A unit-elastic demand curve never touches or crosses either of the axes. Why?
When demand is unit-elastic, total expenditure must be the same at every point on the curve. Suppose that at any point the curve, the demand curve were to touch the horizontal axis, meaning that the price would equal zero. Then total expenditure would be zero. Therefore, if the demand curve remains unit-elastic along its entire length, it can never cross the horizontal axis. By the same reasoning, it cannot cross the vertical axis. Because the slope of the demand curve is negative, any unit-elastic curve simply must get closer and closer to the axes as it moves away from its middle points. But it will never touch either axis.
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