Download Week 4 – Elasticity and Tax Incidence

Week 4 – Elasticity, Tax Incidence and
Tax Burden
Note: first midterm – Friday Oct 26 at 3 p.m.
Elasticity = sensitivity or reponsiveness
Changes in one variable as another variable
changes
How sensitive is the quantity demanded to
changes in the price of the product? Answer
is given by elasticity of demand.
How sensitive is the quantity of tomatoes
supplied by businesses to changes in the price
of tomatoes in Ontario? Answer is given by
the elasticity of supply of tomatoes in
Ontario.
Elasticity of Demand
ED = dQ/dP x P/Q
ED = percentage change in quantity demanded
percentage change in price
….how consumers respond to a change in
market price
Elasticity of Supply
ES = dQ/dP x P/Q
ES = percentage change in quantity supplied
percentage change in price
…how producers respond to a change in
market price
If demand is P = 100 – Q, what is the
elasticity of demand at Q = 80?
At Q = 80, P = $20
ED = dQ/dP x P/Q = 1/(-1) x 20/80 = ¼
What does it mean to say that the elasticity
of demand at this point is ¼?
It means that if P = $20 and the price
changes by 4%, we expect that the quantity
demanded will change by about 1%.
(Why “about”?)
Terminology:
Demand is elastic if ED > 1
Demand is inelastic if ED < 1
Demand is unit(ary) elastic if ED = 1
Ripley’s Believe-it-or-not
Strange, but true, fact
Elasticity is different at every different
point along a linear demand curve
P
A
B
C
Demand
Curve
Q
Is a linear demand curve realistic?
Thinking about different goods, some have
more elastic demands; others have less
elastic demands.
What affects elasticity of demand?
Availability of close substitutes is key
Also amount spent on this good by the
consumer
How are elasticity of demand and changes in
revenue related?
See it on a graph (when demand is elastic):
P
A
B
C
Demand
Curve
Q
When demand is inelastic
P
A
B
C
Demand
Curve
Q
When demand is unit elastic
P
A
B
C
Demand
Curve
Q
When demand is elastic, a fall in price will
raise total revenue
When demand is elastic, a rise in price will
lower total revenue
When demand is inelastic, a fall in price will
lower total revenue
When demand is inelastic, a rise in price will
raise total revenue
When demand is unit elastic, a fall or a rise in
price will have no effect on total revenue
P
A
B
C
Demand
Curve
P
Elasticity and Taxation
An illustration of the use of “elasticity”
Think about the tax on one particular product
(not a general tax on many products)
– e.g., gasoline, liquor, cigarettes
This is called an “excise” tax
Could be a “flat-rate” tax
e.g., $5 per bottle of liquor, $0.30 per litre
of gasoline, $10 per carton of cigarettes
Could be an “ad-valorem” tax
e.g., 10% of the price on a bottle of liquor,
25% on a litre of gasoline, 30% on a carton of
cigarettes.
To keep it simple, we look only at flat-rate
excise tax.
Two interesting questions (and elasticity
comes into both!):
1.
Who really pays an excise tax, and what
does this depend on?
2. How does taxation affect the allocation
of society’s economic resources and
economic well-being?
In economics language:
1.
What is the incidence of an excise tax
(who bears the burden of an excise
tax)?
2. How much is the excess burden of an
excise tax (also known as the
deadweight loss due to the tax)?
Incidence of an excise tax
Political Science –
Government decides who will bear the tax by
levying it on the consumers (buyers) or on the
producers (sellers).
Economics –
Statutory incidence ≠ Economic Incidence
The market decides who will bear the tax –
depends on how consumers and producers
react to the tax.
In other words: incidence of the tax depends
on the elasticity of demand and the elasticity
of supply.
Economic analysis:
A tax drives a “wedge” between buyers and
sellers.
Buyers pay one price (including the tax), but
sellers receive another price.
We can show this on graph by:
If the tax is levied on consumers, we will have
two demand curves. One represents the
amount buyers pay, the other represents the
amount sellers receive.
Imagine a tax of $10 per sheet on plywood
sheets…
Price
$60
$50
$40
Tax
(per unit
amount)
$25
Original
Demand
(D)
$15
Net-of-tax
Demand
(D-T)
0
100,000
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Demand was:
D: P = 60 - .0001Q
This is now the “gross-of-tax” demand
curve
New “net-of-tax” demand curve is:
D-T: P = 50 - .0001Q
If, instead, the tax is levied on sellers…
If the tax is levied on producers, we will have
two supply curves. The original supply curve
represents the net amount sellers receive
(not including the tax) for supplying different
numbers of units of the good. The S+T curve
represents the amount buyers will pay for the
same numbers of units of the good (including
the tax).
Imagine again a tax of $10 per sheet on
plywood sheets, this time levied on sellers…
Price
(S+T) Gross amount
paid by buyers to
suppliers (including
tax)
$35
$25
Original
Supply (S)
net-of-tax
Tax (T)
$21
$15
$11
0
100,000
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Supply was:
S: P = 11 + .00004Q
This is now the “net-of-tax” supply curve
The gross-of-tax supply curve (the amount
buyers will have to pay to suppliers –
including the tax) is:
S+T: P = 21 + .00004Q
Analyzing the economic incidence of a tax on
consumers/buyers:
Price
$60
Supply
$25
Demand
$11
0
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Analyzing the economic incidence of a tax on
producers/sellers:
Price
$60
Supply
$25
Demand
$11
0
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Buyers’ share of tax = P1 – P0
Sellers’ share of tax = P0 – PS
Note that statutory incidence ≠ economic
incidence
Tax is levied by governments on either
consumers or producers.
However, tax is generally shared between
buyers and sellers.
Amount that buyers pay vs. amount sellers
pay depends on elasticity of demand and
elasticity of supply according to this formula:
BS/SS = ES/ED
The math of a tax on buyers:
The math of a tax on sellers:
Compare the results:
Does our elasticity formula work?
Incidence of an excise tax with extreme
elasticities:
Excess Burden of an Excise Tax
When a tax is levied, it changes the behaviour
of buyers and sellers. Because the gross
price is higher, consumers want to consume
less.
Because the net price is lower, suppliers want
to supply less.
Therefore, less output is produced and
consumed in this industry (i.e., economic
resources are reallocated to other industries
and away from this industry)
How much well-being is lost as a result of the
tax?
Well-being can be measured as the sum of
consumer surplus + producer surplus
Consumer surplus is the surplus of consumer
utility over the amount paid for the good
(measured in dollars).
Producer surplus is the surplus of revenues to
producers over the amount necessary to get
them to supply the good (measured in dollars)
Identify consumer surplus and producer
surplus on this graph:
Price
$60
Supply
$25
Demand
$11
0
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Now, look at the effects on consumer surplus
and producer surplus of a tax on consumers:
Price
$60
Supply
$25
Demand
$11
0
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Now look at the effects on consumer surplus
and producer surplus of a tax on sellers:
Price
$60
Supply
$25
Demand
$11
0
350,000
Market for 4’ x 8’ sheets of ¾” plywood
Quantity
Per month
Identify on the graphs:
Amount of tax revenue
Amount of tax revenue “paid” by consumers
(buyers’ share of total tax paid)
Amount of tax revenue “paid” by suppliers
(suppliers’ share of total tax paid)
Loss of consumer surplus
Loss of producer surplus
Deadweight Loss (Excess Burden)
How is excess burden affected by
elasticity? Let’s look at some
examples.
The math of excess burden (tax on
buyers):
The math of excess burden (tax on
suppliers):
Remember, taxes bring benefits too. We
have only been looking at the costs of
taxation.