Econ 201
Spring 2009
Lecture 4.1
Elasticity
Taxes & Subsidies
4-28-09
Demand Elasticity Calculation
• Economist use the price elasticity of demand
to summarize how responsive quantity
demanded is to price
• Demand curves are not always linear; and
responsiveness can change with price
% change in Qd
elasticity 
% change in price
Overview of Elasticity
• Own-price demand
elasticity
• Measures movement (Qd)
along the demand curve in
response to a change in
the (own) price of the
good
 xx  (Qx d / Qx d ) /(Px / Px )
• Cross-price demand
elasticity
– Measures change in Qd
due to a shift in demand
 xy  (Qx d / Qx d ) /(Py Py )
 xx  (Qx d / Qx d ) /(Px / Px )
Demand Elasticity
for the linear demand curve
Demand Elasticity
$2
$3
$4
$5
-2
$6
0
$7
-10
-4.5
-2.66667
-1.75
-1.2
-0.83333
-0.57143
-0.375
-0.22222
$8
0.10
0.11
0.13
0.14
0.17
0.20
0.25
0.33
0.50
Ed
$9
-1
-0.5
-0.33333
-0.25
-0.2
-0.16667
-0.14286
-0.125
-0.11111
Den (P)
$10
Num (Q)
1
2
3
4
5
6
7
8
9
10
Price
price per unit
Qd
$10
$9
$8
$7
$6
$5
$4
$3
$2
$1
-4
-6
Ed
-8
-10
-12
Elasticity
Calculating Elasticity
•
Elasticity is calculated at a point on the demand curve
– Several choices:
• Initial point, final point, average (arc) elasticity
– At $5 -> Qd = 6; At $6 ->Qd = 7
– Elasticity of demand (intital point):
d 
(Q1  Q2 ) / Q1
(6  7) / 6
(1/ 6)
5



( P1  P2 ) / P1 ($5  $4) / $5 (1/ 5)
6
Why Bother?
– Affect’s a firm’s
revenues & profitability
– Affect’s pricing
strategy
Demand for Eggs
Individual A
Individual B
50
$ Per Dozen
• Own-price elasticity
tells us how
responsive quantity
demanded is to price
changes
40
30
20
10
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
# Eggs per month
What Affects (Own) Price Elasticity
• Availability and closeness of substitutes
– Fewer close substitutes -> inability to shift
consumption to other goods -> can only
decrease current consumption
• Demand will be more inelastic
• Proportion of Income
– Lower % of income -> lower price sensitivity > lower price responsiveness (inelastic)
• Affordability study
What Does Cross-price
Elasticity Tell Us?
• Sign of cross-price elasticity is important
– (+) sign -> increases in price (Py) of other
good results in an increase in consumption of
this good (Qx)
• Shifts demand for X to the right -> substitute
– (-) sign -> increase in Py results in decrease
in Qx
• Shifts demand for X to the left -> complement
More on Cross-Price
• Magnitude of the shift (or elasticity) tells
us:
– If a substitute
• How close/good a substitute
– Closer substitute -> bigger shift in demand for X
» Larger cross-price elasticity
– If a complement
• How important it is to “joint” consumption
– E.g. if “fixed proportions” -> bigger shift in demand for X
» Large (absolute) cross-price elasticity
Why Else It Might Be Useful
• Firm’s perspective
– Strategic:
• Substitutes: allows us to anticipate changes in
demand to competitors prices
• Complements: allows us to anticipate the impact
of changes in prices of suppliers on the demand
for our product
• Policy Evaluation
– Evaluate impact of taxes used to subsidize
other goods/services
Evaluating the Impact of
Government Intervention
• Policy Instruments Available
– Taxes
• Typically: per-unit tax on output
• Others: lump-sum, value added (VAT)
– Subsidies
• Rebate on per-unit produced
– Price Floors
• Minimum price that can be charged (e.g., minimum wage)
– Price Ceilings
• Limit on the maximum price that can be charged (WIN)
– Quotas
• Limits on amounts produced/imported
• Infant industry/protectionism
Key Assumptions
• No Market Failure
– No externalities
• i.e., benefits or costs that are not accounted for in
the marketplace (e.g., no free riders, no pollution
costs that aren’t captured in the product’s price)
– Perfectly competitive markets
• Large # of suppliers and buyers
• Evaluate Market Efficiency
– Look at losses/gains in consumer/producer
surplus
Effect of a Tax on the Supply Curve
• To the supplier: increases per-unit costs
– Shifts supply curve to the left
• Reduces amount supplied and raises the
market clearing price
• How do we measure the effects of the tax?
– Efficiency or deadweight losses are losses in
consumer and producer surplus relative to the
“ideal” market
How Do We Analyze the Effects of
Taxes and Subsidies
• The efficient ideal market
– “perfectly competitive” market
• Consumers and suppliers are price-takers, i.e. have no
market power
Effect of a Tax on the Supply Curve
Deadweight Loss
How Do We Evaluate the
Impact of a Tax?
• Framework for analysis is comparing
benefits and costs
– Costs of the tax
• Reduction in equilibrium quantity
• Increase in price paid
– Costs can be calculated as the deadweight
loss in $ if demand and supply curves are
known
What Are the Benefits?
• Depends on what we do with the taxes
– Suppose we use it to subsidize another good
• Subsidy appears as a reduction in per-unit costs to
the firm getting the subsidy
Figure A-1.
The Deadweight Loss from a Price Subsidy
SOURCE: Congressional Budget Office.
Evaluating The Impact
• Costs:
– Deadweight loss: sum of reduction in consumer and
producer surplus for the taxed good
• Reflects reduction in Qd and higher price paid
• Benefits
– Gain in CS and PS from subsidized cost
• Will Benefits > Tax
– Depends on the relative demand elasticities for the 2
goods
Evaluating the Impact
• “A Positive Analysis” (Distributional
Consequences)
– Who gains/loses from the tax and subsidy?
– Both producers and consumers of the taxed
good lose (in terms of lost surpluses)
– Relative demand/elasticities determine who loses most
» More inelastic demand -> greater is CS loss
– Producers and Consumers of subsidized
good win (lower price and more Q)
– Relative demand supply elasticities determine who
benefits most
Total Social Welfare
•
Ideally the impact of a program should be
evaluated as: {Pareto efficient}
–
–
–
•
1) can any one (or more) person’s welfare be
improved
2) without any one else’s welfare being reduced
http://en.wikipedia.org/wiki/Pareto_efficiency
More realistically: Could the winners
compensate the losers? {Pigouvian}
–
–
Is the deadweight loss of the taxed good less than
the surplus gain from the subsidized good?
http://en.wikipedia.org/wiki/Pigovian_tax
So Do They Do This
in the Real World?
• The Senate has approved a bill that would
require gasoline producers to blend 36 billion
gallons of ethanol into gasoline by 2022, an
increase from the current standard of 7.5 billion
gallons by 2012. The House did not include such
a provision in the version it passed, and it is
uncertain whether any final legislation will
emerge this year and what it will say about
ethanol if it does.
• What would be the impact of such legislation on
the demand for ethanol? For corn-based food
prices?