When demand is inelastic, revenues increase and production costs decrease as the quantity produced declines, total profits will always increase with a higher price. Therefore, monopolists:

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Monopolists will raise prices when demand is inelastic to increase total revenue, as the percentage drop in quantity demanded is less than the percentage increase in price, leading to higher profits. They will continue to do so until they reach the elastic portion of the demand curve, where further price increases would reduce total revenue.

When Demand Is Inelastic, Revenues Increase and Production Costs Decrease