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In the news lately, stories of the big bad monopolies abound. We constantly hear of government regulation in software, utilities, transportation, and financial institutions. The justice department closely scrutinizes mergers and acquisitions so that firms don't end up with too much market power. All of this begs the question, what's the big deal? Where does our fear of monopolies originate? After all, in a free market economy, there is no coercion. Presumably, the economy is still driven solely by mutually beneficial exchange whether one firm exists or many.

Thus far in our treatment of economics, we have assumed that there exist a large number of firms in a market. This assumption enabled us to treat firms as price takers, since no firm in particular had any more market power than any other. In this Sparknote, we will investigate the impact of a relaxation of the multiple firms assumption on equilibrium. We will demonstrate the importance of the assumption in our understanding of perfect competition.

In the first section, we will define a monopoly and walk through the mechanics behind calculating equilibrium in a monopolistic market. We will also investigate the monopoly's impact on social welfare. In the second section, we extend the model of a monopoly to 2 firms and then to n firms. We define the assumptions underlying Cournot, Bertrand, and Stackelberg duopolies. We then walk through examples designed to clarify the mechanics behind the various models of duopoly, and generalize to the n firm case in a Cournot framework.

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