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 q f with marginal cost c ◮ Capacities K f with marginal r f ◮ Capacity constraint q f ≤ K f ◮ Long term private marginal cost of 1 kWh is c + r f ◮ Environmental damage par kWh of fossil fuel δ > 0 ◮ Long term social marginal cost of 1 kWh is c + r f + δ

Model Analysis Market power Intermittent source i ◮ Production q i with 0 marginal cost ◮ Capacities K i with marginal cost r i ∈ [ r i , + ∞ ) with distribution f and cumulative F and total capacity ¯ K ◮ Capacity constraint q i ≤ K i ◮ 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 r i ◮ Long term marginal cost of 1 kWh on average r i 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 = q w = q ¯ w = K f

Model Analysis Market power Social optimum K f , K i and q w f maximize: � � S ( ¯ KF ( K i ) + q w f ) − ( c + δ ) q w ν +(1 − ν ) [ S ( K f ) − ( c + δ ) K f ] f � ˜ r i − ¯ K r i dF ( r i ) − r f K f r i s.t. K i + q w = K f f K f ≥ q w 0 ≥ f ¯ K i = KF (˜ r i )

Model Analysis Market power Social optimum: Illustration Capacities ✻ Consumption q = K f S ′− 1 ( c + r f ) q = K f ¯ KF (ˆ r i ) q = K f = K i K i ✲ ˆ r i r i ν − c δ ν − c

Model Analysis Market power Competitive equilibrium State w (wind) State ¯ w (no wind) ★ ✥ ✤ ✜ Thermal power Thermal and wind power ✧ ✦ ✣ ✢ p w p ¯ w ★ ✥ ✠ ✇ Retailers ✧ ✦ p ❄ Consumers

Model Analysis Market power Competitive equilibrium with carbon tax τ State w (wind) State ¯ w (no wind) ★ ✥ ✤ ✜ Thermal power Thermal and wind power ✧ ✦ ✣ ✢ w = c + τ + r f p ¯ p w = c + τ = ˜ r i 1 − ν ★ ✥ ν ✠ ✇ Retailers ✧ ✦ w + (1 − ν ) p w = c + τ + r f p = ν p ¯ ❄ Consumers

Model Analysis Market power Results with carbon tax ◮ Pigou tax τ = δ implements first-best ◮ Total investment K f + K i might increase or decrease with the carbon tax

Model Analysis Market power Carbon tax and investment Consumption ✻ Capacities q = K f S ′− 1 ( c + r f ) K f + K i K f + K i q = K f ¯ KF (ˆ r i ) q = K f = K i K i ✲ ˆ r i r i ν − c τ ν − c d ( K f + K i ) = S ′′− 1 ( c + τ + r f ) + ¯ Kf ( ν ( c + τ )) ν d τ

Model Analysis Market power Feed-in tariff (FIT) ◮ Regulated price for intermittent energy p i ◮ Tax t per kWh consumed ◮ Budget-balance constraint: K f t ≥ ν ( p i − p w ) K i ◮ First-best if p i = c + δ and p + t = c + r f + 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: p w + g = ˜ r i ν p = ν p w + (1 − ν ) p ¯ w + α g ◮ Optimal share α ∗ leads to a price of REC g = δ ◮ Retail price p = c + r f + δα < c + r f + 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 q w f and K f maximize: � � ν [ P ( q w f + K i ) − ( c + τ w )] q w P ( K f ) − ( c + τ ¯ w ) f + (1 − ν ) K f − r f K f s.t. ˜ r i P ( K i + q w f ) = ν ¯ = KF (˜ r i ) K i

Model Analysis Market power First-order conditions � � 1 + dK i q w P ( q w f + K i ) + P ′ ( q w q w f = c + τ w : f + K i ) f dq w f r f w + P ( K f ) + P ′ ( K f ) K f = c + τ ¯ K f : 1 − ν

Model Analysis Market power Implementation of first-best ◮ State-contigent taxes; � q w � δ + p w 1 + dK i τ w f = dq w ǫ K f f δ + p ¯ w τ ¯ w = ǫ w < τ w with τ ¯ w and carbon tax τ w ◮ Price cap p ¯

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: λ s kWh produced in state ¯ w with s stored in state w ◮ Private and social benefit of storing energy? ◮ Efficient storage maximizes: � � S ( ¯ KF ( K i ) + q w f − s ) − ( c + δ ) q w ν f +(1 − ν ) [ S ( K f + λ s ) − ( c + δ ) K f ] � ˜ r i − ¯ r i dF ( r i ) − r f K f K r i s.t. K i + q w = K f + λ s f − s

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 ) + r f ] − ˜ r i ◮ Private marginal benefit of storage with carbon tax: w − ν p w (1 − ν ) p ¯ ◮ Equal to the social benefit with equilibrium prices 1 − ν , p w = ˜ r f r i w = c + τ + p ¯ 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 w and ◮ Share β of reactive consumers paying wholesale price p ¯ p w ◮ Share 1 − β of non reactive consumers paying fixed price p = ν p w + (1 − ν ) p ¯ w ◮ Market clearing conditions: β q ¯ w = r + (1 − β ) q ¯ K f r ¯ r i ) + q w β q w KF (˜ = r + (1 − β ) q ¯ r f

Model Analysis Market power Marginal benefit of making consumers reactive ◮ Expected welfare with a proportion β of reactive consumers: β [ ν S ( q w r )+(1 − ν ) S ( q ¯ w r ) − ν ( c + δ ) q w r )]+(1 − β ) S ( q ¯ f − (1 − ν )( c + δ ) K f � ˜ r i − ¯ K r i dF ( r i ) − r f K f . r i ◮ Differentiating with respect to β : [ ν S ( q w r ) + (1 − ν ) S ( q ¯ w r i ( q w r ) − S ( q ¯ r )] − ˜ r − q ¯ r ) � �� � � �� � + − r − q ¯ w +[(1 − ν )( c + δ ) + r f ] ( q ¯ 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