1. Chapter 16 Equilibrium

2. Market Equilibrium
A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.

3. Market Equilibrium Market demand Market supply p q=S(p) q=D(p)
D(p), S(p)

4. Market Equilibrium Market demand Market supply p q=S(p) p* q=D(p) q*
D(p), S(p)

5. Market Equilibrium Market demand Market supply p q=S(p)
D(p*) = S(p*): the market is in equilibrium. p*
q=D(p) q*
D(p), S(p)

6. Market Equilibrium Market demand Market supply p q=S(p)
D(p’) < S(p’): an excess of quantity supplied over quantity demanded. p’ p*
q=D(p)
D(p’)
S(p’)
D(p), S(p)

7. Market Equilibrium Market price will fall towards p*. Market demand
Market supply p
q=S(p)
D(p’) < S(p’): an excess of quantity supplied over quantity demanded. p’ p*
q=D(p)
D(p’)
S(p’)
D(p), S(p)
Market price will fall towards p*.

8. Market Equilibrium Market demand Market supply p q=S(p)
D(p”) > S(p”): an excess of quantity demanded over quantity supplied. p* p”
q=D(p)
S(p”)
D(p”)
D(p), S(p)

9. Market Equilibrium Market price will rise towards p*. Market demand
Market supply p
q=S(p)
D(p”) > S(p”): an excess of quantity demanded over quantity supplied. p* p”
q=D(p)
S(p”)
D(p”)
D(p), S(p)
Market price will rise towards p*.

10. Market Equilibrium
An example of calculating a market equilibrium when the market demand and supply curves are both linear.

11. Market Equilibrium Market demand Market supply p S(p) = c+dp p*
D(p) = a-bp q*
D(p), S(p)

12. Market Equilibrium What are the values of p* and q*? Market demand
Market supply p
S(p) = c+dp
What are the values of p* and q*? p*
D(p) = a-bp q*
D(p), S(p)

13. Market Equilibrium
At the equilibrium price p*, D(p*) = S(p*). That is,
which gives
and

14. Market Equilibrium p Market demand Market supply S(p) = c+dp
D(p) = a-bp
D(p), S(p)

15. Market Equilibrium
Can we calculate the market equilibrium using the inverse market demand and supply curves?
Yes, it is the same calculation.

16. Market Equilibrium
the equation of the inverse market demand curve. And
the equation of the inverse market supply curve.

17. Market Equilibrium Market inverse demand D-1(q), S-1(q)
Market inverse supply
S-1(q) = (-c+q)/d p*
D-1(q) = (a-q)/b q* q

18. Market Equilibrium At equilibrium, D-1(q*) = S-1(q*). Market demand
Market inverse supply
S-1(q) = (-c+q)/d
At equilibrium, D-1(q*) = S-1(q*). p*
D-1(q) = (a-q)/b q* q

19. Market Equilibrium and
At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is,
which gives
and

20. Market Equilibrium Market demand Market supply D-1(q), S-1(q)
S-1(q) = (-c+q)/d
D-1(q) = (a-q)/b q

21. Market Equilibrium Two special cases:
quantity supplied is fixed, independent of the market price, and
quantity supplied is extremely sensitive to the market price.

22. Market Equilibrium
Market quantity supplied is fixed, independent of price. p
S(p) = c+dp, so d=0
and S(p) º c.
q* = c q

23. Market Equilibrium Market demand
Market quantity supplied is fixed, independent of price. p
S(p) = c+dp, so d=0
and S(p) º c. p*
D-1(q) = (a-q)/b
q* = c q

24. Market Equilibrium Market demand
Market quantity supplied is fixed, independent of price. p
S(p) = c+dp, so d=0
and S(p) º c.
p* = (a-c)/b
p* = D-1(q*); that is, p* = (a-c)/b.
D-1(q) = (a-q)/b
q* = c q

25. Market Equilibrium with d = 0 give Market demand
Market quantity supplied is fixed, independent of price. p
S(p) = c+dp, so d=0
and S(p) º c.
p* = (a-c)/b
p* = D-1(q*); that is, p* = (a-c)/b.
D-1(q) = (a-q)/b
q* = c q
with d = 0 give

26. ü Market Equilibrium 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. ü

27. Market Equilibrium
Market quantity supplied is extremely sensitive to price. p
S-1(q) = p*. p* q

28. Market Equilibrium Market demand
Market quantity supplied is extremely sensitive to price. p
S-1(q) = p*. p*
D-1(q) = (a-q)/b q* q

29. Market Equilibrium Market demand
Market quantity supplied is extremely sensitive to price. p
S-1(q) = p*.
p* = D-1(q*) = (a-q*)/b so q* = a-bp* p*
D-1(q) = (a-q)/b
q* = a-bp* q

30. Quantity Taxes
A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.
Quantity taxes might be levied on sellers or buyers.

31. Quantity Taxes
What is the effect of a quantity tax on a market’s equilibrium?
How are prices affected?
How is the quantity traded affected?
Who pays the tax?
How are gains-to-trade altered?

32. Quantity Taxes
A tax rate t makes the price paid by buyers, pb, higher by t from the price received by sellers, ps.

33. Quantity Taxes Even with a tax the market must clear.
i.e. quantity demanded by buyers at price pb must equal quantity supplied by sellers at price ps.

34. 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.

35. Quantity Taxes & Market Eqm
Market demand
Market supply p
No tax p* q*
D(p), S(p)

36. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on sellers raises the
market supply curve
by $t. $t p* q*
D(p), S(p)

37. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on sellers raises the
market supply curve
by $t, raises the buyers’ price and lowers the quantity traded. pb $t p* qt q*
D(p), S(p)

38. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on sellers raises the
market supply curve
by $t, raises the buyers’ price and lowers the quantity traded. pb $t p* ps qt q*
D(p), S(p)
And sellers receive only ps = pb - t.

39. Quantity Taxes & Market Eqm
Market demand
Market supply p
No tax p* q*
D(p), S(p)

40. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on buyers lowers the market demand curve by $t. p* $t q*
D(p), S(p)

41. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on buyers lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. p* ps $t qt q*
D(p), S(p)

42. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on buyers lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. pb pb pb p* ps $t qt q*
D(p), S(p)
And buyers pay pb = ps + t.

43. Quantity Taxes & Market Eqm
Market demand
Market supply p
A quantity tax levied
on sellers at rate $t has
the same effects on the market’s equilibrium as does a quantity tax levied on buyers at rate
$t. pb pb pb $t p* ps $t qt q*
D(p), S(p)

44. Quantity Taxes & Market Eqm
Who pays the tax of $t per unit traded?
The division of the $t between buyers and sellers is the incidence of the tax.

45. Quantity Taxes & Market Eqm
Market demand
Market supply p pb pb pb p* ps qt q*
D(p), S(p)

46. Quantity Taxes & Market Eqm
Market demand
Market supply p
Tax paid by buyers pb pb pb p* ps qt q*
D(p), S(p)

47. Quantity Taxes & Market Eqm
Market demand
Market supply p
Tax paid by buyers pb pb pb p*
Tax paid by sellers ps qt q*
D(p), S(p)

48. Quantity Taxes & Market Eqm
E.g. suppose the market demand and supply curves are linear.

49. Quantity Taxes & Market Eqm
and
With the tax, the market equilibrium satisfies so
and
and
Solving these two equations gives
Therefore,

50. Quantity Taxes & Market Eqm
the equilibrium price if there is no tax (t = 0) and qt the quantity traded at equilibrium
when there is no tax.
As t ® 0, ps and pb ®

51. Quantity Taxes & Market Eqm
As t increases, ps falls,
pb rises, and qt falls.

52. Quantity Taxes & Market Eqm
The tax paid per unit by the buyer is
The tax paid per unit by the seller is

53. Quantity Taxes & Market Equm
The total tax paid (by buyers and sellers combined) is

54. Tax Incidence and Own-Price Elasticities
The incidence of a quantity tax depends upon the own-price elasticities of demand and supply.

55. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p pb $t p* ps qt q*
D(p), S(p)

56. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
Change to buyers’ price is pb - p*.
Change to quantity demanded is Dq. pb $t p* ps qt q*
D(p), S(p) Dq

57. Tax Incidence and Own-Price Elasticities
Around p = p* the own-price elasticity of demand is approximately

58. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p pb $t p* ps qt q*
D(p), S(p)

59. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
Change to sellers’ price is ps - p*.
Change to quantity demanded is Dq. pb $t p* ps qt q*
D(p), S(p) Dq

60. Tax Incidence and Own-Price Elasticities
Around p = p* the own-price elasticity of supply is approximately

61. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
Tax paid by buyers pb pb pb p*
Tax paid by sellers ps qt q*
D(p), S(p)

62. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
Tax paid by buyers pb pb pb p*
Tax paid by sellers ps qt q*
D(p), S(p)
Tax incidence =

63. Tax Incidence and Own-Price ElasticitiesSo

64. 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.

65. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
As market demand becomes less own-
price elastic, tax
incidence shifts more to the buyers. pb $t p* ps qt q*
D(p), S(p)

66. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
As market demand becomes less own-
price elastic, tax
incidence shifts more to the buyers. pb $t p* ps qt q*
D(p), S(p)

67. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
As market demand becomes less own-
price elastic, tax
incidence shifts more to the buyers. pb $t
ps= p*
qt = q*
D(p), S(p)

68. Tax Incidence and Own-Price Elasticities
Market demand
Market supply p
As market demand becomes less own-
price elastic, tax
incidence shifts more to the buyers. pb $t
ps= p*
qt = q*
D(p), S(p)
When eD = 0, buyers pay the entire tax, even though it is levied on the sellers.

69. 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.

70. Deadweight Loss and Own-Price Elasticities
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).
The lost total surplus is the tax’s deadweight loss, or excess burden.

71. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
No tax p* q*
D(p), S(p)

72. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
No tax CS p* q*
D(p), S(p)

73. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
No tax CS p* PS q*
D(p), S(p)

74. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
No tax CS p* PS q*
D(p), S(p)

75. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
The tax reduces both CS and PS pb CS $t p* ps PS qt q*
D(p), S(p)

76. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
The tax reduces both CS and PS, transfers surplus to government pb CS $t p*
Tax ps PS qt q*
D(p), S(p)

77. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
The tax reduces both CS and PS, transfers surplus to government pb CS $t p*
Tax ps PS qt q*
D(p), S(p)

78. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
The tax reduces both CS and PS, transfers surplus to government pb CS $t p*
Tax ps PS qt q*
D(p), S(p)

79. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
The tax reduces both CS and PS, transfers surplus to government, and lowers total surplus. pb CS $t p*
Tax ps PS qt q*
D(p), S(p)

80. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p pb $t p* ps
Deadweight loss qt q*
D(p), S(p)

81. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
Deadweight loss falls
as market demand
becomes less own-
price elastic. pb $t p* ps qt q*
D(p), S(p)

82. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
Deadweight loss falls
as market demand
becomes less own-
price elastic. pb $t p* ps qt q*
D(p), S(p)

83. Deadweight Loss and Own-Price Elasticities
Market demand
Market supply p
Deadweight loss falls
as market demand
becomes less own-
price elastic. pb $t
ps= p*
qt = q*
D(p), S(p)
When eD = 0, the tax causes no deadweight loss.

84. Deadweight Loss and Own-Price Elasticities
Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.
If either eD = 0 or eS = 0 then the deadweight loss is zero.