Post on 03-Jan-2016
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BSc Southampton, MSc (LSE), PhD (LSE)
Professor of Economics, University of Bath (UK) (UK)MSc (LSE), PhD (LS
Visiting Professor: Cornell University (USA)
Dartmouth College (USA)
University of Illinois Urbana-Champaign (USAUniversity of Paris (France)
University of Trier (Germany)
John G. Sessions
Located in the south west of England
Population approximately 90000 90 minute train journey to
London; 15 minutes from Bristol
The City of Bath
The University of Bath
Sales and Purchase Taxes: Who Bears the Burden?
John G. SessionsUniversity of Bath and IZA
8
Hanoi University
3 October 2014
1. Introduction
Imagine that a government wishes to raise some tax revenue
Two schemes are being considered:
(i) Sales Tax;
(ii) Purchase Tax
1. Introduction
Sales Tax - £t imposed on seller of the good
Seller responsible for forwarding tax to government
Purchase Tax - £t imposed on buyer of the good
Buyer responsible for forwarding tax to government
1. Introduction
Distinguish between:
(i) Ad Valorem tax;
and
(ii) Unit tax
1. Introduction
Ad Valorem tax is imposed on value of good sold / purchased
e.g. UK VAT 17.5 %
Unit tax is imposed on quantity of good sold / purchased
Consider, for simplicity the latter
1. Introduction
Which scheme would you, as a consumer, prefer?
To understand this, we need to examine how markets work
i.e. we need to understand demand and supply
2. Markets
Definition: A market is a set of arrangements by which buyers and sellers are in contact to exchange goods or services
To understand how markets work, we therefore need to examine the behaviour of buyers and sellers
Otherwise known as ‘Demand’ and ‘Supply’
2. Markets
Demand: Quantity of a good buyers wish to purchase at every conceivable price. Thus, demand is not a particular quantity
Supply: Quantity of a good sellers wish to sell at every conceivable price. Thus, supply is not a particular quantity
N.B. distinction between demand (supply) and quantity demanded (supplied)
2. Markets
Demand / Supply denotes schedule of demands / supplies at each and every conceivable price
Quantity demanded / quantity supplied denotes a particular demand / supply at a particular price
Hypothesis - at ‘high’ prices we have qd < qs and at low prices the converse. Moreover, at some intermediate ‘equilibrium’ price, p*, the market clears
2. Markets
We define the equilibrium price p* as the price which clears the market
Thus: p > p* => excess supply p < p* => excess demand
And, in a free market, the actions of buyers and sellers move p towards p*
p
q 0
Figure 1: Market Equilibrium
Demand
Supply
q*
p*
p
q 0
p1
Excess Supply
Demand
Supply
qd(p1) q* qs(p1)
p*
Figure 2: Price Floor
p
q 0
p1
Excess Demand Demand
Supply
qs(p1) q* qd(p1)
p*
Figure 3: Price Ceiling
p
q 0
Supply
Demand
p*
pf
q1 q*
pc
Figure 4: ‘Near Side’ is Satisfied
3. Demand
The demand curve shows the relationship between price and quantity demanded (qd) ceteris paribus
That is:
(i) qd at particular price per unit;
(ii) (maximum) price per unit consumers willing to pay for a particular quantity
3. Demand
Formally
qd = qd(p)
Quantity demanded depends upon price
‘Normal’ Demand Function
q
p 0
qd
Figure 5: Normal Demand Function; qd = qd(p)
q
p 0
5
10
… quantity demanded at a particular price
Figure 5: Normal Demand Function; qd = qd(p)
qd
3. Demand
We can equivalently think of price depending upon the quantity consumed
pd = pd(q)
‘Inverse’ Demand Function
p
q 0
pd
Figure 6: Inverse Demand Function; pd = pd(q)
p
q 0
5
10
… buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit)
Figure 6: Inverse Demand Function; pd = pd(q)
3. Demand
We usually (i.e. normally) write the demand function in its normal form vis:
qd = qd(p)
But …
3. Demand
… we tend to draw the funtion in its inverse form:
pd = pd(q)
Why? …
3. Demand Inconsistency dates back over 100 years to the
printing of the first Economic textbook …
Alfred Marshall Principles of Economics (1895)
Printing error!
No real problem …
p
q 0
5
10
… buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit)
Figure 6: Inverse Demand Function; pd = pd(q)
p
q 0
5
10
… quantity demanded at a particular price
Figure 6: Normal Demand Function; qd = qd(p)
3. Demand But be aware …
Can cause undue algebraic problems!
Be aware … can cause undue algebraic problems!
Consider linear demand and supply functions …
3. Demand Normal (Linear) Demand Function:
Inverse (Linear) Demand Function:
q
p 0
Figure 7: Normal (Linear) Demand Function
p
q 0
Figure 8: Inverse (Linear) Demand Function
3. Demand
Usually, we presume that qd depends negatively on (own) price, but this is not always the case (Giffen goods)
Note: ‘Movements Along’: Arise as a result of changes in own price.
‘Shifts An’: Arise when anything else changes.
Consider the latter
3. Demand
What ‘other things’ might bring about a shift in the demand curve
To answer that question, we need to look ‘behind the demand curve’ and drop our assumption of ceteris paribus – i.e. that other things remain equal.
3. Demand Four factors that might not remain equal:
(1) Price of Related Goods
(2) Consumer Incomes
(3) Tastes
(4) Tax
3. Demand
Tax
Consider unit purchase tax
Consumer liable for £t per unit purchased
Thus, imposition of tax will reduce consumer’s reservation price for the good
p
0 q
pd
Figure 9: (Unit) Purchase Tax
p
0 q
tax
pd
ptd
Figure 9: (Unit) Purchase Tax
p
0 10 q
pd
ptd
Figure 9: (Unit) Purchase Tax
5
3
t = £2
4. Supply
The Supply Curve Shows the relationship between price and quantity supplied ceteris paribus
That is:
qs at particular price per unit
(minimum) price per unit suppliers willing to accept for particular quantity.
p
q 0
Figure 8: (Inverse) Supply Function ; ps = ps(q)
p
q 0
5
10
… quantity supplied at a particular price
Figure 10: (Inverse) Supply Function ; ps = ps(q)
p
q 0
5
10
… seller’s reservation price (i.e. minimum price seller wiling to accept per unit)
Figure 10: (Inverse) Supply Function ; ps = ps(q)
4. Supply
Behind the supply curve (ceteris paribus)
Four factors:
(1) Technology;
(2) Input Costs;
(3) Government Regulation;
(4) Tax.
4. Supply
Tax
Consider unit sales tax
Seller liable for £t per unit purchased
Thus, imposition of tax will increase seller’s reservation price for the good
p
0 q
Figure 11: (Unit) Sales Tax
p
0 q
tax
Figure 11: (Unit) Sales Tax
p
0 q
Figure 11: (Unit) Sales Tax
t = £2 11
9
10
5. Comparison
How do the two types of tax impact upon buyers and sellers?
Assume first a sales tax – i.e. a tax is imposed upon sellers per unit sold
How does this affect market equilibrium?
p
0 q
Figure 12: (Unit) Sales Tax
p
0 q
t
Figure 12: (Unit) Sales Tax
5. Comparison
Thus, a unit sales tax:
(i) Reduces the quantity traded;
(ii) Raises the equilibrium price
5. Comparison
Now, consider a unit purchase tax …
p
0 q
Figure 13: (Unit) Purchase Tax
p
0 q
Figure 13: (Unit) Purchase Tax
5. Comparison
Thus, a unit purchase tax:
(i) Reduces the quantity traded
(ii) Reduces the equilibrium price
5. Comparison
So, which alternative, as a buyer, would you prefer?
Must consider gross and net price
Unit tax drives a wedge between price paid and received
5. Comparison
Unit Sales Tax …
Seller is responsible for paying the tax
Net price seller receives is equilibrium price less tax
5. Comparison
Unit Sales Tax …
Seller is responsible for paying the tax
Net price seller receives is equilibrium price less tax
p
0 q
t
Figure 14: (Unit) Sales Tax
p
0 q
t
Buyer Pays
Seller Receives
Figure 14: (Unit) Sales Tax
6. Comparison
Unit Purchase Tax
Buyers is responsible for tax
Net price buyer pays is equilibrium price plus tax
p
0 q
Figure 15: (Unit) Purchase Tax
p
0 q
t
Figure 15: (Unit) Purchase Tax
p
0 q
t
Buyer Pays
Seller Receives
Figure 15: (Unit) Purchase Tax
5. Comparison
It can be shown that the burden of the tax does not depend upon whom it is imposed
The buyer and seller will share the burden depending upon the slopes of their demand and supply curves
These slopes affect the ability of buyers and seller to ‘pass on’ the burden of the tax to one another
p
0 q
Figure 16: (Unit) Sales Tax
p
0 q
t
Figure 16: (Unit) Sales Tax
p
0 q
t
Figure 16: (Unit) Sales Tax
Buyer Pays
Seller Receives
p
0 q
t
Figure 16: (Unit) Sales Tax
A
B
Buyer Pays
Seller Receives
p
0 q
t
A
B
Buyer’s Burden
Seller’s Burden
Figure 16: (Unit) Sales Tax
Buyer Pays
Seller Receives
p
0 q
Figure 15: (Unit) Purchase Tax
p
0 q
t
Figure 17: (Unit) Purchase Tax
p
0 q
t
Figure 17: (Unit) Purchase Tax
Buyer Pays
Seller Receives
p
0 q
t
C
D
Figure 17: (Unit) Purchase Tax
Buyer Pays
Seller Receives
p
0 q
t
C
D
Buyer’s Burden
Seller’s Burden
Figure 17: (Unit) Purchase Tax
5. Comparison
Thus: A + B = t = C + D
A = Buyer’s Burden = C
B = Seller’s Burden = D
The relative tax burden does not depend upon whom the tax is imposed
The buyer and seller will share the burden depending upon the slopes of their demand and supply curves
5. Comparison
Try to prove this using the following linear (normal) demand and supply equations:
Solve for the pre- and post-tax equilibria under both a sales and purchase tax and show that the relative burdens are the same
5. Comparison
It can be shown that …
… under both a unit sales tax and a unit purchase tax
5. Comparison
It can be shown, for example, that a seller is able to pass on more of the burden of a sales tax the steeper (i.e. less elastic) is the buyer’s demand curve …
p
0 q
t
Figure 18: (Unit) Sales Tax
A
B
A = Buyer’s Burden
B = Seller’s Burden
p
0 q
t
A
B
A1
B1
A = Buyer’s Burden
B = Seller’s Burden
Figure 18: (Unit) Sales Tax
5. Comparison
In the limit, if the demand curve is vertical (i.e. perfectly inelastic) then the seller is able to pass on all of the burden of a sales tax to the buyer …
p
0 q
t
A
B
A = Buyer’s Burden
B = Sellers Burden
A2
Figure 19: (Unit) SalesTax
5. Comparison
Note, vertical demand curve implies b = 0 such that:
Buyer (Seller) bears all (none) of the burden
6. Conclusion
The relative burden a unit tax is determined by the relative slopes of the demand and supply curves
These slopes determine the extent to which buyers and sellers can ‘pass on’ the burden of the tax to one another
Who is legally liable for the tax is not important
Solve for the pre- and post-tax equilibria under both a sales and purchase tax and show that the relative burdens are the same
7. Measuring Welfare
Demand and supply curves – reservation price schedules of buyers and sellers
That is, the maximum (minimum) price buyers (sellers) are prepared to pay (accept)
If we know the prices that buyers (sellers) actually pay (receive), then we can derive a measure of aggregate surplus and, thus, social welfare
p
q
Figure 16: Consumer Surplus (CS)
pd
0 1 2 3 4 q* = 5
p* = 2
10
8
6
4
p
q
Figure 16: Consumer Surplus (CS)
pd
0 1 2 3 4 q* = 5
p* = 2
10
8
6
4
TWP = 10 + 8 + 6 + 4 + 2 = 30p*q* = 20CS = 10
p
q 0
Figure 16: Consumer Surplus (CS)
Demand
q*
p*
Expenditure =p*q*
CS
p
q 0
Figure 17: Producer Surplus (PS)
Supply
q*
p*
PS
Revenue = p*q*
q*
p*
p
q 0
Figure 18: Social Welfare (W)
Demand
Supply
q*
p*
PS
CS
W = CS + PS
p
0 q
t
CS
PS
Figure 19: Social Welfare and Tax
Buyer Pays
Seller Receives
p
0 q
t
CS
PS
T = tq
Figure 19: Social Welfare and Tax
p
0 q
t
CS
PS
DWLT
Figure 19: Social Welfare and Tax
8. Final Comments
The relative burden of a unit tax is determined by the relative slopes of the demand and supply curves
Who is legally liable for the tax does not affect the relative burden
But, both sales and purchase unit taxes lead to the same deadweight loss in social welfare.
Solve for the pre- and post-tax equilibria under both a sales and purchase tax and show that the relative burdens are the same
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