Structural Models for Customer Behavior under Nonlinear

Pricing Schemes

Raghu IyengarColumbia University

Scenario

Consider two wireless calling plans -

How do customers choose a plan and decide on usage?

Impact of access fee and marginal price on - Customer behavior Firm profitability

Plan Access Fee, Free Minutes

Marginal Price

A $30, 200 minutes

$0.40

B $40, 350 minutes

$0.35

Pricing Scheme – Wireless Services

Cost

of

Con

sum

pti

on

Consumption

Included Minutes

F

qt2qt1

R2

p1 = 0

p2 > p1

underageoverage

If consumption is qt1 then total cost = F (access fee)

If consumption is qt2 then R2 = F + (qt2 – Incl. Min.) p2

Plan A

Access fee = $30

Free minutes = 200

Marginal price =$0.40

Issues

Marginal price depends on consumption

Choice and consumption are related

Customers can defect

Dissertation

Develop structural models for explaining: Choice of calling plans within a service

provider Consumption of minutes Defection decisions (churn)

Policy experiments (Firm decisions)

Myopic customers (Essay-1) Forward-looking customers (Essay-2)

Presentation Outline

Past Research Structural model (Essay-1) Data description Null models / estimation results Policy experiments Essay-2 (brief description)

Past Research

Marketing Subset of decisions Simpler pricing schemes – linear price,

two-part tariffs

Economics Labor supply Nonlinear income taxes

Essay1 - Myopic Customers

(beginning of month)

(during the month)Actual Usage

Anticipated Consumption

Plan Choice Defection

Modeling – Choice and Consumption Process

Utility Specification

For customer i , plan j and decision time t :

x1ijt : Minutes consumed x2it : Outside good (numeraire) zijt, wijt : Vectors containing covariates (past usage) ij : Plan specific intercept ijt : Choice errors

Utility Maximization – Budget Set

For customer i , plan j and time t :

F1

A1 B

p1

p2

C1 C2

Optimal Consumption

F2

A2 B

p1

p2C

1C2

Optimal Consumption

Plan1 Plan2

Choice Decision

Value of a plan = Maximum utility that a consumer derives under that plan

Value = f (Optimal Consumption)

Customers choose plan with the highest value at the beginning of every time period

Actual Consumption

Actual Consumption = Optimal Consumption + Error

If Aj < Optimal Qty. < B

Optimization errorOptimal Qty.

Actual Qty.

Economic Restrictions

Slutsky restrictions

Ensures quasiconcavity of utility function

Customer Heterogeneity

i – Set of all customer-specific parameters

Si contains demographics for customer i and are population-level parameters

Hierarchical Bayesian Model

Data

Wireless Service Provider Monthly billing data : September,

2001- May, 2003 New customers : August, 2001-

December, 2001 300 customers 5151 observations – each a monthly bill Average 17 months per customer

Data

Four calling plans 200, 300, 350 and 500 peak minutes Access Fee - $30, $35, $40, $50 Marginal Price - $0.40 per minute 70% of the data covered by these

four plan types

Summary statistics 98 people churn 5% observations have a plan change

Variables

State dependence Effect of past choices on current decisions Dummy variable that captures past choice

Past usage variables

Promotional events Free roadside assistance, valentine’s day

promotion Dummy variable that captures a promotion

Null Models

Null Models

Biggest challenge – how to incorporate the entire pricing schedule

Two null models – they differ in how the expectation process is specified

Expected Consumption

Plan Choice Defection

Actual Usage

Null Models

Null Model - 1 Previous month’s usage as the expected

consumption

Null Model – 2 Expectation formation uses covariates

Both models incorporate customer heterogeneity

Model Comparison

Structural model is overwhelmingly supported by the data (Kass and Raftery, 1995)

Models Log-Marginal Log-BFNull Model-1 -9169.42Null Model-2 -9156.49 12.93Structural Model -8962.92 193.57

Estimates – Structural Model

The subscripts z and w refer to the covariates in the vector zijt and wijt respectively

Estimates – Structural Model

Overage variables Negative effect on choice and

consumption Upgrade plans or lower usage

Underage variables Negative effect on utility of plans Positive effect on consumption Downgrade plans or increase usage

Managerial Questions

How do the different components of the pricing scheme affect customers’ decisions?

What is the relationship between pricing, customer responses and customer lifetime value?

Policy Experiments

Policy Experiments

Access price / marginal price

Price increase / price decrease

Temporary / permanent

Policy Experiments – Marginal Price Change

Plan 3 – Price Increase

Plan 3 – Price Decrease

Effect of 25% Permanent Change in Marginal Price for Plan 3

Time varying elasticity Adjacent plan effect Asymmetric price effect

Plan

1 2 3 4200 300 350 500Minut

es

Policy Experiments – Marginal Price Change

Effect of 25% Temporary Change in Marginal Price for Plan 3

Ripple effect

Plan 3 – Price Increase

Plan 3 – Price Decrease

Policy Experiments – Customer Value

Access price effect is higher than marginal price for most cases

Highest effect of access price on “low usage” users on Plan 1

Highest effect of marginal price on “high usage” users on Plan 4

5% Decrease in the plan prices

300

350

500

200

Minutes$35

$40

$50

$30

Access Fee

2 3 41Plan

Conclusions

Developed a structural model Adaptable to other service contexts

Used policy experiments for gauging the effect of changes in pricing schemes on Customer behavior Firm profitability

Essay-2 : Learning Models

Essay-2 : Learning Models

Myopic learning model Consumers are uncertain about

actual usage while choosing plans

They have prior beliefs about the distribution of actual usage

They observe their actual usage and update (learn) their beliefs

Essay-2 : Myopic Learning Model

;

Belief specification

0.2 0.4 0.6 0.8 1

2

4

6

8

0.2 0.4 0.6 0.8 1

1

2

3

4

Usage

Essay-2 : Forward-Looking Model Assumptions

Mental hassle costs associated with plan changes

Customer and plan-specific variance

Customers’ beliefs Priors on the different variances Usage on a plan leads to an update of

the belief parameters associated with only that plan

Essay-2 : Forward-Looking Model Tradeoff

Stick with a plan : get more precise information about the variance associated with only that plan

Change plans : improve the knowledge of the variance under the chosen plan but pay mental hassle costs of switching

Dynamic Programming

Extensions

Competition

Rollover and other features

Roaming, long distance and other types of minutes