Question

Assume that a popular brand of men's shoes was selling at $500.00 per pair. At that price, a number of stores in a "District" sold 100 pairs of shoes in a week. The District manager then declares a sale of 20% on that brand of shoes. As a result, 160 pairs of shoes are sold in the following week.

(a). Using arc elasticity formula, calculate the price elasticity of demand.

(b). What is the mathematical relationship between price and quantity of shoes?

You must show your work here.

Answer 1

a)P1 = $500

Q1 = 100

P2 = 500 - (20% of 500) = $400

Q2 = 160

Using Midpoint Formula

PEd = [( Q2 - Q1) / ( Q2 + Q1) / 2] /[( P2 - P1) / (P2 + P1) / 2]

= [(160 - 100) / ( 160 + 100)/2] / [(400 - 500) ( 400 + 500)/2)]

= (60 / 130) / (100 / 450)

= 0.46 / 0.22

= 2.1

Since Elasticity of Demand is greater than 1, so we can say that price elasticity of demand for shoes is Elastic.

b) When Price is $500 Quantity Demanded for shoes is 100. When price reduces to $400 Quantity Demanded for shoes increases to 160. Thus, there is inverse relation between price and quantity of shoes.