[PPT] - Investment, Dynamic Consistency and the Sectoral Regulators PowerPoint Presentation

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Introduction Model Equilibrium Examples Extensions Conclusion

Investment, Dynamic Consistency and the Sectoral Regulator’s Objective

Duarte Brito1 Pedro Pereira2 João Vareda2

1UNL, 2AdC

May 19th, 2010

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Introduction

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Investment

in many regulated industries incumbents make large investments

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Regulatory Trade-o¤

static e¢ciency: control market power and dynamic e¢ciency: promote investment

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Dynamic Consistency Problem

e.g.: access prices before investment: high access prices after investment: low access prices

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Dynamic Consistency Problem

reduces investment

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Solution

distort Regulator’s Objective Function

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Solution

ensure Regulator’s decision without commitment same with commitment

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Requirements

exists Third Party that:

1 sets Regulator’s Objective

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Requirements

exists Third Party that:

1 sets Regulator’s Objective 2 immune to dynamic consistency

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Third Party: Legislator

legislative cycle longer regulatory cycle

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Overview of Presentation

1 Model

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Overview of Presentation

1 Model 2 Equilibrium

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Overview of Presentation

1 Model 2 Equilibrium 3 Examples

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Overview of Presentation

1 Model 2 Equilibrium 3 Examples 4 Extensions

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Introduction

Overview of Presentation

1 Model 2 Equilibrium 3 Examples 4 Extensions 5 Conclusion

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 1: Players

1 Duopoly: incumbent, entrant

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 1: Players

1 Duopoly: incumbent, entrant 2 Regulator

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 1: Players

1 Duopoly: incumbent, entrant 2 Regulator 3 Legislator

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 2: Incumbent

1 vertically integrated: wholesaler+retailer

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 2: Incumbent

1 vertically integrated: wholesaler+retailer 2 invests

("quality; #marginal costs)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 2: Incumbent

1 vertically integrated: wholesaler+retailer 2 invests

("quality; #marginal costs)

3 wholesaler produces essential input

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 2: Incumbent

1 vertically integrated: wholesaler+retailer 2 invests

("quality; #marginal costs)

3 wholesaler produces essential input 4 access price price of essential input: α

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 3: Entrant

1 retailer

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 3: Entrant

1 retailer 2 needs access to essential input

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 4: Regulator

1 sets access price: α

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 4: Regulator

1 sets access price: α 2 unable to commit to access price

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 4: Regulator

1 sets access price: α 2 unable to commit to access price 3 Objective Function:

Γ = θiΠi(α) + Πe(α) + θcCS(α)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 5: Legislator

1 sets Regulator’s objective function: fθi, θcg

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 5: Legislator

1 sets Regulator’s objective function: fθi, θcg 2 able to commit to weights

(change laws harder than change access price)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 6: Timing

1 Legislator sets Objective Function

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 6: Timing

1 Legislator sets Objective Function 2 Incumbent invests

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 6: Timing

1 Legislator sets Objective Function 2 Incumbent invests 3 Regulator sets access price

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 6: Timing

1 Legislator sets Objective Function 2 Incumbent invests 3 Regulator sets access price 4 Duopolists play market game

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 7: Main Assumptions

1 Incumbent’s pro…t increasing in α

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 7: Main Assumptions

1 Incumbent’s pro…t increasing in α 2 consumer surplus decreasing in α

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Model

Model 7: Main Assumptions

1 Incumbent’s pro…t increasing in α 2 consumer surplus decreasing in α 3 weights vary w/ investment:

n θj

i, θj c j j = n, o

Duarte Brito, Pedro Pereira, João Vareda

UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Equilibrium

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Case of Under-investment

Incumbent’s incentives to invest smaller social incentives to invest

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Notation

αj θj

i, θj e

= arg max

α

Γ = θiΠi + Πe(α) + θcCS(α) αj

ω = arg max α

W = Πi(α) + Πe(α) + CS(α)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Lemma

αj θj

i, θj c

increasing in θj

i

decreasing in θj

c

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Low Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 < θo c

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Low Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 < θo c 2 Incumbent: invests

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Low Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 < θo c 2 Incumbent: invests 3 Regulator: αn (θn i , θn c) = αn ω

[αo(θo

i , θo c ) < αo ω]

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Intermediate Investment Cost

1 Legislator:

θn

i > 1 = θn c

θo

i = 1 < θo c

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Intermediate Investment Cost

1 Legislator:

θn

i > 1 = θn c

θo

i = 1 < θo c 2 Incumbent: invests

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: Intermediate Investment Cost

1 Legislator:

θn

i > 1 = θn c

θo

i = 1 < θo c 2 Incumbent: invests 3 Regulator: αn (θn i , θn c) > αn ω

[αo(θo

i , θo c ) < αo ω]

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: High Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 = θo c

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: High Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 = θo c 2 Incumbent: does not invest

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Proposition: High Investment Cost

1 Legislator:

θn

i = 1 = θn c

θo

i = 1 = θo c 2 Incumbent: does not invest 3 Regulator: αn (θn i , θn c) = αn ω

[αo(θo

i , θo c ) = αo ω]

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Equilibrium

Comment

reproduce equilibrium with commitment

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Examples

Examples

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Examples

Examples

1 Hotelling w/ negatively sloped demands:

Biglaiser and DeGraba (2001), Brito et al. (2010)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Examples

Examples

1 Hotelling w/ negatively sloped demands:

Biglaiser and DeGraba (2001), Brito et al. (2010)

2 quantity competition w/ spillovers:

Foros (2004), Kotakorpi (2006)

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Extensions

Extensions

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Extensions

Extensions

1 over-investment

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Extensions

Extensions

1 over-investment 2 investment independent weights

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Extensions

Extensions

1 over-investment 2 investment independent weights 3 retail regulation

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Conclusion

Conclusion

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Conclusion

Conclusion

1 solution to dynamic consistency problem:

distort regulator’s objective away from social welfare

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Conclusion

Conclusion

1 solution to dynamic consistency problem:

distort regulator’s objective away from social welfare

2 need independent third party

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Conclusion

Conclusion

1 solution to dynamic consistency problem:

distort regulator’s objective away from social welfare

2 need independent third party 3 derive very general su¢cient conditions

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011

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Introduction Model Equilibrium Examples Extensions Conclusion Conclusion

Thank you!

Duarte Brito, Pedro Pereira, João Vareda UNL, AdC ACORN-REDECON, Lima, 2011