Question

1. “High-Tech Hair Brush means no more bad hair days” (Vancouver Sun Newspaper, Friday, January 6, 2017, p. C2). “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 – for instance, using the values above, from 7,000 to 11,000 units and from 15,000 to 19,000 units. 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.

Please explain these with steps. thanks

Answer 1

40 (2) Let the equation of normal demand curreve is q = atbp, where a is the interccept and b is the slope. The parameter b shaws the change in demand divided by change in preice. Now, change in demand = 7000-15000 = -8000 and change in preice = 350-150=200 → Slope = -8000 - -40 - b Replacing slope in the demand equation at price= 150 and quantity = 15000, we get 15000 = a -40(ISU) => a = 15000 + 6000 -> a =21000 So entencept = 91000 end slope --40 > Equation of normal demond: 9=21000-40p] => 40 P = 21000 - 9 -> P- 91000-ta P = 525-0.0259 ]cloverese demand equation So, the intercept ada and slope of inverse demand are 525 and-0.025 respectively. 1) Using the normal demand, when price=$175, q=21000-40 (175) = 14000 and at price = $200,9 - 21600-40(200) = 13000 - Elasticity = % change in q - Goog 14000/400 = % change in p - 13000 14000)/19000 - - 0.5 Elasticity (200-175/200 = 0.5 (1) The negative sign of elasticity is due to movement of price and quantity in opposite direction, i.e. p increases from 175 to 200 and a decreases from 14000 to 13000. The magnitude of the elasticity shows the extent of change & is a due to change in p. of Elasticity 1, demand is elastic, at felasticity 1 <1, demand is inelastic and it Elasticityl=l, demand is unitary elastic Eiv) Income increased from 60,000 to 70,000, ise. by 70000-6000o_ 16,70 and increax on demand from 7000 to 11,000, i.e. by 11000-7000 - 57%. Income elasticity of demand at sthitite 59/0 = % change in a % change in incon 57.1°% - 3.42 . 16.7% However, who the elasticity at a = 15000 would be different. Cocoa = 16.7% 7 7000

At a = 15000, % change in q = 19000-15000 isoco = 96.76 come etcity = 26.7% 16.7% -1.6 V A negative price elasticity of demand and positive income elasticity of demand meant the good is a normal good. A negative ancome elasticity of demand means that good as inferion because its demand falls with increase in income and vice versa. On the other hand, a positive elasticity of demand means that the good is a giften good which. violates the normal law of demand. Foragiffen good quantity increases when prece increases and vice versa.