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Optimal Pricing, Subsidies and Solar Panels A two-sided market approach Ral Bajo-Buenestado 12 Markus Kinateder 1 1 Department of Economics, University of Navarra 2 Baker Institute for Public Policy, Rice University 36 th USAEE conference

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Optimal Pricing, Subsidies and Solar Panels

A two-sided market approach Raúl Bajo-Buenestado12 Markus Kinateder1

1Department of Economics, University of Navarra 2Baker Institute for Public Policy, Rice University

36th USAEE conference Washington DC, September 24th 2018

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 1

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Introduction

Overview

1

Introduction

2

Model Setup

3

Equilibrium in the absence of environmental policies

4

Equilibrium in the presence of environmental policies

5

Conclusions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 2

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Introduction

Motivation

  • Distributed Generation (DG) has become a popular option

for many households

Solar PV (rooftop panels) is the top choice

  • Emergence of new kind of agents: “producer-consumers”

(prosumers)

  • Why such an increase of popularity of DG (solar)?

Decrease in cost of solar panels –see IRENA (2017) Subsidies are also key (abundant literature)

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 3

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Introduction

Motivation

  • The emergence of solar panels has some positive effects
  • But there is also an indirect negative impact on consumers:

The Cost Recovery problem

Customers with solar PV reduce their energy consumption and then reduce the contribution they make to the network costs The network costs that are under-recovered from customers with solar PV have to be paid by all other customers

Australia’s Energy Networks Association (2014)

This problem is exacerbated w/ subsidies to solar panels

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 4

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Introduction

Research question and contributions

  • Some papers already pointed out these distortions...

...but there is no formal model showing them

  • We fill this gap by providing a model in which agents

endogenously choose their “role” in the market

  • For different policies we study:

Incentives for agents to become prosumers Redistributional impact on all other consumers

  • We model the electricity market as a two-sided one

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 5

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Introduction

Main features of two-sided markets

a) Two groups of end-users b) Platform enables interaction between the groups of end-users c) The groups of end-users provide each other network benefits

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 6

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Introduction

Main features of two-sided markets

a) Two groups of end-users b) Platform enables interaction between the groups of end-users c) The groups of end-users provide each other network benefits Example: videogames

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 6

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Introduction

Main features of two-sided markets

a) Two groups of end-users b) Platform enables interaction between the groups of end-users c) The groups of end-users provide each other network benefits Example: shopping malls

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 7

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Introduction

Electricity Markets

Electricity markets can be seen as a two-sided market

  • Weiller and Pollitt (2013) already suggested this idea

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 8

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Introduction

Electricity Markets

Electricity markets can be seen as a two-sided market

  • Weiller and Pollitt (2013) already suggested this idea

a) Two groups of end-users

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 8

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Introduction

Electricity Markets

Electricity markets can be seen as a two-sided market

  • Weiller and Pollitt (2013) already suggested this idea

b) Platform enables interaction between end-users

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 9

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Introduction

Electricity Markets

Electricity markets can be seen as a two-sided market

  • Weiller and Pollitt (2013) already suggested this idea

c) End-users provide each other network benefits

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 10

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Introduction

Electricity Markets

Electricity markets can be seen as a two-sided market

  • Weiller and Pollitt (2013) already suggested this idea

c) End-users provide each other network benefits

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 11

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Introduction

An important clarification

  • We study incentives/distortions created JUST by policies
  • But we abstract away from

Potential costs or savings derived from energy prices Other energy-related costs and prices

  • Assumption: residential solar PV is at grid parity

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 12

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Model Setup

Overview

1

Introduction

2

Model Setup

3

Equilibrium in the absence of environmental policies

4

Equilibrium in the presence of environmental policies

5

Conclusions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 13

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Model Setup

Platform & Agents

  • Independent Transmission system operator (TSO)

Monopoly platform Connects generators (G) and consumers (C) Manages the T&D of electricity

  • A unit-measure, continuum of agents choose to become:

a) Generators (join side G), NG b) Consumers (join side C), NC c) “Both” producers and consumers of electricity, NX

Prosumers (rooftop solar panel owners)

d) Not to join the platform (off-grid agents)

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 14

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Model Setup

Prosumers

  • Prosumers sell or buy depending on the sun (randomly)

a) Sell with probability θi b) Buys with probability (1−θi)

  • Selling/buying: a random variable ∼ Bernoulli distribution

with parameter θi ∈ (0,1)

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 15

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Model Setup

End users’ valuations

  • vj: agents’ idiosyncratic surplus of joining side j ∈ {G,C}

Independent for each agent Consumers are heterogeneous in both parameters v ≡ (vG,vC) ∈ R2, drawn from a joint distribution F(·)

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 16

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Model Setup

End users’ valuations

  • vj: agents’ idiosyncratic surplus of joining side j ∈ {G,C}

Independent for each agent Consumers are heterogeneous in both parameters v ≡ (vG,vC) ∈ R2, drawn from a joint distribution F(·)

  • Prosumers’ idiosyncratic surplus = θivG +(1−θi)vC

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 16

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Model Setup

Additional parameters

TSO fees

  • Consumers and prosumers pay fees to the TSO

Fixed fee (lump-sum): F Variable fee (per-unit of electricity): p

  • Fees are set by the TSO to compensate for transmission,

network expansion, O&M and other delivery costs Cross-side positive network effect

  • αj for j ∈ {G,C} = cross-side positive network effect

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 17

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Model Setup

Market timing

1

TSO chooses fees p ≡ (p,F)

2

Nature chooses v ≡ (vG,vC)

3

Agents observe p, θ,α and v, and choose side

4

Agents interact, and payoffs are realized

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 18

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Model Setup

Sides’ demands

  • Let us denote uj the utility of joining side j ∈ {G,C,X}
  • Side j demand is given by a combination of

a) A Participation Constraint (PC): uj > 0 b) An Incentive Compatibility Constraint (ICC): uj > u−j

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 19

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Equilibrium in the absence of environmental policies

Overview

1

Introduction

2

Model Setup

3

Equilibrium in the absence of environmental policies

4

Equilibrium in the presence of environmental policies

5

Conclusions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 20

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Equilibrium in the absence of environmental policies

Demand for solar panels

  • No policies that promote solar panels

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 21

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Equilibrium in the absence of environmental policies

Demand for solar panels

  • No policies that promote solar panels

Proposition In the absence of environmental policies, then NX = 0

If there are no policies, then there are no prosumers in equilibrium

  • Recall: the implicit assumption → grid parity

But grid parity has been achieved in very few places

  • Consistent w/ anecdotal evidence: Alabama, Oklahoma...

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 21

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Equilibrium in the absence of environmental policies

TSO’s regulated pricing

  • TSO’s profit = fees raised from agents minus costs

Per-transaction cost: c > 0 Fixed cost per consumer: C > 0

TSO costs –> infrastructure costs, losses, O&M costs, etc.

  • TSO = benevolent social planner

Fulfill the balanced-budget condition (π = 0) Set fees such that Revenue = Costs

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 22

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Equilibrium in the absence of environmental policies

TSO’s regulated pricing

  • TSO’s profit with no environmetal policies:

(recall —> no prosumers in the market)

π = (ˆ p−c)NGNC +( ˆ F −C)NC

where ˆ p and ˆ F TSO’s fees

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 23

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Equilibrium in the absence of environmental policies

TSO’s regulated pricing

  • TSO’s profit with no environmetal policies:

(recall —> no prosumers in the market)

π = (ˆ p−c)NGNC +( ˆ F −C)NC

where ˆ p and ˆ F TSO’s fees

TSO pricing such that π = 0: ˆ p = c+ C − ˆ F NG

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 23

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Equilibrium in the absence of environmental policies

TSO’s regulated pricing

Figure: TSO’s iso-profit line (π = 0)

ˆ p ˆ F

Marginal Cost pricing: (c,C)

c+ C

NG

C +cNG

C c All the (ˆ p, ˆ F) combinations in the line are equivalent

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 24

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Equilibrium in the presence of environmental policies

Overview

1

Introduction

2

Model Setup

3

Equilibrium in the absence of environmental policies

4

Equilibrium in the presence of environmental policies

5

Conclusions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 25

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Equilibrium in the presence of environmental policies

Environmental policies

1) Upfront installation-based (lump-sum) subsidies

California Solar Initiative (CSI) Australian Solar Rebate Greece (National Development Law 3908/2011)

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 26

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Equilibrium in the presence of environmental policies

Environmental policies: lump-sum subsidy

  • Prosumer utility under upfront lump-sum subsidy

uu

X ≡ θi[vG +αGNC +αG(1−θ)NX]+(1−θi)[vC +(αC −

p)NG +(αC −p)θNX]−F +S

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 27

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Equilibrium in the presence of environmental policies

Environmental policies: lump-sum subsidy

  • Prosumer utility under upfront lump-sum subsidy

uu

X ≡ θi[vG +αGNC +αG(1−θ)NX]+(1−θi)[vC +(αC −

p)NG +(αC −p)θNX]−F +S

Proposition If S > θiF ⇒ NX > 0

If subsidy is sufficiently large then there are prosumers in equilibrium

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 27

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Equilibrium in the presence of environmental policies

Lump-sum subsidy: TSO’s regulated pricing

  • TSO’s profit with a lump-sum subsidy S > θF:

(recall —> now there are prosumers in the market)

πu = (ˆ pu −c)(NG +θNX)[NC +(1−θ)NX] +( ˆ Fu −C)NC +( ˆ Fu −S−C)NX

where ˆ pu and ˆ Fu TSO’s fees

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 28

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Equilibrium in the presence of environmental policies

Lump-sum subsidy: TSO’s regulated pricing

  • TSO’s profit with a lump-sum subsidy S > θF:

(recall —> now there are prosumers in the market)

πu = (ˆ pu −c)(NG +θNX)[NC +(1−θ)NX] +( ˆ Fu −C)NC +( ˆ Fu −S−C)NX

where ˆ pu and ˆ Fu TSO’s fees

TSO pricing such that π = 0: ˆ pu = c+ (C − ˆ Fu)(NC +NX)+SNX (NG +θNX)[NC +(1−θ)NX]

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 28

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Equilibrium in the presence of environmental policies

Lump-sum subsidy: TSO’s regulated pricing

Figure: TSO’s iso-profit line (π = 0) with lump-sum subsidy

ˆ pu ˆ Fu (c,C)

c+

SNX

(NG+θNX)[NC+(1−θ)NX] C +

SNX NC+NX

Fees to consumers are greater in comparison to the no policy case All (ˆ pu, ˆ Fu) combinations in the line are not equivalent anymore

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 29

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Equilibrium in the presence of environmental policies

Environmental policies

2) Production-based subsidies

Feed-in-tariffs (FIT) –> solar panel owners sell electricity to the grid with a premium over the retail price Germany

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 30

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Equilibrium in the presence of environmental policies

Environmental policies: production-based subsidy

  • Prosumer utility under production-based subsidy

up

X ≡ θi[vG +(αG +s)NC +(αG +s)(1−θ)NX]+(1−θi)[vC +

(αC −p)NG +(αC −p)θNX]−F

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 31

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Equilibrium in the presence of environmental policies

Environmental policies: production-based subsidy

  • Prosumer utility under production-based subsidy

up

X ≡ θi[vG +(αG +s)NC +(αG +s)(1−θ)NX]+(1−θi)[vC +

(αC −p)NG +(αC −p)θNX]−F

Proposition If s >

F NC+(1−θ)NX ⇒ NX > 0

If subsidy is sufficiently large then there are prosumers in equilibrium

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 31

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Equilibrium in the presence of environmental policies

Production-based subsidy: TSO’s regulated pricing

  • TSO’s profit with a production-based subsidy s >

F NC+(1−θ)NX :

(recall —> now there are prosumers in the market)

πp = (ˆ pp −c)NG [NC +(1−θ)NX]+ +(ˆ pp −s−c)(θNX)[NC +(1−θ)NX]+( ˆ Fp −C)(NC +NX)

where ˆ pp and ˆ Fp TSO’s fees

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 32

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Equilibrium in the presence of environmental policies

Production-based subsidy: TSO’s regulated pricing

  • TSO’s profit with a production-based subsidy s >

F NC+(1−θ)NX :

(recall —> now there are prosumers in the market)

πp = (ˆ pp −c)NG [NC +(1−θ)NX]+ +(ˆ pp −s−c)(θNX)[NC +(1−θ)NX]+( ˆ Fp −C)(NC +NX)

where ˆ pp and ˆ Fp TSO’s fees

TSO pricing such that π = 0: ˆ pp = c+ sθNX[NC +(1−θ)NX]+(C − ˆ Fp)(NC +NX) (NG +θNX)[NC +(1−θ)NX]

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 32

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Equilibrium in the presence of environmental policies

Production-based subsidy: TSO’s regulated pricing

Figure: TSO’s iso-profit line with Upfront Subsidy

ˆ p ˆ F (c,C)

c+

sθNX[NC+(1−θ)NX] (NG+θNX)[NC+(1−θ)NX]

C + sθNX[NC+(1−θ)NX]

NC+NX

Fees to consumers are greater in comparison to the no policy case All (ˆ pp, ˆ Fp) combinations in the line are not equivalent anymore

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 33

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Equilibrium in the presence of environmental policies

Environmental policies

3) Net Mering

Extremely popular policy in the US (in many States) We show that this policy provides an implicit subsidy to solar panel

  • wners

Work in progress...

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 34

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Conclusions

Overview

1

Introduction

2

Model Setup

3

Equilibrium in the absence of environmental policies

4

Equilibrium in the presence of environmental policies

5

Conclusions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 35

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Conclusions

Conclusions

  • First paper that models the electricity market as two-sided
  • Study agents’ incentives to become a prosumers

Prosumers in the market ONLY if there are subsidies

  • Fees to consumers (not to prosumers) are greater in

comparison to the no enviromental policy case

Consumers pay the extra burden generated by the subsidy Subsidies increase fees to those that cannot afford solar panels

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 36

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Conclusions

Conclusions

  • Wrap up the Net Metering case
  • Compare the three policies (numerical simulation?)
  • Model extensions

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 37

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Conclusions

Thanks! Questions?

Your feedback is much appreciated: rbajo@unav.es

Bajo-Buenestado & Kinateder (2018) Optimal Pricing, Subsidies & Solar Panels (36th USAEE) 38