Q.What would be the shape of the demand curve so that the total revenue curve is
(a) A horizontal (perfectly elastic) demand curve — constant price. (b) A rectangular hyperbola — constant total revenue (unitary elastic).
Total revenue is , so the shape of the demand curve determines the shape of the curve.
(a) = a positively sloped straight line through the origin. A straight line through the origin has the form , where the slope is a constant. Since , this means for every output — the price does not change as quantity changes. A constant price at all outputs is a horizontal (perfectly elastic) demand curve, which is exactly the demand curve faced by a firm under perfect competition.
(b) = a horizontal line. A horizontal curve means total revenue is the same constant at every output: . Hence , which is the equation of a rectangular hyperbola. Along a rectangular-hyperbola demand curve the price elasticity of demand is unity (equal to 1) at every point, so revenue neither rises nor falls as quantity changes.
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