The main use Rothbard makes of elasticity of demand is to show that the seller’s revenue is largest at the unit elastic point of a linear demand curve. If a seller asks a price high enough, the quantity demanded by the buyers will be zero and the seller’s revenue will also be zero. If the seller asks a zero price, the quantity demanded by the buyers will be a large as possible, but again the seller’s revenue will be zero. As price is continuously reduced from its highest level, the seller’s revenue will continue to increase as one moves down the demand curve, revenue will be largest at the mid-point of a linear demand curve, and then revenue will decline as price continuously falls past the mid-point until revenue is zero at a price of zero. It follows that a seller who has already produced his product, will ask a price at the mid-point of the demand curve for his product to maximize his revenue, i.e., he will neither raise nor lower his price from that point because doing so will lower his revenue.
In the chapter on monopoly, Rothbard goes over Mises’s argument concerning the alleged harm of a monopoly seller in which Mises points out that a monopoly seller will raise price and restrict output (thereby allegedly harming consumers in comparison to a competitive seller) only if the demand for his product is inelastic at the competitive price. If when the seller becomes a monopolist he is already charging a price at the mid-point of the demand curve for his product, he will not raise his price and restrict his output sold. Having a monopoly position, according to Mises, is a necessary but not sufficient condition for the monopoly to act in ways that violate consumer sovereignty.
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