Download How does the quantity demanded respond to a change in price?

Chapter 5
Elasticity
Dilemma: As an economic analyst hired by a
supplier of good X, your task is to
determine how to increase revenue:
How does the quantity demanded respond to a
change in price?
If you decrease supply ⇒ you increase the price of X.
If you increase supply ⇒ you must lower the price of X.
Definition: Total Revenue = [Price * Quantity]
TRx = Px * Qx
If increase the Px ⇒ increase TRx, but Qx sold decreases.
Which force is stronger?
• Must determine the responsiveness of quantity demanded
to a change in price.
Elasticity: units free measure of responsiveness.
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Price Elasticity of Demand:
• Responsiveness measure of the quantity demanded of a good to
a change in its price.
εD = %%∆∆QP
Dx
⇐
negative number, so use absolute value.
x
εD = [%∆Q / %∆P] = [(∆Q/Q) ( ∆P/P)] =[ ∆Q/∆P * P/Q]
Inelastic Demand:
Px
Dx
0
QE
Perfectly inelastic demand.
Regardless of price, quantity
demand is constant.
Qx
If the percentage change in quantity demanded is less that the
percentage change in Price ⇒ elasticity of demand will be
between 0 and 1:
i.e.: if [ % ∆QD < % ∆P] ⇒ [0 < εD < 1].
⇒
Inelastic Demand
• If the % change QD > % change in Price ⇒ [εD > 1]
i.e.: if [ % ∆QD > % ∆P] ⇒
[ εD > 1].
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⇒
Elastic Demand
****************
•
If [ % ∆QD = % ∆P] ⇒
[ εD = 1].
Px
Unit elastic demand
Dx
Qx
0
• If demand is infinitely responsive to price ⇒
Px
PE
0
[ εD =∞ ].
Perfectly elastic demand.
Perfect Substitutes
Dx
Qx
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Elasticity Along Straight Line:
Px
Dx
εD >1 ⇒ elastic
•
εD =1
0<εD <1
⇒
inelastic
Qx
0
• Elasticity of demand falls as price falls and quantity
demanded increases.
• Unit elasticity at midpoint.
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Elasticity of Demand Depends on:
(1) The Closeness of Substitutes
•
Close substitutes ⇒ more elastic is demand.
For example:
Necessities: poor substitutes ⇒ inelastic demand
Luxuries: many substitutes ⇒ elastic demand
(2) The Proportion of Income Spent on the Good
•
The higher proportion of income spent ⇒ the more
elastic.
•
If only a small proportion of income spent ⇒ then a
change in price has little impact on consumers budget
overall ⇒ inelastic.
(3) Time Elapsed Since Price Change
•Short-run ⇒ some substitutions fixed.
•Long-run ⇒ all substitutions made.
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Elasticity, Total Revenue and Expenditure
Change in producers total revenue depend on the
extent that quantity sold changes as price changes.
• If Dx is elastic ⇒ 1% price ⇓ ⇒ >1 % ⇑ Q sold ⇒
TR ⇑
If the demand for X is elastic, a 1 percentage decrease in
the price of X will lead to a greater than a 1 percentage
increase in quantity sold. Total revenue will increase.
• If Dx is unit elastic ⇒ 1% price ⇓ ⇒ =1 % ⇑Q
sold
⇒
TR constant
If the demand for X is unit elastic, a 1 percentage decrease
in the price of X will lead to an equal 1 percentage
increase in quantity sold. Total revenue will remain the
same.
• If Dx is inelastic ⇒ 1% price ⇓ ⇒ <1 % ⇑Q sold ⇒
TR ⇓
If the demand for X is inelastic, a 1 percentage decrease in
the price of X will lead to a less than 1 percentage
increase in quantity sold. Total revenue will decrease.
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Total Revenue Test:
Px
Dx
Elastic
•
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Example: B.C. Ferries:
If they ⇑ price in the
elastic portion of the
demand curve ⇒ TR ⇓.
If they ⇓ price in the
elastic portion of Dx ⇒
TR ⇑.
Unit Elastic
Inelastic
Qx
10
0
TR
(P*Q)
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correspond
s to Elastic
portion
0
correspond
s to
Inelastic
portion
Qx
10
When Demand is elastic, a price decrease leads to an
increase in total revenue, and a price increase leads to a
decrease in total revenue.
When Demand is inelastic, a price decrease leads to a
decrease in total revenue, and a price increase leads to an
increase in total revenue.
Buying Plans Influenced by other factors:
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Cross Elasticity of Demand
-measure of responsiveness of the demand for a good to a
change in the price of a substitute or complement.
Cross εD = %∆ in Quantity demanded
%∆ in Pricesub. or Pricecomp.
- sign of this elasticity is positive for a substitute good,
and
negative for a complement good.
Income Elasticity of Demand:
-As income grows, demand for a good depends on the
income εD for the good.
-Income εD is a measure of the responsiveness of demand
to a change in income, other things remaining the same.
Income εD = %∆ in Quantity demanded of X
%∆ in Income
- sign can be positive or negative:
(1) Income εD > 1 (normal good, income elastic)
As income increases, demand increases faster than
income.
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QD
Dx
Income
0
(2) (0< Income εD <1) (normal good, income inelastic)
As income increases, QD increases, but at a slower rate
than the increase in income (necessities).
QD
Dx
0
Income
(3) εD < 0 (inferior good)
As Income increases, quantity demanded increases. But
only to a point (M); After that point, consumers start to
replace (inferior) good X with superior alternative.
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QD
Positive
income
elasticity
Negative
income
elasticity
Dx
0
Income
M
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Elasticity of Supply
Measures responsiveness of the quantity supplied of a
good to a change in its price:
εS =%%∆∆QP
Sx
x
Inelastic Supply:
Px
Perfectly inelastic supply.
Regardless of price, quantity
supplied is constant.
Sx
0
εS =0
Qx
QE
⇐ perfectly inelastic
Px
Price at which suppliers
are willing to sell any
quantity demanded.
Supply curve is horizontal
Sx
εS =∞
0
QE
Qx
Magnitude of εS Depends On:
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(perfectly elastic).
• Factor Substitution Possibilities:
→unique / rare factors of production ⇒ εS low.
→common factors of production ⇒ εS high.
• Time Frame for Supply Decisions:
→ monetary supply immediate.
→ short run  some factors not changed.
→ long run  all factors of production adjusted.
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