Appendix C – Math Essentials: Calculating Percentage Change, Slope, and Elasticity
APPENDIX C
MATH ESSENTIALS:
CALCULATING
PERCENTAGE CHANGE,
SLOPE, AND ELASTICITY
Learning Objectives
LO C.1: Understand how to calculate percentage changes.
LO C.2: Use slope to calculate elasticity.
Appendix Outline
Percentage Change (LO C.1)
Slope and Elasticity (LO C.2)
X over Y, or Y over X?
Elasticity changes along with constant slope
Problems and Applications
1. Calculate the percentage change in each of the following examples:
[LO C.1]
a. 8 to 12.
b. 18 to 14.
c. 130 to 120.
d. 95 to 105.
Answer:
Using the mid-point method, percentage change in X =
a. 8 to 12:
C-1
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Education.
Appendix C – Math Essentials: Calculating Percentage Change, Slope, and Elasticity
2. Find the percentage change in price in each of the following examples
using the mid-point method. [LO C.1]
a. The price of a $4.50 sandwich increases to$5.50.
b. The sale discounts the price of a sofa from $750 to $500.
Answer: Using the mid-point method, percentage change in X
=
a. 8 to 10: [(10 – 8)/[(10 + 8)/2]] x 100 = 22.22%
3. Use the demand curve in CP-1 to answer the following questions. Use
the mid-point method in your calculations. [LO C.2]
a. What is the price elasticity of demand for a price change from $0 to
$20?
b. What is the price elasticity of demand for a price change from $20 to
$40?
c. What is the price elasticity of demand for a price change from $40 to
$60?
Answer:
Price elasticity of demand =
Price elasticity of demand =
C-2
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix C – Math Essentials: Calculating Percentage Change, Slope, and Elasticity
4. Use the demand schedule in Table CP-1 to answer the following
questions. Use the mid-point method in your calculations. [LO C.2]
a. What is the price elasticity of demand for a price change from $4 to
$8?
b. What is the price elasticity of demand for a price change from $8 to
$16?
c. What is the price elasticity of demand for a price change from $20 to
$24?
Answer:
Price elasticity of demand = % Change in QD/% Change in Price
Price elasticity of demand =
C-3
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix C – Math Essentials: Calculating Percentage Change, Slope, and Elasticity
5. Use the demand schedule in Table CP-2 to answer the following
questions. Use the mid-point method when calculating elasticity. [LO C.2]
a. What is the price elasticity of demand for a price change from $2 to
$3? What is the slope of the demand curve for a price change from $2
to $3?
b. What is the price elasticity of demand for a price change from $3 to
$5? What is the slope of the demand curve for a price change from $3
to $5?
c. What is the price elasticity of demand for a price change from $6 to
$7? What is the slope of the demand curve for a price change from $6
to $7?
Answer:
Price elasticity of demand = % Change in QD/% Change in Price
Price elasticity of demand = Slope =
a. The price elasticity of demand for a price change from $2 to $3:
b. The price elasticity of demand for a price change from $3 to $5:
c. The price elasticity of demand for a price change from $6 to $7:
C-4
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Appendix C – Math Essentials: Calculating Percentage Change, Slope, and Elasticity
C-5
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.