Question

The Belmount Company produces boots that sell for $ 20 a pair. During 2019, their sales volume was 10,000 pairs per month. In January 2020, a competitor, the V.R. Nelson Company cut the prices of its boots from $ 25 to $ 18 a pair. The following month, Belmount sold just 7,000 pairs of boots.

a) Determine the cross-arc elasticity of demand between Belmount and Nelson boots (assume that the Belmount price remains constant).

b) Suppose the price arc elasticity for Belmount boots is -2.0. Also, that Nelson kept the price of her boots at $ 18. How much price reduction will Belmount need to establish to increase its sales volume to the previous figure of 10,000 pairs per month?

c) Compare the total revenue of Belmount with sales volumes of 7,000 and 10,000 pairs after the Nelson Company's price reduction.

d) Does the analysis suggest the boots of the two companies are good or bad substitutes?

Answer 1

A) Cross price elasticity is calculated as %change in quantity demanded of Belmount / %change in price of Nelson

%change in quantity demanded of Belmount = [(7,000 - 10,000) / 10,000] * 100 = -30%

%change in price of Nelson = [(18 - 25) / 25] * 100 = -28%

Cross price elasticity of demand = [(-20%) / (-28%)] = 1.07

B) To avoid quantity demanded falling by 30%, Belmount can decrease its price by 15% because elasticity of demand * %change in price = %change in quantity demanded

C) Due to reduction in price of Nelson, quantity demanded of Belmount fall to 7,000 from 10,000 units while price of Belmount is same at $20.

Total Revenue when quantity demanded is 10,000 units is 10,000 * 20 = 200,000

Total Revenue when quantity demanded is 7,000 units is 7,000 * 20 = 140,000

D) As the cross price elasticity of demand is positive among them, goods are substiute because fall in price of one good reduce quantity demanded ofother and vice versa.