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 (USA University of Paris (France) University of Trier (Germany) John G. Sessions

Located in the south west of England Population approximately 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. Sessions University 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 q d < q s 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 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*q* p*p*

p q 0 p1p1 Excess Supply Demand Supply q d (p 1 ) q * q s (p 1 ) p*p* Figure 2: Price Floor

p q 0 p1p1 Excess Demand Demand Supply q s (p 1 ) q * q d (p 1 ) p*p* Figure 3: Price Ceiling

p q 0 Supply Demand p*p* pf pf q 1 q * pcpc Figure 4: ‘Near Side’ is Satisfied

3.Demand The demand curve shows the relationship between price and quantity demanded (q d ) ceteris paribus That is: (i) q d at particular price per unit; (ii)(maximum) price per unit consumers willing to pay for a particular quantity

3.Demand Formally q d = q d (p) Quantity demanded depends upon price ‘Normal’ Demand Function

q p 0 Figure 5: Normal Demand Function; q d = q d (p)

q p … quantity demanded at a particular price Figure 5: Normal Demand Function; q d = q d (p)

3.Demand We can equivalently think of price depending upon the quantity consumed p d = p d (q) ‘Inverse’ Demand Function

p q 0 Figure 6: Inverse Demand Function; p d = p d (q)

p q … buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit) Figure 6: Inverse Demand Function; p d = p d (q)

3.Demand We usually (i.e. normally) write the demand function in its normal form vis: q d = q d (p) But …

3.Demand … we tend to draw the funtion in its inverse form: p d = p d (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 … buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit) Figure 6: Inverse Demand Function; p d = p d (q)

p q … quantity demanded at a particular price Figure 6: Normal Demand Function; q d = q d (p)

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 q d 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 Figure 9: (Unit) Purchase Tax

p 0 q tax Figure 9: (Unit) Purchase Tax

p 0 10 q Figure 9: (Unit) Purchase Tax 5 3 t = £2

4.Supply The Supply Curve Shows the relationship between price and quantity supplied ceteris paribus That is: q s at particular price per unit (minimum) price per unit suppliers willing to accept for particular quantity.

p q 0 Figure 8: (Inverse) Supply Function ; p s = p s (q)

p q … quantity supplied at a particular price Figure 10: (Inverse) Supply Function ; p s = p s (q)

p q … seller’s reservation price (i.e. minimum price seller wiling to accept per unit) Figure 10: (Inverse) Supply Function ; p s = p s (q)

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 Figure 11: (Unit) Sales Tax

p 0 q t = £

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 Figure 12: (Unit) Sales Tax

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 Figure 13: (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

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 Figure 14: (Unit) Sales Tax

p 0 q t Buyer Pays Seller Receives Figure 14: (Unit) Sales Tax

6.Comparison Unit Purchase Tax Buyers is responsible for tax Net price buyer pays is equilibrium price plus tax

p 0 q Figure 15: (Unit) Purchase Tax

p 0 q t

p 0 q t Buyer Pays Seller Receives Figure 15: (Unit) Purchase Tax

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 Figure 16: (Unit) Sales Tax

p 0 q t

p 0 q t Buyer Pays Seller Receives

p 0 q t Figure 16: (Unit) Sales Tax A B Buyer Pays Seller Receives

p 0 q t A B Buyer’s Burden Seller’s Burden Figure 16: (Unit) Sales Tax Buyer Pays Seller Receives

p 0 q Figure 15: (Unit) Purchase Tax

p 0 q t Figure 17: (Unit) Purchase Tax

p 0 q t Buyer Pays Seller Receives

p 0 q t C D Figure 17: (Unit) Purchase Tax Buyer Pays Seller Receives

p 0 q t C D Buyer’s Burden Seller’s Burden Figure 17: (Unit) Purchase Tax

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 Figure 18: (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 18: (Unit) Sales Tax

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 A = Buyer’s Burden B = Sellers Burden A2A2 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 Solve for the pre- and post-tax equilibria under both a sales and purchase tax and show that the relative burdens are the same

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) pdpd q * = 5 p* =

p q Figure 16: Consumer Surplus (CS) pdpd q * = 5 p* = TWP = = 30 p * q* = 20 CS = 10

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

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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