BSc Southampton, MSc (LSE), PhD (LSE)

1. John G. Sessions • 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)

2. The City of Bath • Located in the south west of England • Population approximately 90000 • 90 minute train journey to London; 15 minutes from Bristol

6. The University of Bath

8. Sales and Purchase Taxes: Who Bears the Burden? John G. Sessions University of Bath and IZA Hanoi University 3 October 2014

9. 1. Introduction • Imagine that a government wishes to raise some tax revenue • Two schemes are being considered: (i) Sales Tax; (ii) Purchase Tax

10. 1. Introduction • Sales Tax - £timposed 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

11. 1. Introduction • Distinguish between: (i) Ad Valorem tax; and (ii) Unit tax

12. 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

13. 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

14. 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’

15. 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)

16. 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 qd < qs and at low prices the converse. Moreover, at some intermediate ‘equilibrium’ price, p*, the market clears

17. 2. Markets • We define the equilibrium price p*as the price which clears the market • Thus: p> p*=> excess supply p < p*=> excess demand • And, in a free market, the actions of buyers and sellers move p towards p*

18. Figure 1: Market Equilibrium p Supply p* Demand q 0 q*

19. Figure 2: Price Floor p Supply Excess Supply p1 p* Demand q 0 qd(p1) q* qs(p1)

20. Figure 3: Price Ceiling p Supply p* p1 Excess Demand Demand q 0 qs(p1) q* qd(p1)

21. Figure 4: ‘Near Side’ is Satisfied p Supply pf p* pc Demand q 0 q1 q*

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

23. 3. Demand • Formally • qd = qd(p) • Quantity demanded depends upon price • ‘Normal’ Demand Function

24. Figure 5: Normal Demand Function; qd = qd(p) q p 0

25. Figure 5: Normal Demand Function; qd = qd(p) q … quantity demanded at a particular price 5 p 0 10

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

27. Figure 6: Inverse Demand Function; pd = pd(q) p q 0

28. Figure 6: Inverse Demand Function; pd = pd(q) p … buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit) 5 q 0 10

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

30. 3. Demand • … we tend to draw the funtion in its inverse form: • pd= pd(q) • Why? …

31. 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 …

32. Figure 6: Inverse Demand Function; pd = pd(q) p … buyer’s reservation price (i.e. maximum price buyer wiling to pay price per unit) 5 q 0 10

33. Figure 6: Normal Demand Function; qd = qd(p) p … quantity demanded at a particular price 5 q 0 10

34. 3. Demand • But be aware … • Can cause undue algebraic problems! • Be aware … can cause undue algebraic problems! • Consider linear demand and supply functions …

35. 3. Demand • Normal (Linear) Demand Function: • Inverse (Linear) Demand Function:

36. Figure 7: Normal (Linear) Demand Function q p 0

37. Figure 8: Inverse (Linear) Demand Function p q 0

38. 3. Demand • Usually, we presume that qd 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

39. 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.

40. 3. Demand • Four factors that might not remain equal: (1) Price of Related Goods (2) Consumer Incomes (3) Tastes (4) Tax

41. 3. Demand • Tax • Consider unit purchase tax • Consumer liable for £tper unit purchased • Thus, imposition of tax will reduceconsumer’s reservation price for the good

42. Figure 9: (Unit) Purchase Tax p q 0

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

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

45. 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.

46. Figure 8: (Inverse) Supply Function ; ps = ps(q) p q 0

47. Figure 10: (Inverse) Supply Function ; ps = ps(q) p … quantity supplied at a particular price 5 q 0 10

48. Figure 10: (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

49. 4. Supply Behind the supply curve(ceteris paribus) Four factors: (1)Technology; (2) Input Costs; (3) Government Regulation; (4) Tax.

50. 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