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Why will a monopolist (a firm that can choose to set its own price to maximize its profits, and faces no competition) always decide to produce at a point on the demand curve where demand is elastic?
Because the monopolist wants to set marginal revenue equal to a positive marginal cost, and marginal revenue is only positive on the elastic part of the demand curve.
Because total revenue is maximized on the elastic part of the demand curve.
Because marginal revenue is positive on the inelastic part of the curve, and monopolists wish to avoid this.
This is incorrect. The monopolist will not always produce on the elastic part of the demand curve.