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 Figure 1: (Unit) Purchase Tax
p 0 q tax Figure 1: (Unit) Purchase Tax
p 0 10 q 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 t = £
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
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
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
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
p 0 q t 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 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 A 1 B1B1 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 A2A2 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) pdpd q * = 5 p* =
p q Figure 16: Consumer Surplus (CS) pdpd q * = 5 p* = TWP = = 30 p * q* = 10 CS = 20
p q 0 Figure 16: Consumer Surplus (CS) Demand q*q* p*p* Expenditure =p * q * CS
p q 0 Figure 17: Producer Surplus (PS) Supply q*q* p*p* PS Revenue = p * q * q*q* p *
p q 0 Figure 18: Social Welfare (W) Demand Supply q*q* p*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
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