Question

A department store has estimated the demand curve for a popular brand of women’s dress shoes as a function of price. Use the table to answer the question that follow.

Points

Price per pair

Dress shoe sales per week

A

RO 18

100

B

RO 15

200

C

RO 12

300

D

RO 9

400

E

RO 6

500

F

RO 3

600

Calculate demand elasticity between points A and B, between points C and D, and between points E and F.

Answer 1

Between Point A and B:

P1 = 18    Q1 = 100

P2 = 15     Q2 = 200

PED between point A and B = (Q2 - Q1) / (P2 - P1) * (P1 + P2) / (Q1 + Q2)

                                             = (200 - 100) / (15 - 18) * (18 + 15) / (100 + 200)

                                             = (100 / -3) * (33 / 300)

                                             = 3,300 / -900

                                             = -3.67

The absolute value of PED is 3.67.

Between Point C and D:

P1 = 12    Q1 = 300

P2 = 9     Q2 = 400

PED between point C and D = (Q2 - Q1) / (P2 - P1) * (P1 + P2) / (Q1 + Q2)

                                             = (400 - 300) / (9 - 12) * (12 + 9) / (300 + 400)

                                             = (100 / -3) * (21 / 700)

                                             = 2,100 / -2,100

                                             = -1

The absolute value of PED is 1.

Between Point E and F:

P1 = 6    Q1 = 500

P2 = 3     Q2 = 600

PED between point E and F = (Q2 - Q1) / (P2 - P1) * (P1 + P2) / (Q1 + Q2)

                                             = (600 - 500) / (3 - 6) * (6 + 3) / (500 + 600)

                                             = (100 / -3) * (9 / 1,100)

                                             = 900 / -3,300

                                             = -0.27

The absolute value of PED is 0.27.