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How should businesses with inelastic demand decide the price of their product?

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Demand elasticity is the measure of how much the quantity of a good will be demanded for a price change. If demand is inelastic, the quantity demanded will not drop very significantly with an increase in price. If the demand is perfectly inelastic, consumers will demand the same quantity, regardless of price. For this reason, businesses that produce a product with an inelastic demand tend to charge higher prices.

That being said, the business is still restricted by its supply curve. For this reason, even with a perfectly inelastic good a business cannot set prices at will. Once the market has been saturated, the consumer will not buy more of the product. For this reason, the price of the product is still determined by the intersection of the supply and demand curves, regardless of elasticity.

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