The battery-powered brush starts collecting data when a user begins brushing. The smart brush may seem like overkill considering the price - $270.00 Canadian. By contrast, Amazon sells [ordinary] brushes for as little as $1.50 Canadian.” Suppose that estimates for the “smart brush” suggest that at a price of $150.00 they would have North American sales of 15,000 brushes whereas at a price of $350.

“Beauty brands l’Oreal and Karastase want to make bad hair days a thing of the past. The two companies have teamed up with tech company Withings on a Hair Coach Brush that uses a microphone, gyroscope and other sensors to monitor how fast and how hard a person is brushing. An accompanying app recommends how to brush for optimal quality and minimal breakage and split ends. It can also take into account hair-influencing factors like heat of humidity and even discern if hair is wet or dry. The “smart brush” has been garnering buzz at the [Consumer Electronics Show] CES tech show in Las Vegas.” The battery-powered brush starts collecting data when a user begins brushing. The smart brush may seem like overkill considering the price - $270.00 Canadian. By contrast, Amazon sells [ordinary] brushes for as little as $1.50 Canadian.” Suppose that estimates for the “smart brush” suggest that at a price of $150.00 they would have North American sales of 15,000 brushes whereas at a price of $350.00, they would achieve sales of 7,000 smart brushes. i. Using the values provided above, and the “POINT/SLOPE” FORMULA approach demonstrated in class, determine the SLOPE and the INTERCEPT for the L’Oreal and Karastase smart brush AND the resulting INVERSE and NORMAL Demand curves. ii. Using the NORMAL Demand Curve found above, determine the Quantities Demanded if the price increases from $175.00 to $200.00 AND then the value of the Own-Price Elasticity of Demand (or the Demand Elasticity) for the L’Oreal and Karastase Hair Coach brush. iii. Carefully explain how the “sign” and the “magnitude” of the elasticity determined in part ii above would be interpreted? iv. Suppose the market’s INCOME increased from $60,000.00 to $70,000 and, as a result, the demand for the L’Oreal and Karastase Hair Coach Brush increased by 4,000 units at every price point. Using these new values, determine the value of the Income Elasticity? v. Carefully explain how the sign of the elasticity determined allows us to describe the “type” of good the L’Oreal and Karastase Hair Coach Brush is assumed to be and why.