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Duopoly Reaction Curves

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Megalomaniacs Inc., the washing powder producer has today confirmed, amidst great fanfare and publicity, that it has hired Mr Megatron, the renowned empire building manager. Mr Megatron is a controversial figure that has in the past consistently pursued vast increases in the size of the companies that he runs with limited regard to profits. The shareholders of Megalomaniacs Inc. largely voted in favour of the installation of Mr Megatron, after ousting their former manager in a stormy shareholders’ meeting last week.

WhiteEnvy is the arch rival of Megalomaniacs – the two companies between them control virtually all of the washing powder market in a tightly contested duopoly that has lasted for years. The company swiftly dismissed the move as one that will drive down profits and harm the interests of the shareholders of Megalomaniacs. For their own part, WhiteEnvy shareholders affirmed their loyalty to the existing manager as someone that has “always acted in their best interests”.

Washing powder is a largely homogeneous commodity; returns to scale in the production of this good are constant and costs are virtually identical between the two firms. Using both diagrammatic and algebraic exposition (for the former you will need to analyse the shifts in the reaction curve(s) and for the latter you need to assume a linear demand curve; do not use specific numerical values or numerical examples, only algebra) explain in detail whether the hiring of the a new manager is a good decision for Megalomaniacs’ shareholders and for the new manager himself in terms of achieving their objectives. In the same manner you need to analyse and explain to what extent the decision by WhiteEnvy to stick to its existing manager is wise for its shareholders’ interests or whether it too should consider a similar change. Please consider alternative duopoly setting scenarios carefully explaining why the actions by each firm are justified in furthering its objectives and comment on the profit implications of these actions for each company. Also algebraically calculate and comment on the consumer surplus implications of each scenario that you include and show how it compares with the initial scenario before the hiring of Mr. Megatron.

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