Stackelberg_Example

Stackelberg_Example - A Stackelberg Price Leadership Model...

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A Stackelberg Price Leadership Model with Application to Deregulated Electricity Markets Z. Yu (IEEEl Member), F.T. Sparrow, T.L. Morin, G. Nderitu Institute for Interdisciplinary Engineering Studies Room 334,1293 Potter, Purdue University West Lafayette, IN 47906, USA Email: z yu @ ecn . purdue . edu Abstract - This paper presents a Stackelberg price leadership model for simulating deregulated electricity markets consisting of one or a few large producers and a larger number of fringe producers. It is assumed that the large producer(s) would adopt oligopoly strategy using their market power while the small producers would use Bertrand-like strategy. The model is a multi-objective profit maximization program. The multi-objectives are converted into the same number of partial Lagrangian functions with power production and supply as the control variables. A set of KKT conditions is then derived considering the game strategies of the producers. Test results show that the model successfully produces a total profit that is greater than the profit from a welfare maximization model but is less than that from a collusion model. Producers who adopt Cournot strategy are better off with higher profits as compared with marginal cost pricing. Keywords - Stackelberg model, price, deregulation, electricity, gaming, welfare, profit. I. INTRODUCTION The general formulation of imperfect competition may be described by a so-called conjectural variations model (CVM) [page 645.11 as follows: WS) ads) - = 0, V S. Or equivalently, n(S) is the profit of producer S, q(S) is the supply quantity by S, P is market price, MC[S, q(S)] is the marginal cost of k represents producers other than One way to solve this CVh4 model is to use the Stackelberg method. In the method, it is assumed that the market in question is composed of a single price leader and a fringe of quasi-competitive producers. In paper, we further assume that the leader is also a large producer with a large market share who would adopt Cournot strategy[l, 2, and 31. We also assume that the fringe producers would adopt competitive pricing strategy, which could be described as Bertrand- like strategy [l, 41. That is, the fringe producers bid their marginal cost functions. Further, it is assumed that the total supply of the fringe producers is insufficient for the whole market so that the leader will have room tcl play its strategy. This setting can be easily extended tcl the case where a few large producers dominate the market subject to the strategy of some fiinge producers. Traditionally, the price leadership model is solved in two parts: a master problem for the leader and a sub- problem for the fringe producers [5, 61. Iteration is cimied out between the two problems and convergence is usually guaranteed for “well-behaved” problems.
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This note was uploaded on 05/06/2010 for the course ECON econ 170 taught by Professor Mcdevitt during the Spring '10 term at UCLA.

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Stackelberg_Example - A Stackelberg Price Leadership Model...

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