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.

Answer 1

Answer:
1)Let the equation of normal demand curve is q=a+b p ,

where 'a' is the intercept and 'b' is the slope .

The parameter b shares the change in demand divided by change in price.

Now, change in demand

= 7000-15000

= -8000

change in price is

= 350-150

= 200

slope = -8000/200

= -40

= b

replacing slope in the demand equation at price

150 and quantity = 15000

15000 =a-40(150)

15000+6000 =a

a =21000

so intercept =21000

and the slope is -40

equation of normal demand curve

q= 21000-40p

40p = 21000-q

p = (21000/40) -(1/40)q

p = 525-0.025 q   inverse demand curve equation

so , the intercept and slope of inverse demand are 525 and -0.025 respectively

2) Using the normal demand , when price =$175

q=21000 -40(175)

q= 21000-7000

q= 14000

and at price = $200

q = 21000 -40(200)

q= 21000-8000

q= 13000

Elasticity of demand =(% change in q / % change in p)

=

= -0.5

=0.5

3)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 q decreases from 14000 to 13000 .

The magnitude of the elasticity shows the extent of change in q due to change in p.

If >1 , demand is elastic ,

if   < 1, demand is inelastic and

if = 1 demand is unitary elastic.

4) Income increased from 60000 to 70000

i.e by (70000-60000) / 60000

= 16.7%

and increase in demand from 7000 to 11000

i.e (11000-7000) / 7000

= 57%

income elasticity of demand = (%change in q) /(% change in income)

= (57.1%) / (16.7%)

=3.42

However , elasticity at q =15000 would be different

At q =15000

%change in q = ( 19000-15000) / 15000

= 26.7%

income elasticity = (26.7%) /(16.7%)

= 1.6

5) A negative price elasticity of demand and positive income elasticity of demand means the good is a normal good .

A negative income elasticity of demand means that good is inferior because its demand falls with increase in income and viceversa .

on the other hand , a positive elasticity of demand means that the good is a giffen good which violates the normal law of demand .

For giffen good, quantity increases when price increases and vice versa.