Download ###Price, Income and Cross Elasticity

Price, Income
and Cross Elasticity
Elasticity – the concept
• The responsiveness of one variable
to changes in another
• When price rises, what happens
to demand?
• Demand falls
• BUT!
• How much does demand fall?
Elasticity – the concept
• If price rises by 10% - what
happens to demand?
• We know demand will fall
• By more than 10%?
• By less than 10%?
• Elasticity measures the extent
to which demand will change
Elasticity
• 4 basic types used:
• Price elasticity of demand
• Price elasticity of supply
• Income elasticity of demand
• Cross elasticity
Elasticity
• Price Elasticity of Demand
– The responsiveness of demand
to changes in price
– Where % change in demand
is greater than % change in price –
elastic
– Where % change in demand is less
than % change in price - inelastic
Elasticity
The Formula:
Ped =
% Change in Quantity Demanded
___________________________
% Change in Price
If answer is between 0 and -1: the relationship is inelastic
If the answer is between -1 and infinity: the relationship is elastic
Note: PED has – sign in front of it; because as price rises
demand falls and vice-versa (inverse relationship between
price and demand)
Price (£)
Elasticity
The demand curve can be a
range of shapes each of which
is associated with a different
relationship between price and
the quantity demanded.
Quantity Demanded
Elasticity
Price
Total
revenue is of
price
x
The importance
elasticity
quantity sold. In this
is the information it
example,
TRthe
= £5
x 100,000
provides on
effect
on
=
£500,000.
total revenue of changes in
price.
This value is represented by
the grey shaded rectangle.
£5
Total Revenue
D
100
Quantity Demanded (000s)
Elasticity
Price
If the firm decides to
decrease price to (say) £3,
the degree of price
elasticity of the demand
curve would determine the
extent of the increase in
demand and the change
therefore in total revenue.
£5
£3
Total Revenue
D
100
140
Quantity Demanded (000s)
Elasticity
Price (£)
Producer decides to lower price to attract sales
% Δ Price = -50%
10
% Δ Quantity Demanded = +20%
Ped = -0.4 (Inelastic)
Total Revenue would fall
5
Not a good move!
D
5 6
Quantity Demanded
Elasticity
Price (£)
10
Producer decides to reduce price to increase sales
% Δ in Price = - 30%
% Δ in Demand = + 300%
Ped = - 10 (Elastic)
Total Revenue rises
Good Move!
7
D
5
Quantity Demanded
20
Elasticity
• If demand is
price elastic:
• Increasing price
would reduce TR
(%Δ Qd > % Δ P)
• Reducing price
would increase
TR
(%Δ Qd > % Δ P)
• If demand is
price inelastic:
• Increasing price
would increase
TR
(%Δ Qd < % Δ P)
• Reducing price
would reduce TR
(%Δ Qd < % Δ P)
Price Elasticity of Demand
Definition:
Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us
how much more. The degree of sensitivity of consumers to a change in price is measured by the concept of
price elasticity of demand.
Price elasticity formula: Ed = percentage change in Qd / percentage change in Price.
If the percentage change is not given in a problem, it can be computed using the following formula:
Percentage change in Qd = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd.
Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price.
Putting the two above equations together:
Ed = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative
number. But, we focus on the magnitude of the change by neglecting the minus sign and use absolute value
Examples:
1. If the price of Product A increased by 10%, the quantity demanded decreased by 20%. Then the
coefficient for price elasticity of the demand of Product A is:
Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2
2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased
from $2 to $4 per unit, the coefficient for Ed is:
Ed = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {(1000 - 900) / 1/2(1000 + 900)} / {(2 - 4) / 1/2
(2+4)} = - 0.16
Take the absolute value of - 0.16, Ed = 0.16
Elasticity
• Income Elasticity of Demand:
– The responsiveness of demand
to changes in incomes
• Normal Good – demand rises
as income rises and vice versa
• Inferior Good – demand falls
as income rises and vice versa
Elasticity
• Income Elasticity of Demand:
• A positive sign denotes a normal good
• A negative sign denotes an inferior good
Income Elasticity of Demand
Definition:
Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's
quantity demanded and income. It measures the sensitivity of quantity demand change of
product X to a change in income.
Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in
Income
If the percentage change is not given in a problem, it can be computed using the following
formula:
Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd.
Percentage change in Y = (Y1-Y2) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New
income.
Putting the two above equations together:
Ey = {(Q1-Q2) / [1/2 (Q1+Q2)] } / (Y1-Y2) / [1/2 (Y1 + Y2)]
Characteristics:
Ey > 1, Qd and income are directly related. This is a normal good and it is income elastic.
0< Ey<1, Qd and income are directly related. This is a normal good and it is income inelastic.
Ey < 0, Qd and income are inversely related. This is an inferior good.
Ey approaches 0, Qd stays the same as income changes, indicating a necessity.
Example:
If income increased by 10%, the quantity demanded of a product increases by 5 %. Then the
coefficient for the income elasticity of demand for this product is::
Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating
this is a normal good and it is income inelastic.
Elasticity
• For example:
• Yed = - 0.6: Good is an inferior good but inelastic –
a rise in income of 3% would lead to demand falling
by 1.8%
• Yed = + 0.4: Good is a normal good but inelastic –
a rise in incomes of 3% would lead to demand rising
by 1.2%
• Yed = + 1.6: Good is a normal good and elastic –
a rise in incomes of 3% would lead to demand rising
by 4.8%
• Yed = - 2.1: Good is an inferior good and elastic –
a rise in incomes of 3% would lead to a fall in demand
of 6.3%
Elasticity
• Cross Elasticity:
• The responsiveness of demand
of one good to changes in the price
of a related good – either
a substitute or a complement
% Δ Qd of good t
__________________
Xed =
% Δ Price of good y
Elasticity
• Goods which are complements:
– Cross Elasticity will have negative
sign (inverse relationship between
the two)
• Goods which are substitutes:
– Cross Elasticity will have a positive
sign (positive relationship between
the two)
Cross Elasticity of Demand
Definition:
Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of
quantity demand change of product X to a change in the price of product Y.
Formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y.
If the percentage change is not given in a problem, it can be computed using the following
formula:
Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 = new
Qd of X.
Percentage change in Py = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New
Price of Y.
Putting the two above equations together:
Exy = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
Characteristics:
Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes.
Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not related.
Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements.
Examples:
1. If the price of Product A increased by 10%, the quantity demanded of B increases by 15 %.
Then the coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating
A and B are substitutes.
2. If the price of Product A increased by 10%, the quantity demanded of B decreases by 15 %.
Then the coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = - 1.5 < 0,
indicating A and B are complements.
Elasticity
• Price Elasticity of Supply:
– The responsiveness of supply to changes
in price
– If Pes is inelastic - it will be difficult for
suppliers to react swiftly to changes in price
– If Pes is elastic – supply can react quickly
to changes in price
%
Δ Quantity Supplied
____________________
Pes =
% Δ Price
Price Elasticity of Supply
Definition:
Law of supply tells us that producers will respond to a price drop by producing less,
but it does not tell us how much less. The degree of sensitivity of producers to a
change in price is measured by the concept of price elasticity of supply.
Price elasticity formula: Es = percentage change in Qs / percentage change in Price.
If the percentage change is not given in a problem, it can be computed using the
following formula:
Percentage change in Qs = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qs, and Q2
= new Qs.
Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 =
New Price.
Putting the two above equations together:
Es = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]}
Because of the direct relationship between Qs and Price, the Es coefficient will always
be a positive number.
Examples:
1. If the price of Product A increased by 10%, the quantity supplied increases by
5%. Then the coefficient for price elasticity of the supply of Product A is:
Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = 0.5
2. If the quantity supplied of Product B has decreased from 1000 units to 200 units as
price decreases from $4 to $2 per unit, the coefficient for Es is:
Es = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {(1000 - 200) /
1/2(1000 + 200)} / {(4-2) / 1/2 (4+2)} = 2
Characteristics & Determinants
Characteristics:
Es approaches infinity, supply is perfectly elastic. Producers are very sensitive to price change.
Es > 1, supply is elastic. Producers are relatively responsive to price changes.
Es = 1, supply is unit elastic. Producers’ response and price change are in same proportion.
Es < 1, supply is inelastic. Producers are relatively unresponsive to price changes.
Es approaches 0, supply is perfectly inelastic. Producers are very insensitive to price change.
It is impossible to judge elasticity of a supply curve by its flatness or steepness. Along a linear
supply curve, its elasticity changes.
Determinants:
1. Time lag: How soon the cost of increasing production rises and the time elapsed since the
price change influence the Es. The more rapidly the production cost rises and the less time
elapses since a price change, the more inelastic the supply. The longer the time elapses, more
adjustments can be made to the production process, the more elastic the supply.
2. Storage possibilities: Products that cannot be stored will have a less elastic supply. For
example, produces usually have inelastic supply due to the limited shelf life of the vegetables
and fruits.
Determinants of Elasticity
• Time period – the longer the time under
consideration the more elastic a good is likely
to be
• Number and closeness of substitutes –
the greater the number of substitutes,
the more elastic
• The proportion of income taken up by the
product – the smaller the proportion the
more inelastic
• Luxury or Necessity - for example,
addictive drugs
Importance of Elasticity
• Relationship between changes
in price and total revenue
• Importance in determining
what goods to tax (tax revenue)
• Importance in analysing time lags
in production
• Influences the behaviour of a firm