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A monopolist faces the downward-sloping market demand and maximizes profit by setting output where marginal revenue equals marginal cost, then charging the corresponding demand price. Since MR < P for a monopolist, equilibrium output is lower and price higher than competitive level. The monopolist earns economic profit in long run (no entry threat), and can maintain barriers to entry through patents, scale economies, or control of inputs.
From your study of monopoly, you know that a monopolist is the sole seller in a market, which means it faces the downward-sloping market demand curve directly. This single fact drives everything else about monopoly pricing. In a competitive market, each firm is a price-taker — it can sell as much as it wants at the going market price, so its marginal revenue equals the price. For a monopolist, selling one more unit requires lowering the price on all units sold (because the demand curve slopes down). This means marginal revenue (MR) is always less than price for a monopolist — the extra revenue from selling the additional unit is reduced by the price cut applied to all previous units.
The profit-maximizing output rule is the same as always: produce where MR = MC. But the pricing step is different. Once the monopolist finds the profit-maximizing quantity Q* where MR = MC, it does not charge that MR — it looks up to the demand curve to find the highest price consumers will pay for Q*. This two-step process — find Q* from the MR = MC intersection, then read P* off the demand curve above it — is the defining procedure of monopoly analysis. The gap between price and marginal cost at Q* is the monopolist's markup, and it represents a transfer of value from consumers to the firm.
The efficiency cost is real. At the competitive outcome, price equals marginal cost and all mutually beneficial trades occur. The monopolist restricts output below that level to maintain a higher price, which means some trades that would benefit both buyer and seller do not happen. This forgone surplus is deadweight loss — the hallmark of monopoly inefficiency. The further price is above marginal cost (captured by the Lerner index: (P − MC)/P = 1/|ε|, where ε is the price elasticity of demand), the greater the distortion.
What sustains the monopoly in the long run is the barrier to entry. In competitive markets, economic profit attracts entry until profit is competed away. A monopolist earns persistent economic profit only if entry is blocked — by a patent granting exclusive rights, by economies of scale so large that a new entrant cannot compete profitably (natural monopoly), or by exclusive control of a critical input. Understanding which barrier applies in a given market is essential for predicting whether regulation, antitrust enforcement, or natural erosion of the barrier will eventually restore competitive pricing.