User:MiloKing/Monop multipleEquil

To be added to the monopolistic firms article eventually.

Example of equilibrium switching for a monopolist

Suppose there is a market supplied by a profit-maximizing monopolist. The first buyer is willing to pay $a$ for the first unit, and all buyers thereafter are willing to pay $b$ for each unit, up to a maximum quantity $c$. The marginal cost of providing the first unit is $d$ and the marginal cost of each unit thereafter is $e$. All these terms are constants.

If the monopolist chooses to serve only one customer, their profit will be $a-d$, as they will be able to charge price $a$ for their unit sold, costing them $d$ to produce it.

If the monopolist chooses to serve the whole market, their profit will be $bc-d-e*(c-1)$. They will be able to charge price $b$, and so $bc$ represents their revenue. The cost of providing the goods is $d+e*(c-1)$, as the cost is $d$ for the first unit and $e$ for the next $c-1$ units.

Intermediate options will always be less profitable in this example, as if $b>e$, the monopolist should produce for the whole market, and if $b<e$, it should produce only one unit (or none at all).