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Lecture 5
Review: Elasticity along Linear Demand
Curve
ProfitMaximizing Production Decision for
Monopolist
Comparison of Monopoly and Perfect
Competition
Price elasticity of demand
Note
: price elasticities are always expressed as
a positive number, for convenience
we know that P and Qd always move in opposite
directions so price elasticity of demand will always
negative. we are interested in the
magnitude
of
changes, so use absolute value so “more”/“less”
mean what we want them to.
•
ε
> 1
⇒
elastic
•
ε
< 1
⇒
inelastic
•
ε
= 1
⇒
unit elastic
Alternative mathematical expressions
for price elasticity of demand
•
ε
= %
Δ
Q /%
Δ
P = (
Δ
Q/Q) / (
Δ
P/P)
– now just rearrange.
..
•
ε
= (
Δ
Q/Q)
×
(P/
Δ
P )=(
Δ
Q/
Δ
P)
×
(P/Q) =
– to get…
•
ε
= (P / Q)
×
(1 / slope)
– “pointslope method”
Graphical interpretation of
elasticity
P
Q
P
Q
P 
Δ
P
Q +
Δ
Q
D
A
Δ
P
Δ
Q
Price elasticity & linear
demand
• Price elasticity changes along a
straightline demand curve
P
Q
Pmax/2
Qmax / 2
D
ε
> 1
ε
< 1
ε
= 1
Pointslope method: elasticity
along a linear demand curve
• Demand Curve
– High P, Low Q
– Low P, High Q
• Slope is constant on linear demand
curve
•
ε
= (P / Q)
×
(1 / slope)
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Elasticity and total revenue
(TR=P*Q)
• When price elasticity > 1, changes in price
and changes in total revenue move in
opposite directions
– decrease in price results in an increase in TR
– increase in price results in a decrease in TR
• When price elasticity < 1, changes in price
and changes in total revenue move in the
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 Fall '09
 HAMILTON

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