Intertemporal Emissions Trading and
Allocation Rules: Gainers, Losers
Outline
1. Introduction 2. The Model
1. Design of the Cap-and-Trade Program 2. Industry Structure
3. Game Structure
4. Intertemporal Emissions Trading 5. Hotelling Conditions
6. Abatement Cost Function 3. Benchmark Case
4. Fringe Agents’ Reaction Function 5. Behaviour of the Large Agent
6. Critical Perspectives on Permits Allocation
1. Motivating Question
• What happens on a tradable permits market when distortions occur as a consequence of the initial allocation?
Lit. Review
• Intertemporal emissions trading modelling: Rubin (1996), Schennach (2000);
• Intertemporal emissions trading with market imperfection:
Liski & Montero (2005, 2006);
• Economics of the allocation of tradeable permits: Eshel (2005).
2.1 Design of the Cap-and Trade Program
• Market imperfection arises during the negotiation of the cap and is exogenous to the model;
• Permits are distributed freely on the basis of recent emissions;
• Agent {i=1} is initially allocated a large number of permits;
• Agents {i=2…N} form a competitive fringe;
• Agents may bank and borrow permits without restrictions.
2.2 Industry Structure
• Intra-industry permits market; • Single good economy;
• The interaction with the output market is neglected; • An agent may be either a country, a firm or a cartel; • The competitive market price is determined by fringe
2.3 Game Structure
• There is an information asymmetry on the tradable permits market:
– The large agent is able to forecast the decisions of fringe agents’, as well as the consequences of his decisions.
• Strategic interactions modelled after a Stackelberg game model:
1.Derive the reaction function of the fringe;
2.Report it in the optimization program of the large agent.
2.4 Intertemporal Emissions Trading
• Let Bi(t) be the permits bank, with Bi(t) >0 in case of
banking and Bi(t)<0 in case of borrowing.
• Any change in the permits bank is equal to the
difference between agent's i permits allocation and his emission level at time t. The banking borrowing constraint may be written as:
• with Bi(0)=0 and Bi(T)>0 as banking and borrowing
2.5 Hotelling Conditions
2.5.1 Terminal Condition
• Let [0,T] be the continuous time horizon;
• At time T, cumulated emissions must be equal to the sum of each agent's depollution objective and
2.5 Hotelling Conditions (ctd.)
2.5.2 Exhaustion Condition
• At time T, there is no more permit in the bank (either stocked or borrowed):
• Those conditions ensure that agents gradually meet their depollution objective so that the marginal cost of depollution is equalized in present value over the
2.6 Abatement Cost Function
• Ci[ei (t)] is twice continuously differentiable.
• It is strongly convex with C’i[ei (t)] < 0, C’’i[ei (t)] > 0, and Ci[ei (0)]=0.
• At the equilibrium of a permits market in a static
framework, price-taking agents adjust emissions until the aggregated MAC is equal to the price P at time t:
• Thus, at the equilibrium, there is no arbitrage for price-taking agents.
3 Benchmark Case
• The expression of market power may be derived straightforward when the large agent owns all the stock of permits, and directly integrates the
competitive price into his maximization program. • In this setting, fringe agents' emissions come from
3.1 Optimization program
3.1 Optimization program (ctd.)
• Equilibrium after rearranging terms:
• εi measures the relative variation between an
additional unit of emission and the acceleration of marginal cost.
• A high elasticity (in absolute value) induces a strong link between the two variables.
3.2 Market Power Condition
• Market power is function of fringe agents' elasticity and of the large agent's number of permits:
• Due to the convexity assumption, fringe agents' elasticity is negative, and reveals the possibility for the leader to affect negatively fringe agents' behaviour.
• The large agent's MAC is therefore lower than under perfect competition, since he enjoys a dominant position.
• Overall, the large agent may be characterized as a net gainer and fringe agents as net losers in this setting.
4 Fringe Agents’ Reaction Function
• Fringe agents choose their optimal emissions level according to the possibility to bank and borrow
permits in constraint (1):
• where the expression represents the number of permits bought (>0) or sold (<0).
4 FOC:
• When fringe agents build a permits bank in terminal period: {Bi(T)>0, λ(T)=0, λ(t)=0}
• The reaction function is therefore equal to the static equilibrium condition (4)
• Conversely, the reaction function is equal to (6) when fringe agents do not keep permits in the bank in terminal period and
5 Behaviour of the Large Agent
• The large agent adjusts strategically his optimal
emissions levels according to its initial allocation as expressed by (2) and the banking borrowing
5.1 First case
• Replacing P(t) by (4), the large agent's optimization program becomes:
• Replacing the emissions constraint (2) into the objective function:
5.1 First case (ctd)
• If {B1(T)>0, μ=0},
• It is possible to find an analogous version of the market power condition: the large agent is able to affect fringe agent's MAC through the number of permits he holds in excess of his emissions.
5.2 Second case
• Replacing P(t) by (6), the large agent's optimization program becomes:
5 Recap
• In both cases, the large agent is still able to affect negatively fringe agent's MAC.
• Those preliminary results were established
concerning the terminal period, but there lacks at this stage a precise characterization of the path of the
permits bank during the optimal trajectory.
• However, the spectre of a large agent achieving a market power position may be averted by a careful design of the cap-and-trade program.
6 Critical Perspectives on Permits Allocation
• How to distribute permits to the large agent without introducing market power?
6.1: Comparative statics tell us the distribution of an additional permit to the large agent directly
affects fringe agents through a variation of their marginal cost.
6 Social Welfare
• The goal of a welfare-maximizing social regulator consists in minimizing abatement costs of the large agent and fringe agents respectively, and the
consumer's surplus losses from trade in the output S(t):
6 Social Welfare (ctd.)
• The change of a one-unit allocation of permit on the large agent and fringe agents is found by
differentiating their minimized cost function with respect to
• For instance, in the first case, at the equilibrium the optimal permits allocation satisfies the equality:
7 Concluding Remarks
• Assess the conditions under which a market power position may appear on a tradable permits market, with 2 types of agents differing in terms of size and permits endowment.
• Similarities between the benchmark case and the model: it is possible to identify net losers (i.e., fringe agents) and a net gainer (i.e., the large agent) as the large agent benefits from a lower MAC than under perfect competition and is able to affect negatively fringe agents' MAC.
7 Concluding Remarks (ctd.)
• But the spectre of market power need not be raised if the cap-and-trade program appears properly
designed.
• Razor’s edge condition:
‘an optimal allocation rule for a social planner with
perfect foresight consists in distributing permits up to the point where an additional unit to the large agent damages consumers' surplus and establishes a
7.1 Link with the KP
• Parallel with Russia’s and Ukraine’s Hot Air. – Internal consistency of the permits market; – External consistency of the permits market. • Uncertainty regarding international trading rules • Potential financial benefits without a direct
7.1 KP: Will Russia be a net seller of permits?
Î Under all scenarios, Russia would meet its Kyoto target.
7.1 Monetizing Russia’s Surplus?
7.2 Link with the EU ETS
7.2 EU ETS: Over-allocation or relative success?
EU ETS: A look at the intra-country level
EU ETS Price Volatility
