Question

2. Given the demand curve on the right, make the following calculations: So0 IfA were used as a base reference, what is the price elasticity of the arc between A and B? a. S50 3 $40 37.50 S30 25 $20 b. If B were used as a base reference, what is the price elasticity of the arc between B and A? $10 10 20 30 40 50 60 70 80 90 100110 Number of football cards c. Using the arc convention, what is the elasticity of point C? d. Is elasticity the same along all points? Is the slope of the demand curve the same at all points?

Answer 1

a) Here, P1 = 50 ,   Q1 = 10 , P2 = 25, Q2 = 60

PED of Arc between A and B = ∆Q/∆P *( P1 + P2 / Q1 + Q2)

                                               = (Q2 - Q1) / (P2 - P1) *( P1 + P2 / Q1 + Q2)

                                               = (60 - 10) / (25 - 50) * (50 + 25) / (10 + 60)

                                               = (50 / -25) * (75 / 70)

                                              = -2 * (75 / 70)

                                             = -2.14

The absolute value of PED is 2.14

b) Here, P1 = 25 ,   Q1 = 60 , P2 = 50, Q2 = 10

PED of Arc between A and B = ∆Q/∆P *( P1 + P2 / Q1 + Q2)

                                               = (Q2 - Q1) / (P2 - P1) *( P1 + P2 / Q1 + Q2)

                                               = (10 - 60) / (50 - 25) * (25 + 50) / (60 + 10)

                                               = (-50 / 25) * (75 / 70)

                                              = -2 * (75 / 70)

                                             = -2.14

The absolute value of PED is 2.14

c) PED at point C = -(110 / 55) * (37.50 / 35) = -2 * (37.50 / 35) = -2.14

The absolute value of PED is 2.14

d) Yes, the elasticity is same along all points, i.e., 2.14

     Yes, the slope of the demand curve is same at all points, i.e., -2