Linear demand curves have constant slope, that is, constant derivative dq=dp. Consider now a linear demand curve, q=a+bp with constant elasticity epsilon. Show that such demand curve has the form q=alpha p^{epsilon} where alpha is a constant.
A phone company offers long-distance telephone service to residential customers at a price of 8c per minute. At this price, the company sells 200 million minutes of calling per day. The marginal cost per minute of calling is 5c. So, the residential long-distance telephone service business is benefiting the company $6 million per day. Based on a statistical study of calling patterns, the company estimates that it faces a constant elasticity of demand for long-distance calling by residential customers of -2.0.