Monopoly — Price and Output Determination

A monopolist is the sole seller of a product with no close substitute, so the monopolist's own demand curve IS the market demand curve — downward sloping. Because AR (=price) falls as output rises, and MR falls even faster (at twice the slope, for a straight-line demand curve), $MR < AR$ at every output beyond the first unit.

The monopolist, like any profit-maximising firm, produces the output at which $MC = MR$, and then charges the HIGHEST price the market will bear for that output — read off from the demand (AR) curve at that quantity. Formally, the equilibrium output $Q^{*}$ solves $MR(Q^{*}) = MC(Q^{*})$, and the equilibrium price is $P^{*} = AR(Q^{*})$.

A crucial consequence: a monopolist has no unique supply curve. Under perfect competition, a given price always corresponds to a unique quantity supplied (read off the rising-MC curve), so the MC curve doubles as the supply curve. Under monopoly, the SAME price can correspond to DIFFERENT equilibrium quantities depending on the shape and position of the demand curve the monopolist happens to face — different demand curves, tangent to the same MC curve at different points, can yield the same price but different quantities. Since no fixed price-quantity relationship exists independent of demand, no single supply curve can be drawn for a monopolist. …