lecture 4 elasticity. readings: chapter 4 elasticity 4. consideration of elasticity our model tells...
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Lecture 4
Elasticity
Elasticity
Readings: Chapter 4
Elasticity
4. Consideration of elasticity Our model tells us that when demand increases
both price and quantity will increase. It does not tell us whether the price or quantity increase will be relatively big or small.
To make these sorts of predictions we need information on the price sensitivity of the demand and supply relationships.
Elasticity
Q: How should price sensitivity be measured? The Demand and Supply equations have slope
parameters that measure price sensitivity. Recall: Qd = a - b•P and Qs = c +d•P b = ∆Qd / ∆P = (Qd
2 - Qd1) / (P2 - P1)
d = ∆Qs/ ∆P = (Qs2 - Qs
1) / (P2 - P1)
Elasticity Problem: The slope parameters depend on the
units used to measure price and quantity. If there is inflation, the slope parameter will change
every year. Comparisons of price sensitivity will be meaningless.
Comparisons of the slope parameters in different countries are meaningless because of different national currencies.
Comparisons of the price sensitivity of different commodities will also be impossible because of the differing units used to measure different commodities.
Elasticity Solution: Elasticity provides a universal measure
that is immune to inflation and is comparable across national borders and across different commodities.
Q: What is elasticity? Elasticity = % Δ (dependent variable)
% Δ (independent variable)
It is a unit free measure because it is a ratio of %.
Elasticity
Q: What are the important elasticities? We will use four:
ηd = │(%ΔQd) / (%ΔP)│ = Price Elasticity of Demand
ηs = (%ΔQs) / (%ΔP) = Price Elasticity of Supply
ηm = (%ΔQd) / (%ΔIncome) = Income Elasticity of D
ηxy = (%ΔQxd) / (%ΔPy) = Cross-price Elasticity of D
High elasticity dependent variable highly responsive to changes in the independent variable
Low elasticity dependent variable unresponsive to changes in the independent variable
Elasticity
The price elasticity of demand tells us the price sensitivity of the quantity demanded.
P
Q
D
Elastic Demand
Q
P
D
Inelastic Demand
Elasticity
The price elasticity of supply tells the price sensitivity of the quantity supplied.
P
Q
S
Elastic Supply
Q
P S
Inelastic Supply
Q: How do we use data to calculate the elasticity of demand?
The arc elasticity of demand: Where:
avgP
P
PP
PPP
2/)(
%12
12
avg
dd
Q
Q
QQQ
2/)(
%12
12
P
Qd
d
%
%
Elasticity
Elasticity
Example: Consider the demand for pop (Dpop) when P falls from $1.50 to $1.00
ηd = │(∆Qd/ Qaverage)/(∆P / Paverage)│
ηd =│ 5 / 7.5 │ = │ +66.6% │ = │ -1.67 │= 1.67 │-0.5/1.25│ │ - 40% │
Dpop
P
Q
1.50
1.00
5 10
Elasticity
This is an approximation of the elasticity on the region of the demand curve between
P = $1.50 and $1.00. It is most accurate at the midpoint of this region.
Dpop
P
Q
1.50
1.00
5 10
Elasticity
Q: What about the other elasticities? They have similar arc elasticity formulas:
avg
avgdd
d PP
P
Q
/
/
%
%
avg
avgss
S PP
P
Q
/
/
%
%
avg
avgdd
m mm
m
Q
/
/
%
%
avgyy
avgxdx
y
dx
xy PP
P
Q
,
,
/
/
%
%
Elasticity
Q: How does knowledge of the elasticity of demand help us understand the market?
Knowing the elasticity of demand we can: 1. Predict the relative movements of price and quantity
to changes in supply. 2. Predict what will happen to industry revenue if price
changes.
Elasticity
Predicting the relative movements of P and Q.
S S’
D
S S’
D
d > 1 d < 1
ηd > 1
0<ηd < 1
Elasticity
Predicting the relative movements of P and Q.
S S’
D
S S’
D
d > 1d < 1ηd > 1
0<ηd <1
Elasticity Predictions:
Elastic (ηd >1) Increasing Supply causes small decline in P and large increase in Q.
Inelastic (ηd <1) Increasing Supply causes large decline in P and small increase in Q.
Elastic (ηd > 1) Decreasing P causes increase in Industry Revenue.
Inelastic (ηd <1) Decreasing P causes decline in Industry Revenue.
Exercise: If supply is elastic how will P and Q respond to demand changes? What if supply is inelastic?
Elasticity
Q: Does a straight line demand curve have a constant elasticity?
A straight-line demand curve has a constant slope, but elasticity declines with P.
ηd < 1
ηd > 1
ηd = 1
P
Q
ElasticityQ: How is the slope of a straight line demand
curve related to the elasticity? b = ∆Q / ∆P ηd = │∆Q / Qavg│ = │(∆Q /∆P)•(Pavg/Qavg) │ =b•(Pavg /Qavg)
│ ∆P / Pavg│ This is an approximation of the elasticity on a
region of the demand curve. At a particular point (Q,P) on the demand curve,
the point elasticity of demand will be ηd = b•(P/Q)
Elasticity
With a little thought, you can see why the mid-point has unit elasticity.
● ηd = b•(P/Q) = 1 P
Q
2P
2Q
Elasticity Q: How is the straight-line demand curve
related to revenue?
Q
Q
P
R
Revenue: R = P•Q
ηd = 1
ηd > 1
ηd < 1
Elasticity Q: Is there a point elasticity of supply equation? Yes. If the supply equation is Qs = c + dP then the point
elasticity of supply is ηs = d•(P/Q).
Supply: Qs = c + d•P
ηs = d•(P/Q) P
Q
ElasticityQ: What about the income elasticity of
demand? Recall: ηm = ∆Qd/ Qavg ,
∆m / mavg
If ηm > 0 then the good is a normal good and a rise in income will cause the demand curve to shift right (demand increases).
If ηm < 0 then the good is an inferior good and a rise in income will cause the demand curve to shift left (demand declines).
Elasticity Q: What about the cross-price elasticity of
demand? Recall: ηxy = ∆Qd
x/ Qx,avg ∆Py / Py,avg
If ηxy > 0 , then and increase in the price of y causes the quantity of x demanded to increase, and hence x and y are substitutes.
If ηxy < 0 , then x and y are complements.
Elasticity
http://www.bbc.co.uk/news/world-us-canada-24339308