1. © 2010 W. W. Norton & Company, Inc. 16 Equilibrium

2. © 2010 W. W. Norton & Company, Inc. 2 Market Equilibrium u A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.

3. © 2010 W. W. Norton & Company, Inc. 3 Market Equilibrium p D(p) q=D(p) Market demand

4. © 2010 W. W. Norton & Company, Inc. 4 Market Equilibrium p S(p) Market supply q=S(p)

5. © 2010 W. W. Norton & Company, Inc. 5 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p)

6. © 2010 W. W. Norton & Company, Inc. 6 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q*

7. © 2010 W. W. Norton & Company, Inc. 7 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q* D(p*) = S(p*); the market is in equilibrium.

8. © 2010 W. W. Norton & Company, Inc. 8 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’)

9. © 2010 W. W. Norton & Company, Inc. 9 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’) Market price must fall towards p*.

10. © 2010 W. W. Norton & Company, Inc. 10 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”)

11. © 2010 W. W. Norton & Company, Inc. 11 Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”) Market price must rise towards p*.

12. © 2010 W. W. Norton & Company, Inc. 12 Market Equilibrium u An example of calculating a market equilibrium when the market demand and supply curves are linear.

13. © 2010 W. W. Norton & Company, Inc. 13 Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp p* q*

14. © 2010 W. W. Norton & Company, Inc. 14 Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp p* q* What are the values of p* and q*?

15. © 2010 W. W. Norton & Company, Inc. 15 Market Equilibrium At the equilibrium price p*, D(p*) = S(p*).

16. © 2010 W. W. Norton & Company, Inc. 16 Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is,

17. © 2010 W. W. Norton & Company, Inc. 17 Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives

18. © 2010 W. W. Norton & Company, Inc. 18 Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives and

19. © 2010 W. W. Norton & Company, Inc. 19 Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp

20. © 2010 W. W. Norton & Company, Inc. 20 Market Equilibrium u Can we calculate the market equilibrium using the inverse market demand and supply curves?

21. © 2010 W. W. Norton & Company, Inc. 21 Market Equilibrium u Can we calculate the market equilibrium using the inverse market demand and supply curves? u Yes, it is the same calculation.

22. © 2010 W. W. Norton & Company, Inc. 22 Market Equilibrium the equation of the inverse market demand curve. And the equation of the inverse market supply curve.

23. © 2010 W. W. Norton & Company, Inc. 23 Market Equilibrium q D -1 (q), S -1 (q) D -1 (q) = (a-q)/b Market inverse demand Market inverse supply S -1 (q) = (-c+q)/d p* q*

24. © 2010 W. W. Norton & Company, Inc. 24 Market Equilibrium q D -1 (q), S -1 (q) D -1 (q) = (a-q)/b Market demand S -1 (q) = (-c+q)/d p* q* At equilibrium, D -1 (q*) = S -1 (q*). Market inverse supply

25. © 2010 W. W. Norton & Company, Inc. 25 Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*).

26. © 2010 W. W. Norton & Company, Inc. 26 Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*). That is,

27. © 2010 W. W. Norton & Company, Inc. 27 Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*). That is, which gives

28. © 2010 W. W. Norton & Company, Inc. 28 Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*). That is, which gives and

29. © 2010 W. W. Norton & Company, Inc. 29 Market Equilibrium q D -1 (q), S -1 (q) D -1 (q) = (a-q)/b Market demand Market supply S -1 (q) = (-c+q)/d

30. © 2010 W. W. Norton & Company, Inc. 30 Market Equilibrium u Two special cases: –quantity supplied is fixed, independent of the market price, and –quantity supplied is extremely sensitive to the market price.

31. © 2010 W. W. Norton & Company, Inc. 31 Market Equilibrium Market quantity supplied is fixed, independent of price. p qq*

32. © 2010 W. W. Norton & Company, Inc. 32 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p qq* = c Market quantity supplied is fixed, independent of price.

33. © 2010 W. W. Norton & Company, Inc. 33 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p qq* = c D -1 (q) = (a-q)/b Market demand Market quantity supplied is fixed, independent of price.

34. © 2010 W. W. Norton & Company, Inc. 34 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p q p* D -1 (q) = (a-q)/b Market demand q* = c Market quantity supplied is fixed, independent of price.

35. © 2010 W. W. Norton & Company, Inc. 35 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p q p* = (a-c)/b D -1 (q) = (a-q)/b Market demand q* = c p* = D -1 (q*); that is, p * = (a-c)/b. Market quantity supplied is fixed, independent of price.

36. © 2010 W. W. Norton & Company, Inc. 36 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p q D -1 (q) = (a-q)/b Market demand q* = c p* = D -1 (q*); that is, p * = (a-c)/b. p* = (a-c)/b Market quantity supplied is fixed, independent of price.

37. © 2010 W. W. Norton & Company, Inc. 37 Market Equilibrium S(p) = c+dp, so d=0 and S(p)  c. p q D -1 (q) = (a-q)/b Market demand q* = c p* = D -1 (q*); that is, p * = (a-c)/b. with d = 0 give p* = (a-c)/b Market quantity supplied is fixed, independent of price.

38. © 2010 W. W. Norton & Company, Inc. 38 Market Equilibrium u Two special cases are –when quantity supplied is fixed, independent of the market price, and –when quantity supplied is extremely sensitive to the market price.

39. © 2010 W. W. Norton & Company, Inc. 39 Market Equilibrium Market quantity supplied is extremely sensitive to price. p q

40. © 2010 W. W. Norton & Company, Inc. 40 Market Equilibrium Market quantity supplied is extremely sensitive to price. S -1 (q) = p*. p q p*

41. © 2010 W. W. Norton & Company, Inc. 41 Market Equilibrium Market quantity supplied is extremely sensitive to price. S -1 (q) = p*. p q p* D -1 (q) = (a-q)/b Market demand

42. © 2010 W. W. Norton & Company, Inc. 42 Market Equilibrium Market quantity supplied is extremely sensitive to price. S -1 (q) = p*. p q p* D -1 (q) = (a-q)/b Market demand q*

43. © 2010 W. W. Norton & Company, Inc. 43 Market Equilibrium Market quantity supplied is extremely sensitive to price. S -1 (q) = p*. p q p* D -1 (q) = (a-q)/b Market demand q* = a-bp* p* = D -1 (q*) = (a-q*)/b so q* = a-bp*

44. © 2010 W. W. Norton & Company, Inc. 44 Quantity Taxes u A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded. u If the tax is levied on sellers then it is an excise tax. u If the tax is levied on buyers then it is a sales tax.

45. © 2010 W. W. Norton & Company, Inc. 45 Quantity Taxes u What is the effect of a quantity tax on a market’s equilibrium? u How are prices affected? u How is the quantity traded affected? u Who pays the tax? u How are gains-to-trade altered?

46. © 2010 W. W. Norton & Company, Inc. 46 Quantity Taxes u A tax rate t makes the price paid by buyers, p b, higher by t from the price received by sellers, p s.

47. © 2010 W. W. Norton & Company, Inc. 47 Quantity Taxes u Even with a tax the market must clear. u I.e. quantity demanded by buyers at price p b must equal quantity supplied by sellers at price p s.

48. © 2010 W. W. Norton & Company, Inc. 48 Quantity Taxes and describe the market’s equilibrium. Notice these conditions apply no matter if the tax is levied on sellers or on buyers.

49. © 2010 W. W. Norton & Company, Inc. 49 Quantity Taxes and describe the market’s equilibrium. Notice that these two conditions apply no matter if the tax is levied on sellers or on buyers. Hence, a sales tax rate $t has the same effect as an excise tax rate $t.

50. © 2010 W. W. Norton & Company, Inc. 50 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax

51. © 2010 W. W. Norton & Company, Inc. 51 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* $t An excise tax raises the market supply curve by $t

52. © 2010 W. W. Norton & Company, Inc. 52 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An excise tax raises the market supply curve by $t, raises the buyers’ price and lowers the quantity traded. $t pbpb qtqt

53. © 2010 W. W. Norton & Company, Inc. 53 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An excise tax raises the market supply curve by $t, raises the buyers’ price and lowers the quantity traded. $t pbpb qtqt And sellers receive only p s = p b - t. psps

54. © 2010 W. W. Norton & Company, Inc. 54 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax

55. © 2010 W. W. Norton & Company, Inc. 55 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t $t

56. © 2010 W. W. Norton & Company, Inc. 56 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. $t qtqt psps

57. © 2010 W. W. Norton & Company, Inc. 57 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. $t pbpb pbpb qtqt pbpb And buyers pay p b = p s + t. psps

58. © 2010 W. W. Norton & Company, Inc. 58 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* A sales tax levied at rate $t has the same effects on the market’s equilibrium as does an excise tax levied at rate $t. $t pbpb pbpb qtqt pbpb psps

59. © 2010 W. W. Norton & Company, Inc. 59 Quantity Taxes & Market Equilibrium u Who pays the tax of $t per unit traded? u The division of the $t between buyers and sellers is the incidence of the tax.

60. © 2010 W. W. Norton & Company, Inc. 60 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps

61. © 2010 W. W. Norton & Company, Inc. 61 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers

62. © 2010 W. W. Norton & Company, Inc. 62 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by sellers

63. © 2010 W. W. Norton & Company, Inc. 63 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers

64. © 2010 W. W. Norton & Company, Inc. 64 Quantity Taxes & Market Equilibrium u E.g. suppose the market demand and supply curves are linear.

65. © 2010 W. W. Norton & Company, Inc. 65 Quantity Taxes & Market Equilibrium and

66. © 2010 W. W. Norton & Company, Inc. 66 Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and

67. © 2010 W. W. Norton & Company, Inc. 67 Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and Substituting for p b gives

68. © 2010 W. W. Norton & Company, Inc. 68 Quantity Taxes & Market Equilibrium and give The quantity traded at equilibrium is

69. © 2010 W. W. Norton & Company, Inc. 69 Quantity Taxes & Market Equilibrium As t  0, p s and p b  the equilibrium price if there is no tax (t = 0) and q t the quantity traded at equilibrium when there is no tax. 

70. © 2010 W. W. Norton & Company, Inc. 70 Quantity Taxes & Market Equilibrium As t increases, p s falls, p b rises, andq t falls.

71. © 2010 W. W. Norton & Company, Inc. 71 Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is

72. © 2010 W. W. Norton & Company, Inc. 72 Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is The tax paid per unit by the seller is

73. © 2010 W. W. Norton & Company, Inc. 73 Quantity Taxes & Market Equilibrium The total tax paid (by buyers and sellers combined) is

74. © 2010 W. W. Norton & Company, Inc. 74 Tax Incidence and Own-Price Elasticities u The incidence of a quantity tax depends upon the own-price elasticities of demand and supply.

75. © 2010 W. W. Norton & Company, Inc. 75 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps

76. © 2010 W. W. Norton & Company, Inc. 76 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Change to buyers’ price is p b - p*. Change to quantity demanded is  q. qq

77. © 2010 W. W. Norton & Company, Inc. 77 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately

78. © 2010 W. W. Norton & Company, Inc. 78 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately

79. © 2010 W. W. Norton & Company, Inc. 79 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps

80. © 2010 W. W. Norton & Company, Inc. 80 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Change to sellers’ price is p s - p*. Change to quantity demanded is  q. qq

81. © 2010 W. W. Norton & Company, Inc. 81 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately

82. © 2010 W. W. Norton & Company, Inc. 82 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately

83. © 2010 W. W. Norton & Company, Inc. 83 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers

84. © 2010 W. W. Norton & Company, Inc. 84 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers Tax incidence =

85. © 2010 W. W. Norton & Company, Inc. 85 Tax Incidence and Own-Price Elasticities Tax incidence =

86. © 2010 W. W. Norton & Company, Inc. 86 Tax Incidence and Own-Price Elasticities Tax incidence = So

87. © 2010 W. W. Norton & Company, Inc. 87 Tax Incidence and Own-Price Elasticities Tax incidence is The fraction of a $t quantity tax paid by buyers rises as supply becomes more own-price elastic or as demand becomes less own-price elastic.

88. © 2010 W. W. Norton & Company, Inc. 88 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps As market demand becomes less own- price elastic, tax incidence shifts more to the buyers.

89. © 2010 W. W. Norton & Company, Inc. 89 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps As market demand becomes less own- price elastic, tax incidence shifts more to the buyers.

90. © 2010 W. W. Norton & Company, Inc. 90 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p s = p* $t pbpb q t = q* As market demand becomes less own- price elastic, tax incidence shifts more to the buyers.

91. © 2010 W. W. Norton & Company, Inc. 91 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p s = p* $t pbpb q t = q* As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. When  D = 0, buyers pay the entire tax, even though it is levied on the sellers.

92. © 2010 W. W. Norton & Company, Inc. 92 Tax Incidence and Own-Price Elasticities Tax incidence is Similarly, the fraction of a $t quantity tax paid by sellers rises as supply becomes less own-price elastic or as demand becomes more own-price elastic.

93. © 2010 W. W. Norton & Company, Inc. 93 Deadweight Loss and Own-Price Elasticities u A quantity tax imposed on a competitive market reduces the quantity traded and so reduces gains-to-trade (i.e. the sum of Consumers’ and Producers’ Surpluses). u The lost total surplus is the tax’s deadweight loss, or excess burden.

94. © 2010 W. W. Norton & Company, Inc. 94 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax

95. © 2010 W. W. Norton & Company, Inc. 95 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS

96. © 2010 W. W. Norton & Company, Inc. 96 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax PS

97. © 2010 W. W. Norton & Company, Inc. 97 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS

98. © 2010 W. W. Norton & Company, Inc. 98 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS

99. © 2010 W. W. Norton & Company, Inc. 99 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS

100. © 2010 W. W. Norton & Company, Inc. 100 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

101. © 2010 W. W. Norton & Company, Inc. 101 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

102. © 2010 W. W. Norton & Company, Inc. 102 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

103. © 2010 W. W. Norton & Company, Inc. 103 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government, and lowers total surplus. Tax

104. © 2010 W. W. Norton & Company, Inc. 104 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps CS PS Tax Deadweight loss

105. © 2010 W. W. Norton & Company, Inc. 105 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss

106. © 2010 W. W. Norton & Company, Inc. 106 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss falls as market demand becomes less own- price elastic.

107. © 2010 W. W. Norton & Company, Inc. 107 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss falls as market demand becomes less own- price elastic.

108. © 2010 W. W. Norton & Company, Inc. 108 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p s = p* $t pbpb q t = q* Deadweight loss falls as market demand becomes less own- price elastic. When  D = 0, the tax causes no deadweight loss.

109. © 2010 W. W. Norton & Company, Inc. 109 Deadweight Loss and Own-Price Elasticities u Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own- price elastic.  If either  D = 0 or  S = 0 then the deadweight loss is zero.