The quantity demanded of good X is 300 units when the price of good X is $50, and the quantity demanded of good X is 250 units when the price of good Xis $60. What is the numerical value of arc price elasticity of demand for good X?

Answered: The quantity demanded of good X is 300…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter3: Demand Analysis

Section: Chapter Questions

Problem 6E

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The quantity demanded of good X is 300 units when the price of good X is $50, and the quantity demanded of good X is 250 units when the price of good X
is $60. What is the numerical value of arc price elasticity of demand for good X?

Expert Solution

Step 1

Arc elasticity measures elasticity at the midpoint between the two selected points

$A r c E_{d} = \frac{[(Q d_{2} - Q d_{1}) / m i d p o i n t Q d]}{[(P_{2} - P_{1}) / m i d p o i n t P]} M i d p o i n t Q d = (Q d_{1} + Q d_{2}) / 2 = 300 + 250 / 2 = 275 M i d p o i n t P r i c e = (P_{1} + P_{2}) / 2 = (50 + 60) / 2 = 55 % c h a n g e i n q t y d e m a n d e d = [(Q d_{2} - Q d_{1}) / m i d p o i n t Q d] = (250 - 300) / 275 = - 0.19 % c h a n g e i n p r i c e = [(P_{2} - P_{1}) / m i d p o i n t P] = (60 - 50) / 55 = 0.19 A r c E d = - 0.19 / 0.19 = - 1$

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