Consider a profit-maximizing single-price monopolist that faces a linear demand curve.The firm would not set a price at which demand is inelastic because

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When demand becomes inelastic, an increase in price leads to a decrease in total revenue. As a result, marginal revenue becomes negative in that range of output for a profit-maximizing single-price monopolist. Therefore, the monopolist would avoid setting a price at which demand becomes inelastic as it would result in a loss of profit.

Consider a Profit-Maximizing Single-Price Monopolist That Faces a Linear Demand