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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
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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
3. Demand • Tax • Consider unit purchase tax • Consumer liable for £t per unit purchased • Thus, imposition of tax will reduceconsumer’s reservation price for the good
Figure 1: (Unit) Purchase Tax p tax q 0
Figure 1: (Unit) Purchase Tax p t = £2 5 3 q 0 10
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.
Figure 2: (Inverse) Supply Function ; ps = ps(q) p … quantity supplied at a particular price 5 q 0 10
Figure 2: (Inverse) Supply Function ; ps = ps(q) p … seller’s reservation price (i.e. minimum price seller wiling to accept per unit) 5 q 0 10
4.Supply • Tax • Consider unit sales tax • Seller liable for £t per unit purchased • Thus, imposition of tax will increaseseller’s reservation price for the good
Figure 4: (Unit)Sales Tax p tax q 0
Figure 4: (Unit)Sales Tax p t = £2 11 9 q 0 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?
Figure 5: (Unit)Sales Tax p t q 0
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 …
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
Figure 7: (Unit)Sales Tax p t q 0
Figure 7: (Unit)Sales Tax p Buyer Pays t Seller Receives q 0
6.Comparison • Unit Purchase Tax • Buyers is responsible for tax • Net price buyer pays is equilibrium price plus tax
Figure 15: (Unit) Purchase Tax p t q 0
Figure 7: (Unit) Purchase Tax p Buyer Pays t Seller Receives q 0
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
5.Comparison • Consider first a unit sales tax …
Figure 8: (Unit)Sales Tax p t q 0
Figure 8: (Unit)Sales Tax p Buyer Pays t Seller Receives q 0
Figure 8: (Unit)Sales Tax p Buyer Pays t A B Seller Receives q 0
Figure 8: (Unit)Sales Tax p Buyer’s Burden Buyer Pays t A B Seller’s Burden Seller Receives q 0
5.Comparison • And now a unit purchase tax …
Figure 9: (Unit) Purchase Tax p t q 0
Figure 9: (Unit) Purchase Tax p Buyer Pays t Seller Receives q 0
Figure 9: (Unit) Purchase Tax p Buyer Pays C D t Seller Receives q 0
Figure 9: (Unit) Purchase Tax p Buyer’s Burden C D t Seller’s Burden q 0
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 …
Figure 10: (Unit)Sales Tax p A = Buyer’s Burden B = Seller’s Burden t A B q 0
Figure 10: (Unit)Sales Tax p A= Buyer’s Burden B= Seller’s Burden t A1 A B1 B q 0
