Question

Magic Videos, Inc. estimates the arc price elasticity of demand for video movies to be -3.0. Currently, the company sells 2,000 video movies per week at a price of $5.00. If Magic lowers its price to $3.00, What will the new sales quantity per week be?

Answer 1

Let

P0 = Initial price = $5

P1 = New price = $3

Q0 = Initial quantity = 2,000

Q1 = New quantity. Then using midpoint method,

Elasticity = [(Q1 - Q0) / (Q1 + Q0)] / [(P1 - P0) / (P1 + P0)]

-3 = [(Q1 - 2,000) / (Q1 + 2,000)] / [(3 - 5) / (3 + 5)]

-3 = [(Q1 - 2,000) / (Q1 + 2,000)] / (-2 / 8)

3 = [(Q1 - 2,000) / (Q1 + 2,000)] / (2 / 8)

3 = [{8 x (Q1 - 2,000)} / {2 x (Q1 + 2,000)}]

3 = [{4 x (Q1 - 2,000)} / {(Q1 + 2,000)}]

3 = (4Q1 - 8,000) / (Q1 + 2,000)

3Q1 + 6,000 = 4Q1 - 8,000

Q1 = 14,000