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Introductory Microeconomics ES10001
Topic 1: Introduction to Markets
Sales and Purchase Tax
Sales and Purchase Taxes: Who Bears the Burden?
2
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 the seller of the good
• Seller responsible for forwarding tax to government
• Purchase Tax - £t imposed on the 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 the 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
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
1. Introduction
Consider unit purchase tax
Consumer liable for £t per unit purchased
Thus, imposition of tax will reduce consumer’s reservation price for the good
2. Demand
p
0 q
pd
Figure 1: (Unit) Purchase Tax
p
0 q
tax
pd
ptd
Figure 1: (Unit) Purchase Tax
p
0 10 q
pd
ptd
Figure 1: (Unit) Purchase Tax
5
3
t = £2
Consider unit sales tax
Seller liable for £t per unit purchased
Thus, imposition of tax will increase seller’s reservation price for the good
3. Supply
p
0 q
Figure 2: (Unit) Sales Tax
p
0 q
tax
Figure 9: (Unit) Sales Tax
p
0 q
Figure 9: (Unit) Sales Tax
t = £2 11
9
10
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?
4. Comparison
p
0 q
Figure 10: (Unit) Sales Tax
p
0 q
t
Figure 10: (Unit) Sales Tax
Thus, a unit sales tax:
(i) Reduces the quantity traded;
(ii) Raises the equilibrium price
4. Comparison
Now, consider a unit purchase tax …
4. Comparison
p
0 q
Figure 11: (Unit) Purchase Tax
p
0 q
Figure 11: (Unit) Purchase Tax
Thus, a unit purchase tax:
(i) Reduces the quantity traded
(ii) Reduces the equilibrium price
4. 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
4. Comparison
Unit Sales Tax …
Seller is responsible for paying the tax
Net price seller receives is equilibrium price less tax
4. Comparison
p
0 q
t
Figure 12: (Unit) Sales Tax
p
0 q
t
Buyer Pays
Seller Receives
Figure 12: (Unit) Sales Tax
Unit Purchase Tax
Buyers is responsible for tax
Net price buyer pays is equilibrium price plus tax
4. Comparison
p
0 q
Figure 13: (Unit) Purchase Tax
p
0 q
t
Figure 13: (Unit) Purchase Tax
p
0 q
t
Buyer Pays
Seller Receives
Figure 13: (Unit) Purchase Tax
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
4. Comparison
p
0 q
Figure 14: (Unit) Sales Tax
p
0 q
t
Figure 14: (Unit) Sales Tax
p
0 q
t
Figure 14: (Unit) Sales Tax
Buyer Pays
Seller Receives
p
0 q
t
Figure 14: (Unit) Sales Tax
A
B
Buyer Pays
Seller Receives
p
0 q
t
A
B
Buyer’s Burden
Seller’s Burden
Figure 14: (Unit) Sales Tax
Buyer Pays
Seller Receives
p
0 q
t
Figure 14: (Unit) Purchase Tax
p
0 q
t
Figure 14: (Unit) Purchase Tax
Buyer Pays
Seller Receives
p
0 q
t
C
D
Figure 14: (Unit) Purchase Tax
Buyer Pays
Seller Receives
p
0 q
t
C
D
Buyer’s Burden
Figure 14: (Unit) Purchase Tax
Seller’s Burden
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
4. 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
1. Comparison
It can be shown that …
… under both a unit sales tax and a unit purchase tax
4. 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 …
4. Comparison
p
0 q
t
Figure 15: (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 15: (Unit) Sales Tax
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 …
4. Comparison
p
0 q
t
A
B
A = Buyer’s Burden
B = Sellers Burden
A2
Figure 15: (Unit) SalesTax
Note, vertical demand curve implies b = 0 such that:
Buyer (Seller) bears all (none) of the burden
4. Comparison
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
4. Conclusion
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
5. 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* = 10CS = 20
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
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.
6. Final Comments
p
0 q
p
0 q
t
p
0 q
t
p
0 q
t
p
0 q
t
p
0 q
t
p
0 q
p
0 q
t
