone. The cell phone company offers him
three different annual plans. The cell
phone company knows that people have different preferences over pizza and
talking but doesn’t know “who is who”.
Plan
B: Maurice pays $50 for the phone and he
must pay 20 cents per minute of talking.
Plan
C: Maurice pays $120 for the phone and he must pay 0
cents per minute of talking.
Make
a graph with pizza consumption on the vertical axis and minutes talking on the
horizontal axis. Graph the two plans in
the same graph and label each.
Answer
Take
a careful look at the figure above, do you see that plan B dominates plan C
for people who want talk less than 180 minutes on the phone while plan C (the free
talking plan) dominates plan B for those who want to talk more than 180
minutes.
How
do I see that? Consumers gain utility
from eating pizza and talking on the phone.
Consider a person who wants to talk 500 minutes on the phone. If she
chooses plan C, she will have 180 pieces of pizza while if she chooses plan B,
she will have 250 - .2*500 = 150 slices of pizza so this person will pick plan
C.
The
two different plans create a separating equilibrium as those who “love to talk”
will choose plan C, while those quiet people will self select to choose plan B.
Note
that the two plans cross each other at the point pizza = 180 and minutes =
350. So, anyone who is willing to pay
more than .2 slices of pizza to speak for a 181st minute should pick plan C over
plan B. Why? The price of a marginal minute under plan B
is .2 slices of pizza while the price of a minute under plan C is 0. If you choose plan C over plan B, you reveal
you value an extra minute of talk more than the marginal cost (measured in pizza)
of purchasing that minute.
New Problem
Building
on the previous problem, now suppose the cell phone company offers a modified
Plan B such that the price is set at 10 cents per minute. Under what set of circumstances will this new
pricing policy be profitable for the firm?
Answer
First,
let’s graph the original plans and the new pricing plan.
Under
the new modified plan B, the budget line is less steep because cell phone
talkers only now have to sacrifice .1 slices of pizza per minute they talk
versus under plan B when they had to sacrifice .2 slices.
Notice
several points based on the graph. All
of those people who picked plan B will now prefer Modified plan B because it
offers a lower price per minute. Note
that the green line (modified plan B) lies above plan B so it offers more pizza
and cell phone minutes.
Point
#2 is that some Plan C people will now substitute to modified plan B. These are the people who seek to talk for
less than 700 minutes (where the green line and red line cross). Those people who love to talk will choose
plan C.
Could
it be profitable for the cell phone company to offer Modified plan B rather
than Plan B? Note that by lowering the
price of a cell minute, people who move from plan B to modified Plan B will
talk more minutes. Also note that
people who substitute from plan C to modified plan B will now pay per minute.
It is true that the company would not earn the $120 per plan C enrollment. The
rational company would trade this off.
My
goal here is to teach you how a company uses a non-linear pricing strategy to
allow it to learn about its heterogeneous customer’s preferences. By offering
these different plans, the diverse population reveals “their type”.
The
cell phone company would observe the percentage of all customers who choose
each plan. Since the cell phone company
knows your zip code (because they mail you a bill), it can also calculate the
percentage of all customers who choose Plan B, Modified Plan B and Plan C by
zip code. Such simple data could
indicate patterns for example zip codes with more teenagers may feature a
larger percentage of households choosing plan C. Such information is useful for future
marketing campaigns.
