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Computing Economic Equilibria and its Application to International Trade of CO2 Permits: An Agent-Based Approach
IFOR Events
Seminar:
'Optimization & Applications'
(see information & program)
Feb 20 - May 28, 2012
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| Computing Economic Equilibria and its Application to International Trade of CO2 Permits: An Agent-Based Approach | |
| Author | Benno Büeler |
| Abstract |
Since Adam Smith postulated the `invisible hand' 200 years ago, economists have had an ambivalent position towards competitive economic equilibria. On the one hand it is the fundamental paradigm of the market economy system and intuitively easy to understand. On the other hand its formal treatment poses considerable dificulties. The first proof of existence for certain models was possible only in the 1930's; but the algorithmic treatment of even simple models has often proved to be hard due to the need of an accurate insight into the concrete model-structure which can be hard to obtain. There are various ways to formalize equilibria; in this work equilibria are formalized through the reaction of economic agents to price signals. Here `agent' is used to denote different things, depending on the context: a consumer, a producer, a whole economic sector, or a geographic unit like a country, etcetera. The `reaction' of an agent is defined as the net selling (supply minus demand, export minus import) which is determined by price. The summing of the reaction of all agents is called (market) excess. An equilibrium with non-negative price is found when either supply equals demand or supply exceeds demand and the corresponding price is zero. The choice to study equilibria on the level of the excess-function was motivated by a number of specific advantages including its broad applicability to different economic equilibrium problems, its simplicity of integrating existing and arbitrarily heterogeneous agents in an overall equilibrium model, and its possibility to treat agents in parallel. For MMmr (Markal-Macro multi-region), the energy-economy model studied in this work, the last two advantages are of decisive value. A serious disadvantage of this excess-based view is the possible lacking of structural properties of the excess-function which are required for proving convergence of related algorithms to equilibria. The above mentioned advantages, however, necessitated the development of two main heuristics to solve the equilibrium problem based on the excess-function approach. The first, the Cutting Plane Method (CPM), is derived from a formulation of the equilibrium problem as a Variational Inequality Problem (VIP). The second heuristic is a fixed point method. Contributions to the solution of equilibrium problems include the mathematical analysis of monotonicity of the excess-function, the clarification of the central role of monotonicity when applying CPM, and the treatment of unboundedness of the Lagrangian-function in some cases. This unboundedness appears in the decomposition of the optimization problem which underlies the fixed point problem. Another contribution is the discussion and extension of different strategies to prove the existence of an equilibrium. One of these strategies is finally applied to MMmr. One of the study's empirical result is the robustness and convergence of the fixed point method when a specific dual relationship to the VIP is utilized. The economically oriented part of this study starts with a discourse upon energyeconomy models from the perspective of CO2 emission bounds. Specific attention is given to burden sharing and the implementation of CO2 emission-permits. Based on national energy-economy models (Markal-Macro), different possibilities to model CO2-permits are developed. First, the permits are used to integrate the national models in the international model MMmr. Second, the consequences of the different permit strategies are analyzed. Using data from Sweden, the Netherlands and Switzerland, the two heuristics are finally successfully tested. Even though the resulting numbers must be interpreted cautiously, some interesting economic trends can be observed. Assuming a CO2 emission scenario which reduces linearly the emission by 40 % from 2000 to 2040, the average permit price is calculated to be 14 US cents per liter of fuel if discounted back to the year 2000. Furthermore, the GNP-losses are around 2 % compared to a reference case without emission bounds. In our model these losses can be reduced by one fifth if tradable permits instead of fixed national emission bounds are introduced. Significant economic di,erences were observed between nations. Because the distribution of gains and losses can be influenced directly by the initial endowment with permits, models like MMmr can be useful as a decision support tool when initial endowments or transfer payments are negotiated. |
| PDF, PS, PS.gz | |
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