1. Introductory Microeconomics ES10001 Topic 1: Introduction to Markets Sales and Purchase Tax

2. Sales and Purchase Taxes: Who Bears the Burden ? 2

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

4. 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

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

6. 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

7.  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

8. 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

9. p 0 q Figure 1: (Unit) Purchase Tax

10. p 0 q tax Figure 1: (Unit) Purchase Tax

11. p 0 10 q Figure 1: (Unit) Purchase Tax 5 3 t = £2

12. 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

13. p 0 q Figure 2: (Unit) Sales Tax

14. p 0 q tax Figure 9: (Unit) Sales Tax

15. p 0 q t = £2 11 9 10

16. 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

17. p 0 q Figure 10: (Unit) Sales Tax

18. p 0 q t

19. Thus, a unit sales tax: (i) Reduces the quantity traded; (ii) Raises the equilibrium price 4. Comparison

20. Now, consider a unit purchase tax … 4. Comparison

21. p 0 q Figure 11: (Unit) Purchase Tax

22. p 0 q

23. Thus, a unit purchase tax: (i) Reduces the quantity traded (ii) Reduces the equilibrium price 4. Comparison

24. 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

25. Unit Sales Tax … Seller is responsible for paying the tax Net price seller receives is equilibrium price less tax 4. Comparison

26. p 0 q t Figure 12: (Unit) Sales Tax

27. p 0 q t Buyer Pays Seller Receives Figure 12: (Unit) Sales Tax

28. Unit Purchase Tax Buyers is responsible for tax Net price buyer pays is equilibrium price plus tax 4. Comparison

29. p 0 q Figure 13: (Unit) Purchase Tax

30. p 0 q t

31. p 0 q t Buyer Pays Seller Receives Figure 13: (Unit) Purchase Tax

32. 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

33. p 0 q Figure 14: (Unit) Sales Tax

34. p 0 q t

35. p 0 q t Buyer Pays Seller Receives

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

37. p 0 q t A B Buyer’s Burden Seller’s Burden Figure 14: (Unit) Sales Tax Buyer Pays Seller Receives

38. p 0 q t Figure 14: (Unit) Purchase Tax

39. p 0 q t Buyer Pays Seller Receives

40. p 0 q t C D Figure 14: (Unit) Purchase Tax Buyer Pays Seller Receives

41. p 0 q t C D Buyer’s Burden Figure 14: (Unit) Purchase Tax Seller’s Burden

42. 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

43. 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

44. It can be shown that … … under both a unit sales tax and a unit purchase tax 4. Comparison

45. 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

46. p 0 q t Figure 15: (Unit) Sales Tax A B A = Buyer’s Burden B = Seller’s Burden

47. p 0 q t A B A 1 B1B1 A = Buyer’s Burden B = Seller’s Burden Figure 15: (Unit) Sales Tax

48. 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

49. p 0 q t A B A = Buyer’s Burden B = Sellers Burden A2A2 Figure 15: (Unit) SalesTax

50. Note, vertical demand curve implies b = 0 such that: Buyer (Seller) bears all (none) of the burden 4. Comparison

51. 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

52. 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

53. p q Figure 16: Consumer Surplus (CS) pdpd 0 1 2 3 4 q * = 5 p* = 2 10 8 6 4

54. p q Figure 16: Consumer Surplus (CS) pdpd 0 1 2 3 4 q * = 5 p* = 2 10 8 6 4 TWP = 10 + 8 + 6 + 4 + 2 = 30 p * q* = 10 CS = 20

55. p q 0 Figure 16: Consumer Surplus (CS) Demand q*q* p*p* Expenditure =p * q * CS

56. p q 0 Figure 17: Producer Surplus (PS) Supply q*q* p*p* PS Revenue = p * q * q*q* p *

57. p q 0 Figure 18: Social Welfare (W) Demand Supply q*q* p*p* PS CS W = CS + PS

58. p 0 q t CS PS Figure 19: Social Welfare and Tax Buyer Pays Seller Receives

59. p 0 q t CS PS T = tq Figure 19: Social Welfare and Tax

60. p 0 q t CS PS DWLT Figure 19: Social Welfare and Tax

61. 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

62. p 0 q

63. p 0 q t

64. p 0 q t

65. p 0 q t

66. p 0 q t

67. p 0 q t

68. p 0 q

69. p 0 q t