Download Spring 2016

Surplus Measures Applications
&
Elasticity Measures
Lecture 9
Dr. Jennifer P. Wissink
©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved.
February 27, 2017
Market Equilibrium & Efficiency


Suppose that social and private
valuations of marginal benefits
and marginal costs equal each
other.
Then at a market equilibrium, you
get what economists call
“efficiency”.
– aka Pareto efficiency
– aka allocative efficiency
– That is, NSS is maximized at the
market equilibrium.


GOOD NEWS result for markets!
Now, suppose “something” keeps
us away from Q*.
– The market is not efficient.
– What is the “cost” of that?
– Dead Weight Loss
$
Supply=MC
C
P*
A
Demand=MB
E
O
Q*
Quantity
i>clicker question
Consider demand and supply in the market for unskilled labor. Suppose a binding minimum wage is
imposed. Which one of the following is false when we compare the before and after situation?
A. Consumers’ Surplus under the minimum wage is lower.
B. Net Social Surplus under the minimum wage is higher.
C. There will be surplus labor under the minimum wage.
D. Producers’ Surplus may be higher or lower under the minimum wage.
Before
$wage
NSS
S=MC
C
CS
PS
A
10=w*
E
O
D=MB
Q*
100
Labor Hrs
After
Why Commodity Taxes are
Inefficient
$P
S=MC
C
F
G
A
P*
I
H
D=MB
E
O
QN
QO
Gas gallons
Marshall’s Diamond Water Paradox Resolved
$P diamonds
$P water
Q diamonds
Q water
Sure Seems That Sensitivities Matter

They matter for…
– How much quantity demanded or
quantity supplied will change when a good’s price changes.
– How much equilibrium price and quantity will change when
you do comparative statics.
– How much unemployment will be generated with a price floor.
– How much surplus there is and how it is shared between
buyers and sellers.
– How the economic price incidence of a tax will be shared
between suppliers and demanders.
– And so much more…

So what are they and how can we define this better?
What is an Elasticity?
A
unit free measure.
 Measurement of the percentage change in one
variable that results from a 1% change in
another variable.
 Lots of them!
 Example:
– Suppose when the PX rises by 1%, quantity
demanded of X falls by 5%.
– The own price elasticity of demand is -5 in this
example.
2 Very Important Elasticities

Own Price Elasticity of Demand for X:
– Captures how sensitive
the quantity demanded of X is to a
change in X’s own price.
» Using percent changes

Own Price Elasticity of Supply for X:
– Captures how sensitive
the quantity supplied of X is to a
change in X’s own price.
» Using percent changes
Examples:
Own Price Demand Elasticities

Suppose data tells us that when the
price of gasoline rises by 1% the
quantity demanded falls by 0.2%.
– Gas demand is not very price
sensitive.
– Own price elasticity of demand for
gas is -0.2.

Suppose data tells us that when the
price of gold jewelry rises by 1% the
quantity demanded falls by 2.6%.
– Jewelry demand is very price
sensitive.
– Own price elasticity of demand for
jewelry is -2.6.
Examples:
Own Price Supply Elasticities

Suppose we know that when the price of
DaVinci paintings increases by 1% the
quantity supplied doesn’t change at all.
– The quantity supplied of DaVinci paintings
is completely insensitive to their price.
– Own price elasticity of supply is 0.

Suppose we observe that when the price of
beef increases by 1% the quantity supplied
increases by 5%.
– Beef supply is very price sensitive.
– Own price elasticity of supply is 5.
Beauty of Unit-free Comparisons

Gasoline and jewelry
– It doesn’t matter that gas is sold by the gallon for about $3.50 and
gold is sold by the ounce for about $1500.
– We compare the demand elasticities of -0.2 (gas) and -2.6 (gold
jewelry).
– Gold jewelry demand is more price sensitive.

Paintings and meat
– It doesn’t matter that classical paintings are sold by the
canvas for millions of dollars each while beef is sold by the
pound for about $2.99.
– We compare the supply elasticities of 0 (classical paintings)
and 5 (beef).
– Beef supply is more price sensitive.
Values of Own Price Elasticities
and Terminology

If we “report” them as positive numbers…



Not a problem with supply (owing to law of supply).
Take absolute value with demand (owing to law of demand).
Terms work the same way for own price elasticity of demand and
supply.
price inelastic
0
price elastic
1
unit elastic
2
3
4
5
6
Calculating Elasticities
 LET’S
STICK TO DEMAND ONLY FOR
NOW!
 How does one calculate an elasticity?
 Depends on the accuracy you want and the
information you’ve got.
– (Midpoint) Arc Formula
» an approximation using two sets of data points &
discrete differences.
– Point Formula
» an exact measure at a point, used when we have
the demand function and its slope.
Own Price Elasticity of Demand
 Recall
 D X ,P 
X
Its Definition
Percent Change in Quantity D emanded of X
Percent Change in Price of X
 (Midpoint) Arc
–
–
–
–

D
Formula
P = Own price of the good X at two points, P1 and P2
QD = Quantity demanded of X at those two prices
ΔP = Change in PX
ΔQD = Change in quantity demanded of X
X , PX
Q D /[(Q 1  Q 2 )/2] 100

P/[(P1  P2 )/2] 100
So, since we do not know if A is
“new” or if B is “new”, we just take
the change in the two values and
divide by the midpoint of the
interval.
(Midpoint) ARC Own Price Elasticity of
Demand Calculation


Goal: approximate own price
elasticity of demand between A
and B (ignore C).
Percent change in
QD
Linear Demand Curve
42
is
41
40
(11-12) / [(11+12)/2] = -1/11.5
B
39
= -8.69%.

Percent change in P is
Price
38
A
37
36
C
35
34
33
(38-36) / [(38+36)/2] = 2/37
= 5.40%.

Elasticity is approx.
-8.69% / 5.40% = -1.6
32
31
30
10
11
12
Quantity
13
14
i>clicker question
The own price elasticity of demand between points A and B on the graph below (and
reported using absolute values) is 1.6. If we calculate the own price elasticity of demand
using points A and C we would expect that
A. the elasticity would be the same, that is 1.6, silly, since it’s a straight line!
B. the elasticity would now be smaller than 1.6.
C. the elasticity would now be larger than 1.6.
Linear Demand Curve
42
41
40
B
39
Price
38
A
37
36
C
35
34
33
32
31
30
10
11
12
Quantity
13
14