User:MiloKing/Monop multipleEquil: Difference between revisions

Latest revision as of 20:10, 7 June 2016

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 $b c - d - e * (c - 1)$ . They will be able to charge price $b$ , and so $b c$ 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).

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-To be added to the [[Determination_of_price_and_quantity_supplied_by_monopolistic_firm_in_the_short_run#Determining_the_profit-maximizing_quantity_of_production]] article eventually.
+To be added to the [[Determination_of_price_and_quantity_supplied_by_monopolistic_firm_in_the_short_run|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 <math>a</math> for the first unit, and all buyers thereafter are willing to pay <math>b</math> for each unit, up to a maximum quantity <math>c</math>. The marginal cost of providing the first unit is <math>d</math> and the marginal cost of each unit thereafter is <math>e</math>. All these terms are constants.
+If the monopolist chooses to serve only one customer, their profit will be <math>a - d</math>, as they will be able to charge price <math>a</math> for their unit sold, costing them <math>d</math> to produce it.
+If the monopolist chooses to serve the whole market, their profit will be <math>bc - d - e*(c-1)</math>. They will be able to charge price <math>b</math>, and so <math>bc</math> represents their revenue. The cost of providing the goods is <math>d + e*(c-1)</math>, as the cost is <math>d</math> for the first unit and <math>e</math> for the next <math>c-1</math> units.
+Intermediate options will always be less profitable in this example, as if <math>b > e</math>, the monopolist should produce for the whole market, and if <math>b < e</math>, it should produce only one unit (or none at all).