Question

iRobot sells a full line of robotic vacuum cleaners for the retail home market. iRobot ran a new ad campaign for their Roomba E5 Wi-Fi connected vacuum and although the market response to the company’s adds was good, sales of the $380 E5 declined from 12,000 to 6,500 units per month. During this period, Neato Robotics, a competitor offered a whopping $150 off their regular $500 price on their Botvac D5 laser guided connected model.

a.   Calculate the implied arc cross-price elasticity of demand for the Roomba E5 and explain its meaning.

b.   iRobot’s Roomba E5 sales recovered from 6,500 units to 10,000 units following a price reduction to $300 per unit. Calculate iRobot’s arc price elasticity of demand for this product. Is the demand for the Roomba E5 price elastic?

c.   Assuming the same arc price elasticity of demand calculated in Part B holds for a small price change, determine the further price reduction necessary for iRobot to fully recover lost sales (i.e., regain a volume of 12,000 units).

Answer 1

a. Cross price elasticity = % change in own sales / % change in competitor product price

= ((-12000+6500) / 12000) / (-150 / 500)

= 1.53

This implies that (for this quantum of competitor's price change) every 1% reduction in competitor product's price led to a 1.53% reduction in quantity sold of own product (Roomba)

b. Own price elasticity = % change in own sales / % change in own product price

= ((10000 - 6500) / 6500) / (-80 / 380)

= -2.56

The demand is elastic (that is greater than unitary elastic, since the % change in quantity demanded is more than the % change in price) [absolute values of change]

c. If a growth of 20%, i.e., (12000-10000)/10000, is needed, then price needs to change by

-20% / 2.56

= -7.8%

So the new price should be $300 x (1-7.8%) = $276.6