[PPT] - Constrained Monopoly Pricing with Endogenous Participation Gabriel PowerPoint Presentation

SLIDE 1

Introduction Data Theory Estimation Evaluation

Constrained Monopoly Pricing with Endogenous Participation

Gabriel A. Basaluzzo1 Eugenio J. Miravete2

1Universidad de San Andr´

es

2University of Texas at Austin

& Centre for Economic Policy Research

April 1, 2009

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 2

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Performance of linear vs. nonlinear pricing

Almost non-existing theoretical results.

This is due to the technical complexity of second-degree price discrimination.

This is an open empirical question in an area where there are very few contributions available.

Spence (1977), Roberts (1979), Katz (1983).

The Robinson-Patman Act imposes some policy restrictions to second degree price discrimination:

Price discrimination of intermediate goods is forbidden (secondary line or alleged injury to rivals of the buyer).

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 3

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

What do we do in this paper?

Develop a “feasible” equilibrium model of second-degree price discrimination by a monopolist where:

Consumers’ intensity of preferences is private information. Consumers’ also differ in the subjective valuation of their alternative to abstain from consumption. Due to scarce data availability, we use very limited information.

This is an empirical implementation of the exclusive agency model of Rochet and Stole (2002).

The solution to this model may accommodate common features of current tariffs such as the existence of an allowance (something that no other model can explain).

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 4

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Single dimensional screening (1/3)

Key assumption 1 - Single crossing property: u(q, θ); uqθ(q, θ) > 0.

θ

θ

p(q) q

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 5

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Single dimensional screening (2/3)

Key assumption 2 - F(θ) is IHR to avoid this:

θ

f(θ)

θ

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 6

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Single dimensional screening (3/3)

Participation and consumption decisions are ordered by the same variable, θ, leading to a fully separating equilibrium:

T(q)

q

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 7

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Two dimensional screening

Participation and consumption decisions are ordered by different variables, (t and x). Bunching at the bottom always occurs:

T(q)

q

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 8

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Main task of the paper

Goal: To estimate a structural equilibrium of model of nonlinear pricing where core parameters are conditioned on observable characteristics of a cross-section of local wireless markets as well as

n the particular implementation of the nonlinear tariff by each

carrier in each market.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 9

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Tariff comparison

Once we have obtained the structural parameters we compare the performance of the following tariffs: Fully nonlinear tariff. Linear pricing (no quantity discounts). Flat tariff (just a monthly fee). Optimal two-part tariff. Coasian tariff (fixed fee + marginal cost). Performance evaluation includes:

Profits. Welfare. Market coverage. Quantity undersupply.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 10

Introduction Data Theory Estimation Evaluation Motivation Intuition Agenda

Applications

What do we use our model for? Evaluation of the universal service policy:

Balanced: maximize market coverage while the monopolist still breaks even. Lump-sum subsidy to ensure efficient provision.

Address the importance of a second source of asymmetry of information:

Rochet-Stole vs. Mussa-Rosen.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 11

Introduction Data Theory Estimation Evaluation Description

Market Description

Data only include tariff information. Individual consumption is not available. 50 largest U.S. local cellular monopoly markets (1984-88).

Monopoly is temporary and entry of competitor is exogenous. No need to model entry or entry deterrence strategies.

Data include all tariff plans offered by the incumbent:

Focus on tariff options defining the lower envelope of peak time. Include first and last quarter in the sample.

Complemented with Census, FBI, and U.S. HCN data.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 12

Introduction Data Theory Estimation Evaluation Description

Table 1: Tariff Features

Monthly Fee, Fi Rate per Minute, pi Option No. Mean Std.Dev. Mean Std.Dev. Markets with ONE option (56 observations) 1 28.78 (11.50) 0.39 (0.07) Markets with TWO options (23 observations) 1 14.13 (4.96) 0.55 (0.13) 2 40.68 (9.40) 0.38 (0.10) Markets with THREE options (16 observations) 1 3.24 (1.29) 0.63 (0.14) 2 15.65 (8.62) 0.46 (0.07) 3 33.41 (18.29) 0.31 (0.10)

Mean and standard deviations (between parentheses) of monthly fixed fees Fi and rate per minute pi are measured in dollars. Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 13

Introduction Data Theory Estimation Evaluation Description

Table 2: Descriptive Statistics

First Quarter Last Quarter Variables Mean Std.Dev. Mean Std.Dev.

PLANS

1.4783 0.6909 1.6304 0.7989

COVERAGE

0.0679 0.0681 0.0671 0.0679

TIME

4.1957 2.4094 11.5652 4.0423

MKT-AGE

2.1087 3.1849 24.6087 10.5756

INCOME

28.2225 3.7465 27.5302 3.3053

COMMUTING

26.1609 2.8513 26.2174 2.7778 sdv(COMMUTING) 16.8640 2.9783 16.8627 2.9391

RAIN

3.4107 1.9115 3.0609 2.0246

POVERTY

11.0500 3.0281 11.2304 2.9443

POP-AGE

32.7543 2.8836 32.6826 2.8606

EDUCATION

12.5500 0.2420 12.5370 0.2507

TCELLS

18.1739 18.5320 18.3478 18.4237

HHSIZE

2.6223 0.2877 2.6195 0.2878 sdv(HHSIZE) 1.4665 0.1602 1.4654 0.1604

DENSITY

15.8190 14.0903 15.1110 13.1091

OPERATE

6.5055 1.5614 6.4900 1.4977

PRIME

10.8424 0.6310 9.1809 0.9526

WAGE

6.9580 1.5533 7.3320 1.6649

BELL

0.8261 0.3832 0.8261 0.3832

REGULATED

0.4783 0.5050 0.4565 0.5036 Observations 48 47

All variables defined in Appendix A.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 14

Introduction Data Theory Estimation Evaluation General Approximation

Fully Nonlinear Solution

Principal and agents’ objective functions: Profit maximization: π(q) = P(q) − cq . Consumer surplus (linear demand): v(t, q, x) = tq − γ 2q2 − P(q) − x .

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 15

Introduction Data Theory Estimation Evaluation General Approximation Figure 1: f (θ) — Burr type XII density function

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 t/t 0.2 0.5 1.0 λ 2.0 5.0

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 16

Introduction Data Theory Estimation Evaluation General Approximation Figure 2: G(x) — Exponential distribution

1 2 3 4 5 6 7 8 9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 1/φ exp(−x/φ) φ = 1 φ = 2 φ = 5

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 17

Introduction Data Theory Estimation Evaluation General Approximation

Endogenous participation

Now participation decision is different for each consumer type t. Thus, the total market penetration is given by: M(u, t) = Prob[t, x ≤ u] = G(u)f(t) =

1 − exp
−u

φ

1

λ(t − t)

1 − t − t

t − t 1

λ−1

,

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 18

Introduction Data Theory Estimation Evaluation General Approximation

Monopolist’s problem

The monopolist’s optimal control problem is:

max

q(t),u(t)

Z

T

M(u(t), t) [P(q(t)) − cq(t)] dt , ˙ u(t) = q(t) ≥ 0, ˙ q(t) ≥ 0 , u(t) = tq(t) − γ 2 q2(t) − P(q(t)) ≥ 0 .

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 19

Introduction Data Theory Estimation Evaluation General Approximation

Solution with optimal exclusion

Bunching at the bottom is always optimal for a monopolist:

0=φ exp(−φu(t))(t − t) » u(t) − 1 2 ˙ u2 – + [1 − exp(−φu(t))] (t − t) [2 − ¨ u(t)] − „ 1 λ − 1 « [1 − exp(−φu(t))] [t − ˙ u(t)] , ˙ u(t)=q(t) , q(t)≥qfb(t) , q(t)=qfb(t).

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 20

Introduction Data Theory Estimation Evaluation General Approximation

Approximately Optimal Screening

Firms offer a few tariff options to their customers. Possible existence of marketing and commercialization costs, which are in general unobservable. Foregone profits decrease rapidly with the number of tariff

ptions offered.

Firms choose the number of tariff options provided their expected profits, which depend on distribution of consumer tastes and the realization of marginal costs. Simultaneously, our computed value for these core parameters depend on the actual number of tariff options.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 21

Introduction Data Theory Estimation Evaluation General Approximation

The monopolist solves:

ˆ π(ν|ω) = max

y∈[0,1)2ν ˜

π “ ˜ P(A(y), b(y), q)|ω ” , y1 < y2 < . . . < yν < yν+1 < . . . < y2ν , bν+1−i(y) = c + (t − c)yi i = 1, 2, . . . , ν ti(y) = c + (t − c)yν+i i = 1, 2, . . . , ν A1(y) = [t1(x) − b1(x)]2 2γ , Ai(y) = Ai−1(y) + [bi−1(y) − bi(y)] h ti(y) −

bi−1(y)+bi(y) 2

i2 γ , ˜ P(A(y), b(y), q) = min

i

Ai(y) + bi(y)q .

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 22

Introduction Data Theory Estimation Evaluation

MSM

The vector of structural parameters is ω = (λ, γ, φ, t, c)′ ∈ R5: We condition these parameters on observable market characteristics: ωi = Mzi + εi , ε ∼ N(0, Σ) . Conditional on zi, we can obtain: ˆ ωi = E(ω|zi) = ˆ Mzi .

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 23

Introduction Data Theory Estimation Evaluation

Given ˆ ωi we need to solve for the optimal tariff conditional on the number of options offered in each market (which is taken as given). For each ˆ ωi = ˆ Mzi the model predicts for each market:

Monthly fee ˆ A. Price per minute ˆ b. Market penetration ˆ M(u, t).

In addition, using the information across markets we also

btain a prediction of:

Average household consumption (active subscriber) (Sample: 160 minutes/month). Average monthly bill (Sample: 100 dollars/month).

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 24

Introduction Data Theory Estimation Evaluation

Difficulties

“Few” moments available, in particular for two-part tariffs. If we want to increase the number of regressors in M, we need to consider higher moments of the distribution of fixed monthly fees, price per minute, or share of market penetration. Every new option offered by a carrier doubles the number of moments related to ˆ A and ˆ b. Simulation requires solving the optimal nonlinear tariff and its particular implementation (with a given number of tariff plans) countless number of times. This is a very expensive process.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 25

Introduction Data Theory Estimation Evaluation

Table 5: Welfare, Usage, and Market Penetration First Best Nonlinear Flat Linear Two-Part Coasian ONE Option

MONTHLY FEE

0.0000 150.6434 0.0000 29.1809 108.7219

RATE PER MINUTE

0.1022 0.0000 0.4907 0.3784 0.1022

PROFITS

0.0000 1.0000 0.8579 0.9687 0.9915 0.9147

PROFITS (⋆)

0.0000 2.1609 1.9360 2.1047 2.1434 1.9680

WELFARE

1.0000 0.7383 0.6869 0.7376 0.7365 0.7171

WELFARE (⋆)

5.2581 3.8793 3.7176 3.8737 3.8716 3.7650

COVERAGE

0.1356 0.0558 0.0444 0.0633 0.0542 0.0458

AIRTIME USAGE

269.2043 266.2942 388.4190 226.8420 275.9493 356.1682

UNDERSUPPLY

1.0000 0.4169 0.4580 0.4038 0.4134 0.4595 TWO Options

MONTHLY FEE

0.0000 119.1983 0.0000 24.5869 59.4836

RATE PER MINUTE

0.2724 0.0000 0.6357 0.4851 0.2724

PROFITS

0.0000 1.0000 0.8185 0.9464 0.9881 0.9461

PROFITS (⋆)

0.0000 0.5816 0.5427 0.5545 0.6021 0.5752

WELFARE

1.0000 0.7406 0.6432 0.7378 0.7375 0.7252

WELFARE (⋆)

1.3717 0.9817 0.9876 1.0118 1.0101 0.9919

COVERAGE

0.0620 0.0264 0.0220 0.0314 0.0264 0.0239

AIRTIME USAGE

151.4041 152.0511 212.2645 125.4655 154.9054 188.4619

UNDERSUPPLY

1.0000 0.4161 0.4589 0.4034 0.4125 0.4587 THREE Options

MONTHLY FEE

0.0000 92.9783 0.0000 19.4348 39.8904

RATE PER MINUTE

0.2077 0.0000 0.5403 0.3950 0.2077

PROFITS

0.0000 1.0000 0.8324 0.9368 0.9887 0.9552

PROFITS (⋆)

0.0000 0.2587 0.2302 0.2350 0.2554 0.2515

WELFARE

1.0000 0.7400 0.6539 0.7374 0.7375 0.7277

WELFARE (⋆)

0.5684 0.4231 0.3801 0.4194 0.4206 0.4178

COVERAGE

0.0398 0.0178 0.0152 0.0207 0.0173 0.0166

AIRTIME USAGE

121.0355 121.3356 178.0736 96.2239 123.4832 139.3662

UNDERSUPPLY

1.0000 0.4167 0.4588 0.4035 0.4132 0.4592 Median of the distributions across markets. All variables are defined in the text. PROFITS(⋆) and WELFARE(⋆) indicate the money value

f these variables in millions of dollars for a market with mean potential customer base of about 400,000 customers.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 26

Introduction Data Theory Estimation Evaluation Distribution Effects Robustness

Universal Service

The constrained monopolist’s problem is:

max

P (q)

Z

T

M(u(t), t)dt , s.t. Z

T

M(u(t), t) [P(q(t)) − cq(t)] dt ≥ 0 , M(u(t), t) = » 1 − exp(−u(t) φ ) – 1 λ(t − t) „t − t t − t « 1

λ −1

, u(t) = tq(t) − γ 2 q2(t) − P(q(t)) ≥ 0 , q(t) ∈ argmax

q

n tq − γ 2 q2 − P(q)

,

q1 ≤ q2 ⇒ P(q1) ≤ P(q2), ∀q1, q2 .

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 27

Introduction Data Theory Estimation Evaluation Distribution Effects Robustness

Table 6: Average Effects of Universal Service Policy

First Best Break Even Free ONE Option

WELFARE

1.0000 0.8262 0.9670

COVERAGE

0.1356 0.1727 0.1616

AIRTIME USAGE

269.2043 148.3324 279.8256

UNDERSUPPLY

1.0000 0.5510 1.0395 TWO Options

WELFARE

1.0000 0.8425 0.6317

MARKET PENETRATION

0.0620 0.0764 0.0723

AIRTIME USAGE

151.4041 89.5111 172.9245

UNDERSUPPLY

1.0000 0.5912 1.1421 THREE Options

WELFARE

1.0000 0.8709 0.7902

MARKET PENETRATION

0.0398 0.0468 0.0577

AIRTIME USAGE

121.0355 79.5081 135.5475

UNDERSUPPLY

1.0000 0.6569 1.1199

Results reported for the median of the parameters values. Variables are defined as in Table 5.

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 28

Introduction Data Theory Estimation Evaluation Distribution Effects Robustness Figure 1: F(t) — Who participates under universal service?

0.5 1 1.5 2 2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

t [$/min] 1 - e-u(t)/φ N = 1

Break even Free service First best

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 29

Introduction Data Theory Estimation Evaluation Distribution Effects Robustness Figure 2: F(t) — Consumption profile under universal service?

0.5 1 1.5 2 2.5 100 200 300 400 500 600

q(t) [min]

Break even First best Free service

Basaluzzo-Miravete Constrained Monopoly Pricing

SLIDE 30

Introduction Data Theory Estimation Evaluation Distribution Effects Robustness

Robustness Check

Since due to lack of individual usage data our result depend on particular functional form assumptions, we need to test whether they will change to different specifications:

Alternative maximum consumption. Beta Distributed types: F(t|a, λ) = Γ(a + λ−1) Γ(a)Γ(λ−1) (t − t)a−1(t − t)λ−1−1 (t − t)a+λ−1−2 . Nonlinear demand: v(t, q, x) = tρ+1 γ(ρ + 1) » 1 − “ 1 − γ t q ”ρ+1– − P(q) − x . Non-CRS technology: TC(q) = c 1 + w q1+w .

Basaluzzo-Miravete Constrained Monopoly Pricing