# Monopoly Model

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Categories: CategoryModel CategoryMicro CategoryIndustrialOrganisation CategoryImperfectCompetition

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Created: 2008-08-20

Suggested Citation: See license page.

## Standard Imperfect Competition Framework

## Solving

Monopoly corresponds to the case where the number of firms, N, is one.

Suppose we have a monopolist for the product. The monopolist can control prices and maximizes profits given the known demand function: $$max_{p} \Pi(p) = [q(p) \cdot p - C(q(p))]$$. Note that as in this situation there is only a single firm we shall drop $$Q$$ and use $$q$$ for both individual and total output. Solving we have the FOC:

$$ \[ \frac{q' \cdot (p-c)}{q} = -1 \] $$

Recalling the definition of the elasticity of demand: $$\epsilon(p) = \frac{q'*p}{q}$$ one can rewrite this as:

$$ \[ \epsilon(p) \cdot \frac{p-c}{p} = -1 \] $$

Rmk: We could obtain analogous conditions for the situation where we have price as a function of quantity and the monopolist chooses quantity. This is formulation where price depends on quantity is studied in the Cournot model below. Since monopoly is simply a special case of oligopoly, in which the number of firms, N, is 1, the reader is directed to that section for specific results.