# Elasticity

**Topics:**Supply and demand, Price elasticity of demand, Elasticity

**Pages:**19 (2393 words)

**Published:**July 5, 2013

Demand and Elasticity

Elasticity is a way to measure the responsiveness of a dependent variable to changes in an independent variable. Elasticity is defined as a ratio of the percentage change in a dependent variable to a percentage change in an independent variable.

Elasticity ≡

percentage change of dependent variable Percentage change of independent variable

When: Y = f(X) %ΔY E ≡ %ΔX

Fal l ’05 © Reynolds 2005

Microeconomics

Slide 1

Chapter 9 – Elasticity and Demand

Examples of Elasticity

If, QX = f (PX, PR, M, . . . #buyers),

1) It may be useful to know how a change in the price of good X (ΔPX) will alter the quantity purchased at each price (ΔQX). Price elasticity (EP, εp, ηP, eP ) measures this relationship. 2) Income elasticity is a measure of how a change in income (ΔM) will change the quantity (ΔQX) that will be purchased at each price. 3) Cross elasticity is a measure of how a change in the price of good Y (ΔPY) will change the quantity demanded of good X (ΔQX) Fal l ’05 © Reynolds 2005

Microeconomics

Slide 2

Chapter 9 – Elasticity and Demand

“Own” Price Elasticity of Demand

Price Elasticity of Demand (EP) is a measure of how responsive buyers are to changes in the price of a good. Price elasticity is determined by: ⎛ ΔQ ⎞ 1) the slope of the demand function,⎜ ΔP ⎟ ⎝ ⎠

2) the location on the demand function P (Q, P, or more accurately, ) Q

Fal l ’05 © Reynolds 2005

Microeconomics

Slide 3

Chapter 9 – Elasticity and Demand

Calculation of Price Elasticity

Q % Δ Quantity = % Δ Price ΔP P

By rearranging terms:

10

ΔQ

EP =

ΔQX PX EP = * ΔPX QX

Fal l ’05 © Reynolds 2005

Microeconomics

Slide 4

Chapter 9 – Elasticity and Demand

Calculation of Price Elasticity -

ΔQX PX EP = * ΔPX QX

ΔQX is the slope of ΔPX the demand function

PX is the location QX on the demand function

Fal l ’05 © Reynolds 2005

Microeconomics

Slide 5

Chapter 9 – Elasticity and Demand

Example of “Point” of Price Elasticity

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Demand Equation: Q = 10 –1P P = 10 – 1Q

10

Given the demand equation: Q = 10 – 1P The slope of demand is: Δ Q X = -1 Δ PX B

Price

9 8 7 6 5

A

At a price of $4, QX is 6 units

4 3 2 1

C

EP =

Demand

ΔQX P ⎛4⎞ * = (-1) ⎜ ⎟ =-.67 PX Q ⎝6⎠

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Q/ut Slide 6

Fal l ’05 © Reynolds 2005

Microeconomics

Chapter 9 – Elasticity and Demand

Example of “Point” of Price Elasticity

10

Demand Equation: Q = 10 –1P P = 10 – 1Q

10

Given the demand equation: Q = 10 – 1P The slope of demand is: Δ Q X = -1 Δ PX B

Price

9 8 7 6 5

A

At a price of $8, QX is 2 units

4 3 2 1

C

Demand

EP =

ΔQX P ⎛8⎞ * = (-1) ⎜ ⎟ =-4 PX Q ⎝2⎠

Point price elasticity is different at every price.

Slide 7

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Q/ut

Fal l ’05 © Reynolds 2005

Microeconomics

Chapter 9 – Elasticity and Demand

“Elastic” Demand

Point price elasticity is different at every price. When buyers are responsive to ΔP; • This is “ELASTIC” •The |%ΔQX| > |%ΔPX| • |EP|>1 •Total Revenue and price move in opposite directions. •This occurs at “high prices” Fal l ’05 © Reynolds 2005

Q = 10 – 1P Demand, EP and Total Revenue (TR)

Price Quantity

$0 $1 $2 $3 $4 $5 $6 $7 $8 $9 $10 10 9 8 7 6 5 4 3 2 1 0

EP

0 -0.11 -0.25 -0.43 -0.67 - 1.00 - 1.50 - 2.33 - 4.00 - 9.00 undefined

TR

0 $9 $16 $21 $24 $25 $24 $21 $16 $9 0 Slide 8

Microeconomics

Chapter 9 – Elasticity and Demand

“Inelastic” Demand

Point price elasticity is different at every price. When buyers are not responsive to ΔP; • This is “INELASTIC” •The |%ΔQX| < |%ΔPX| • |EP|

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