BSc Southampton, MSc (LSE), PhD (LSE)

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


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)


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)


p

q 0

5

10

… quantity demanded at a particular price


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


p

0 10 q

pd

ptd


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


p

q 0

5

10

… seller’s reservation price (i.e. minimum price seller wiling to accept per unit)


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


p

0 q


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


p

0 q

t


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


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

p

0 q

t


p

0 q

t

Buyer Pays

Seller Receives


6. Comparison

Unit Purchase Tax

Buyers is responsible for tax

Net price buyer pays is equilibrium price plus tax

p

0 q


p

0 q

t


p

0 q

t

Buyer Pays

Seller Receives


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


p

0 q

t


p

0 q

t


Buyer Pays

Seller Receives

p

0 q

t


A

B

Buyer Pays

Seller Receives

p

0 q

t

A

B

Buyer’s Burden

Seller’s Burden


Buyer Pays

Seller Receives

p

0 q


p

0 q

t


p

0 q

t


Buyer Pays

Seller Receives

p

0 q

t

C

D


Buyer Pays

Seller Receives

p

0 q

t

C

D

Buyer’s Burden

Seller’s Burden


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


A

B

A = Buyer’s Burden

B = Seller’s Burden

p

0 q

t

A

B

A1

B1


B = Seller’s Burden


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


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


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


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


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


p

0 q

t

CS

PS

DWLT


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.


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p

0q

t

BSc Southampton, MSc (LSE), PhD (LSE)

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