Environmental policy with intermittent sources of energy Stefan - - PowerPoint PPT Presentation

Environmental policy with intermittent sources of energy

Stefan Ambec and Claude Crampes

Toulouse School of Economics

September 2015

Model Analysis Market power

Motivation

◮ Intermittent sources of energy (wind, solar,...) ◮ Retail price of electricity does not vary with wind or sun ◮ Pollution (greenhouse gases, SO2, NOX,...) ◮ Several policy instruments:

◮ Carbon tax ◮ Feed-in tariff (FIT) or feed-in premium (FIP) ◮ Renewable portfolio standard (RPS)

◮ Impact of policies with intermittent energy and non-reactive

consumers

Model Analysis Market power

Overview

◮ First-best energy mix with wind power capacity back-up with

thermal power

◮ Carbon tax implements first-best but not FIT or RPS: too

much electricity consumption

◮ Tax on electricity consumption should complement FIT or

RPS to implement first-best

◮ With a monopoly thermal power producer:

◮ Introduction of wind power competitive fringe increases

electricity price

◮ First-best achieved with state-contingent carbon tax or price

cap and carbon tax

◮ Social benefit of energy storage and smart meters

Model Analysis Market power

Related literature

◮ Optimal and decentralized mix of energy with intermittent

sources: Ambec and Crampes (2012), Rubin and Babcock (2013), Garcia, Alzate and Barrera (2012)

◮ Pollution externalities and R&D spillovers with clean and dirty

technologies: Fischer and Newell (2008), Acemoglu et al. (2012)

Model Analysis Market power

Fossil source f

◮ Production qf with marginal cost c ◮ Capacities Kf with marginal rf ◮ Capacity constraint qf ≤ Kf ◮ Long term private marginal cost of 1 kWh is c + rf ◮ Environmental damage par kWh of fossil fuel δ > 0 ◮ Long term social marginal cost of 1 kWh is c + rf + δ

Model Analysis Market power

Intermittent source i

◮ Production qi with 0 marginal cost ◮ Capacities Ki with marginal cost ri ∈ [ri, +∞)

with distribution f and cumulative F and total capacity ¯ K

◮ Capacity constraint qi ≤ Ki ◮ Available only in state w (not in state w) which occurs with

probability ν (probability 1 − ν)

◮ Long term marginal cost of ν kWh (1 kWh in state w) is ri ◮ Long term marginal cost of 1 kWh on average ri

ν

Model Analysis Market power

Consumers

◮ Utility or Surplus S(q) concave (S′ > 0, S′′ < 0) ◮ Demand function D(p) = S′−1(p) ◮ Constant retail price / non-reactive consumers:

q = qw = q ¯

w = Kf

Model Analysis Market power

Social optimum

Kf , Ki and qw

f maximize:

ν

• S( ¯

KF(Ki) + qw

f ) − (c + δ)qw f

• +(1 − ν) [S(Kf ) − (c + δ)Kf ]

− ¯ K ˜

ri ri

ridF(ri) − rf Kf s.t. Ki + qw

f

= Kf Kf ≥ qw

f

≥ Ki = ¯ KF(˜ ri)

Model Analysis Market power

Social optimum: Illustration

✻ ✲

δ q = Kf q = Kf q = Kf = Ki Ki ri ν − c ˆ ri ν − c Capacities Consumption S′−1(c + rf ) ¯ KF(ˆ ri)

Model Analysis Market power

Competitive equilibrium

★ ✧ ✥ ✦ ✤ ✣ ✜ ✢ ★ ✧ ✥ ✦ ✇ ✠ ❄

State ¯ w (no wind) State w (wind) Thermal power Thermal and wind power Retailers p ¯

w

pw p Consumers

Model Analysis Market power

Competitive equilibrium with carbon tax τ

★ ✧ ✥ ✦ ✤ ✣ ✜ ✢ ★ ✧ ✥ ✦ ✇ ✠ ❄

State ¯ w (no wind) State w (wind) Thermal power Thermal and wind power Retailers p ¯

w = c + τ +

rf 1 − ν pw = c + τ = ˜ ri ν p = νp ¯

w + (1 − ν)pw = c + τ + rf

Consumers

Model Analysis Market power

Results with carbon tax

◮ Pigou tax τ = δ implements first-best ◮ Total investment Kf + Ki might increase or decrease with the

carbon tax

Model Analysis Market power

Carbon tax and investment

✻ ✲

τ q = Kf q = Kf q = Kf = Ki Ki Kf + Ki Kf + Ki r i ν − c ˆ ri ν − c Consumption Capacities S′−1(c + rf ) ¯ KF(ˆ ri)

d(Kf + Ki) dτ = S′′−1(c + τ + rf ) + ¯ Kf (ν(c + τ))ν

Model Analysis Market power

Feed-in tariff (FIT)

◮ Regulated price for intermittent energy pi ◮ Tax t per kWh consumed ◮ Budget-balance constraint:

Kf t ≥ ν(pi − pw)Ki

◮ First-best if pi = c + δ and p + t = c + rf + δ therefore t = δ:

budget surplus!

◮ Setting t to bind the budget-balance constraint does not

implement the first-best: over-consumption

Model Analysis Market power

Renewable Portfolio Standard (RPS)

◮ Share α of energy consumption supplied with renewable

energy

◮ Renewable energy credits (REC) issue for each kWh of

renewable energy

◮ Retailers buy REC at price g to comply with RPS ◮ Zero profit condition for wind power producers and retailers:

pw + g = ˜ ri ν p = νpw + (1 − ν)p ¯

w + αg ◮ Optimal share α∗ leads to a price of REC g = δ ◮ Retail price p = c + rf + δα < c + rf + δ too low, too much

electricity consumption

◮ Must be complemented with a tax on electricity or fossil fuel

τ = δ (1 − α) < δ

Model Analysis Market power

Environmental policy with market power

◮ Monopoly thermal power producer ◮ Competitive fringe of of wind power producers ◮ Impact of competition from wind power on price? ◮ Optimal tax? Regulation instruments to reach first-best?

Model Analysis Market power

Program of the monopoly thermal power

qw

f and Kf maximize:

ν [P(qw

f + Ki) − (c + τ w)] qw f + (1 − ν)

• P(Kf ) − (c + τ ¯

w)

• Kf − rf Kf

s.t. P(Ki + qw

f )

= ˜ ri ν Ki = ¯ KF(˜ ri)

Model Analysis Market power

First-order conditions

qw

f

: P(qw

f + Ki) + P′(qw f + Ki)

• 1 + dKi

dqw

f

• qw

f = c + τ w

Kf : P(Kf ) + P′(Kf )Kf = c + τ ¯

w +

rf 1 − ν

Model Analysis Market power

Implementation of first-best

◮ State-contigent taxes;

τ w = δ + pw ǫ

• 1 + dKi

dqw

f

qw

f

Kf τ ¯

w

= δ + p ¯

w

ǫ with τ ¯

w < τ w ◮ Price cap p ¯ w and carbon tax τ w

Model Analysis Market power

Energy storage facility

Model Analysis Market power

Energy storage

◮ s kWh can stored in state w to be used in stated ¯

w

◮ Energy cost of storing (pumping) λ ≤ 1: λs kWh produced in

state ¯ w with s stored in state w

◮ Private and social benefit of storing energy? ◮ Efficient storage maximizes:

ν

• S( ¯

KF(Ki) + qw

f − s) − (c + δ)qw f

• +(1 − ν) [S(Kf + λs) − (c + δ)Kf ]

− ¯ K ˜

ri ri

ridF(ri) − rf Kf s.t. Ki + qw

f − s

= Kf + λs

Model Analysis Market power

Social and private marginal benefit of storage

◮ The FOCs lead to a social marginal benefit of:

λ[(1 − ν)(c + δ) + rf ] − ˜ ri

◮ Private marginal benefit of storage with carbon tax:

(1 − ν)p ¯

w − νpw ◮ Equal to the social benefit with equilibrium prices

p ¯

w = c + τ +

rf 1 − ν , pw = ˜ ri ν and Pigou tax δ = τ

◮ Private incentives in competitive market aligned with social

welfare

Model Analysis Market power

Smart meters with contingent pricing

A reactive consumer

Model Analysis Market power

Smart meters with state-contingent prices

◮ Share β of reactive consumers paying wholesale price p ¯ w and

pw

◮ Share 1 − β of non reactive consumers paying fixed price

p = νpw + (1 − ν)p ¯

w ◮ Market clearing conditions:

Kf = βq ¯

w r + (1 − β)q¯ r

¯ KF(˜ ri) + qw

f

= βqw

r + (1 − β)q¯ r

Model Analysis Market power

Marginal benefit of making consumers reactive

◮ Expected welfare with a proportion β of reactive consumers:

β[νS(qw

r )+(1−ν)S(q ¯ w r )]+(1−β)S(q¯ r)−ν(c+δ)qw f −(1−ν)(c+δ)Kf

− ¯ K ˜

ri ri

ridF(ri) − rf Kf .

◮ Differentiating with respect to β:

[νS(qw

r ) + (1 − ν)S(q ¯ w r ) − S(q¯ r)]

• −

−˜ ri (qw

r − q¯ r)

• +

+[(1 − ν)(c + δ) + rf ] (q¯

r − q ¯ w r )

• +

◮ Risk-averse consumers prefer fixed price contract

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS ◮ Competitive fringe of wind power produce is not enough to

get efficiency

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS ◮ Competitive fringe of wind power produce is not enough to

get efficiency

◮ Regulation with state-contingent carbon taxes or price cap

and carbon tax

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS ◮ Competitive fringe of wind power produce is not enough to

get efficiency

◮ Regulation with state-contingent carbon taxes or price cap

and carbon tax

◮ Investment in more costly intermittent sources for

diversification but does not solve the problem

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS ◮ Competitive fringe of wind power produce is not enough to

get efficiency

◮ Regulation with state-contingent carbon taxes or price cap

and carbon tax

◮ Investment in more costly intermittent sources for

diversification but does not solve the problem

◮ Marginal value of storage = cost difference

Summary

◮ Environmental policies in a model with intermittent energy

(wind power) and constant retailing electricity price

◮ Aim of environmental policy: reducing electricity consumption

and increasing wind power production

◮ A carbon tax does the job ◮ Too much electricity with FIT, FIP or RPS ◮ Competitive fringe of wind power produce is not enough to

get efficiency

◮ Regulation with state-contingent carbon taxes or price cap

and carbon tax

◮ Investment in more costly intermittent sources for

diversification but does not solve the problem

◮ Marginal value of storage = cost difference ◮ Social value of smart meters not always positive because risk