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Sales and Purchase Taxes: Who Bears the Burden?. 1.Introduction. Imagine that a government wishes to raise some tax revenue Two schemes are being considered: (i) Sales Tax; (ii) Purchase Tax. 3 . Demand. Tax Consider unit purchase tax Consumer liable for £ t per unit purchased - PowerPoint PPT Presentation
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Sales and Purchase Taxes: Who Bears the Burden?
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1. Introduction
Imagine that a government wishes to raise some tax revenue
Two schemes are being considered:
(i) Sales Tax;
(ii) Purchase Tax
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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
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p
0 q
pd
Figure 1: (Unit) Purchase Tax
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p
0 q
tax
pd
ptd
Figure 1: (Unit) Purchase Tax
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p
0 10 q
pd
ptd
Figure 1: (Unit) Purchase Tax
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3
t = £2
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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.
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p
q 0
Figure 8: (Inverse) Supply Function ; ps = ps(q)
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p
q 0
5
10
… quantity supplied at a particular price
Figure 2: (Inverse) Supply Function ; ps = ps(q)
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p
q 0
5
10
… seller’s reservation price (i.e. minimum price seller wiling to accept per unit)
Figure 2: (Inverse) Supply Function ; ps = ps(q)
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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
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p
0 q
Figure 3: (Unit) Sales Tax
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p
0 q
tax
Figure 4: (Unit) Sales Tax
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p
0 q
Figure 4: (Unit) Sales Tax
t = £2 11
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10
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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?
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p
0 q
Figure 5: (Unit) Sales Tax
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p
0 q
t
Figure 5: (Unit) Sales Tax
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5. Comparison
Thus, a unit sales tax:
(i) Reduces the quantity traded;
(ii) Raises the equilibrium price
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5. Comparison
Now, consider a unit purchase tax …
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p
0 q
Figure 6: (Unit) Purchase Tax
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p
0 q
Figure 6: (Unit) Purchase Tax
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5. Comparison
Thus, a unit purchase tax:
(i) Reduces the quantity traded
(ii) Reduces the equilibrium price
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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
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5. Comparison
Unit Sales Tax …
Seller is responsible for paying the tax
Net price seller receives is equilibrium price less tax
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5. Comparison
Unit Sales Tax …
Seller is responsible for paying the tax
Net price seller receives is equilibrium price less tax
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p
0 q
t
Figure 7: (Unit) Sales Tax
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p
0 q
t
Buyer Pays
Seller Receives
Figure 7: (Unit) Sales Tax
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6. Comparison
Unit Purchase Tax
Buyers is responsible for tax
Net price buyer pays is equilibrium price plus tax
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p
0 q
Figure 15: (Unit) Purchase Tax
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p
0 q
t
Figure 15: (Unit) Purchase Tax
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p
0 q
t
Buyer Pays
Seller Receives
Figure 7: (Unit) Purchase Tax
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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
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5. Comparison
Consider first a unit sales tax …
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p
0 q
Figure 8: (Unit) Sales Tax
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p
0 q
t
Figure 8: (Unit) Sales Tax
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p
0 q
t
Figure 8: (Unit) Sales Tax
Buyer Pays
Seller Receives
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p
0 q
t
Figure 8: (Unit) Sales Tax
A
B
Buyer Pays
Seller Receives
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p
0 q
t
A
B
Buyer’s Burden
Seller’s Burden
Figure 8: (Unit) Sales Tax
Buyer Pays
Seller Receives
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5. Comparison
And now a unit purchase tax …
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p
0 q
Figure 9: (Unit) Purchase Tax
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p
0 q
t
Figure 9: (Unit) Purchase Tax
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p
0 q
t
Figure 9: (Unit) Purchase Tax
Buyer Pays
Seller Receives
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p
0 q
t
C
D
Figure 9: (Unit) Purchase Tax
Buyer Pays
Seller Receives
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p
0 q
t
C
D
Buyer’s Burden
Seller’s Burden
Figure 9: (Unit) Purchase Tax
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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
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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
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5. Comparison
It can be shown that …
… under both a unit sales tax and a unit purchase tax
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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 …
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p
0 q
t
Figure 10: (Unit) Sales Tax
A
B
A = Buyer’s Burden
B = Seller’s Burden
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p
0 q
t
A
B
A1
B1
A = Buyer’s Burden
B = Seller’s Burden
Figure 10: (Unit) Sales Tax
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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 …
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p
0 q
t
A
B
A = Buyer’s Burden
B = Sellers Burden
A2
Figure 10: (Unit) Sales Tax
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5. Comparison
Note, vertical demand curve implies b = 0 such that:
Buyer (Seller) bears all (none) of the burden
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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
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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
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p
q
Figure 11: Consumer Surplus (CS)
pd
0 1 2 3 4 q* = 5
p* = 2
10
8
6
4
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p
q
Figure 11: 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* = 10
CS = 20
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p
q 0
Figure 11: Consumer Surplus (CS)
Demand
q*
p*
Expenditure =p*q*
CS
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p
q 0
Figure 12: Producer Surplus (PS)
Supply
q*
p*
PS
Revenue = p*q*
q*
p*
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p
q 0
Figure 13: Social Welfare (W)
Demand
Supply
q*
p*
PS
CS
W = CS + PS
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p
0 q
t
CS
PS
Figure 14: Social Welfare and Tax
Buyer Pays
Seller Receives
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p
0 q
t
CS
PS
T = tq
Figure 14: Social Welfare and Tax
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p
0 q
t
CS
PS
DWLT
Figure 14: Social Welfare and Tax
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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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p
0q
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p
0q
t
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p
0q
t
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p
0q
t
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0q
t
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p
0q
t
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0q
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0q
t
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