If the market demand curve has constant price elasticity of -1, the monopolist's price should approach infinity.

Question

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If the market demand curve has a constant price elasticity of -1, it implies that demand is unit elastic at all points on the curve. This means that any increase in price by the monopolist will result in a proportional decrease in quantity demanded, such that the revenue stays the same. Therefore, in order to maximize profits, the monopolist should keep increasing the price until the marginal cost equals the price. In this case, the price should approach infinity as the quantity demanded approaches zero, since the demand curve is flat and unit elastic.

If the Market Demand Curve Has Constant Price Elasticity of -1