Transcript Elasticity   Suppose that a particular variable (B) depends on another variable (A) B = f(A…) We define the elasticity of B with respect to.

Elasticity


Suppose that a particular variable (B)
depends on another variable (A)
B = f(A…)
We define the elasticity of B with respect to A
as
EB , A

% change in B B / B B A




% change in A A / A A B
The elasticity shows how B responds (ceteris
paribus) to a 1 percent change in A
Price Elasticity of Demand

The most important elasticity is the price
elasticity of demand

measures the change in quantity demanded
caused by a change in the price of the good
% change in Q Q / Q Q P
EP 



% change in P P / P P Q

EP will generally be negative

except in cases of Giffen’s paradox
Distinguishing Values of EP
Value of EP at a Point
Classification of
Elasticity at This Point
EP < -1
Elastic
EP = -1
Unit Elastic
EP > -1
Inelastic
Price Elasticity and Total
Expenditure

Total expenditure on any good is equal to
Total Expenditure = PQ

Using elasticity, we can determine how total
expenditure changes when the price of a
good changes
Price Elasticity and Total
Expenditure
Responses of PQ
Demand
Price
Increase
Price
Decrease
Elastic
Falls
Rises
Unit
Elastic
No Change
No Change
Inelastic
Rises
Falls
Income Elasticity of Demand

The income elasticity of demand (EI)
measures the relationship between income
changes and quantity changes
% change in Q Q I
EI 


% change in I I Q

Normal goods  EI > 0


Luxury goods  EI > 1
Inferior goods  EI < 0
Cross-Price Elasticity of Demand

The cross-price elasticity of demand (EQ,P’)
measures the relationship between changes in
the price of one good and and quantity
changes in another
EQ , P '


% change in Q Q P'



% change in P' P' Q
Gross substitutes  EQ,P’ > 0
Gross complements  EQ,P’ < 0
Linear Demand
Q = a + bP + cI + dP’
where:
Q = quantity demanded
P = price of the good
I = income
P’ = price of other goods
a, b, c, d = various demand parameters
Linear Demand

Q = a + bP + cI + dP’
Assume that:



Q/P = b  0 (no Giffen’s paradox)
Q/I = c  0 (the good is a normal good)
Q/P’ = d ⋛ 0 (depending on whether the
other good is a gross substitute or gross
complement)
Linear Demand

If I and P’ are held constant at I* and P’*,
the demand function can be written
Q = a’ + bP
where a’ = a + cI* + dP’*


Note that this implies a linear demand curve
Changes in I or P’ will alter a’ and shift the
demand curve
Linear Demand

Along a linear demand curve, the slope
(Q/P) is constant


the price elasticity of demand will not be constant
along the demand curve
Q P
P
EP 
 b
P Q
Q
As price rises and quantity falls, the elasticity
will become a larger negative number (b < 0)
Linear Demand
Demand becomes more
elastic at higher prices
P
-a’/b
EP < -1
EP = -1
EP > -1
a’
Q