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Chapter Sixteen Equilibrium. Market Equilibrium  A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by.

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Presentation on theme: "Chapter Sixteen Equilibrium. Market Equilibrium  A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by."— Presentation transcript:

1 Chapter Sixteen Equilibrium

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

3 Market Equilibrium p q q d =D(p) Market demand

4 Market Equilibrium p q Market supply q s =S(p)

5 Market Equilibrium p q q d =D(p) Market demand Market supply q s =S(p)

6 Market Equilibrium p q q d =D(p) Market demand Market supply q s =S(p) p* q*

7 Market Equilibrium p q q d =D(p) Market demand Market supply q s =S(p) p* q* At q*, D(p*) = S(p*); the market is in equilibrium

8 Market Equilibrium: excess supply p q q d =D(p) Market demand Market supply q s =S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’)

9 Market Equilibrium: excess supply p q q d =D(p) Market demand Market supply q s =S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’) In a free market, price will fall towards p*.

10 Market Equilibrium: excess demand p q q d =D(p) Market demand Market supply q s =S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”)

11 Market Equilibrium: excess demand p q q d =D(p) Market demand Market supply q s =S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”) In a free market, price will rise towards p*.

12 Market Equilibrium: linear case  An example of calculating a market equilibrium when the market demand and supply curves are linear.

13 Market Equilibrium: linear case p q D(p) = a-bp Market demand Market supply S(p) = c+dp p* q*

14 Market Equilibrium: linear case p q D(p) = a-bp Market demand Market supply S(p) = c+dp p* q* What are the values of p* and q*?

15 Market Equilibrium: linear case At the market equilibrium, q d = q s The demand and supply functions are At the equilibrium price p*, D(p*) = S(p*)

16 Market Equilibrium: linear case At the equilibrium price p*, D(p*) = S(p*). That is,

17 Market Equilibrium: linear case At the equilibrium price p*, D(p*) = S(p*). That is, which gives

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

19 Market Equilibrium: linear case p q D(p) = a-bp Market demand Market supply S(p) = c+dp

20 Market Equilibrium  Two special cases: quantity supplied is fixed, independent of the market price (perfectly inelastic supply) quantity supplied is extremely sensitive to the market price (perfectly elastic supply)

21 Market Equilibrium Perfectly inelastic supply Supply is fixed at q=q* p qq*

22 Market Equilibrium d=0 (supply independent of price) and c= q* p qq* = c For a linear supply function ( S(p) = c+dp ), this implies

23 Market Equilibrium d=0 (supply independent of price) and c= q* p qq* = c For a linear supply function ( S(p) = c+dp ), this implies What is the corresponding market price?

24 Market price when supply fixed at q* Demand function is In equilibrium, D(p*) = q*  q* = a – bp  p* = ( a – q*)/b  p* = ( a – c )/b Recall that the general solution for p* is When d = 0 (supply independent of price), this becomes p* = ( a – c )/b

25 Market Equilibrium p qq* = c D -1 (q) = (a-q)/b Market demand Inverse demand function expresses p as a function of q

26 Market Equilibrium p q p* D -1 (q) = (a-q)/b Market demand q* = c p* = ( a - q*)/b

27 Market Equilibrium  Two special cases are when supply is fixed, independent of market price (perfectly inelastic) when quantity supplied is extremely sensitive to the market price

28 Market Equilibrium Market quantity supplied is extremely sensitive to price. p q

29 Market Equilibrium Market quantity supplied is extremely sensitive to price. p q p* At the fixed price p*, unlimited quantities are available What is the market equilibrium quantity?

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

31 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*

32 Market Equilibrium Market quantity supplied is extremely sensitive to price. Price fixed at p*, so substitute p* into the demand function to get p q p* Market demand q* = a-bp*

33 Quantity Taxes  A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded  If the tax is levied on sellers then it is an excise tax  If the tax is levied on buyers then it is a sales tax

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

35 Quantity Taxes  A tax of t per unit makes the price paid by buyers, p b, higher (by the amount t) than the price received by sellers, p s. We say that the tax ‘drives a wedge’ between the seller’s price and the buyer’s price

36 Quantity Taxes  BUT even with a tax, the market must clear  I.e. quantity demanded by buyers at price p b must equal quantity supplied by sellers at price p s.

37 Quantity Taxes and describe the market equilibrium Notice that these conditions apply no matter whether the tax is levied on sellers or on buyers

38 Quantity Taxes and describe the market’s equilibrium. These two conditions apply regardless of whether the tax is levied on sellers or on buyers. Hence, a sales tax (at rate $t per unit) has the same effect as an excise tax (at rate $t per unit).

39 Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* No tax

40 Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* $t An excise tax raises the market supply curve by $t

41 Quantity Taxes & Market Equilibrium p q 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

42 Quantity Taxes & Market Equilibrium p q 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

43 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax

44 Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* An sales tax lowers the market demand curve by $t $t

45 Quantity Taxes & Market Equilibrium p q 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

46 Quantity Taxes & Market Equilibrium p q 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

47 Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* A sales tax levied at rate $t has the same effects on the market equilibrium as does an excise tax levied at rate $t $t pbpb pbpb qtqt pbpb psps

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

49 Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps

50 Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers

51 Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by sellers

52 Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers Note that the loss in consumer surplus > tax paid

53 Quantity Taxes & Market Equilibrium  Example: suppose the market demand and supply curves are linear.

54 Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and

55 Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and Substituting for p b gives

56 Quantity Taxes & Market Equilibrium and give The quantity traded at equilibrium is

57 Quantity Taxes & Market Equilibrium As t  0, p s and p b  the no-tax equilibrium price and q t the no-tax equilibrium quantity 

58 Quantity Taxes & Market Equilibrium As t increases, p s falls, p b rises, andq t falls.

59 Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is

60 Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is The tax paid per unit by the seller is

61 Quantity Taxes & Market Equilibrium The total tax paid (by buyers and sellers combined) is

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

63 Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps

64 Tax Incidence and Own-Price Elasticities p q 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

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

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

67 Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps

68 Tax Incidence and Own-Price Elasticities p q 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

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

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

71 Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers

72 Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers Tax paid by sellers Tax incidence =

73 Tax Incidence and Own-Price Elasticities Tax incidence =

74 Tax Incidence and Own-Price Elasticities Tax incidence = So

75 Tax Incidence and Own-Price Elasticities Tax incidence is The shares of a $t quantity tax paid by buyers and sellers rises are equal if demand and supply elasticities are equal (in absolute value). If supply is more elastic than demand, buyers pay a greater share than sellers

76 Tax Incidence and Own-Price Elasticities p q 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.

77 Tax Incidence and Own-Price Elasticities p q 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.

78 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

79 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.

80 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax

81 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax CS PS

82 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax CS PS

83 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS

84 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

85 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

86 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS The tax reduces both CS and PS, transfers surplus to government Tax

87 Deadweight Loss and Own-Price Elasticities p q 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

88 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS Tax Deadweight loss

89 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss

90 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss falls as market demand becomes less own- price elastic.

91 Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss falls as market demand becomes less own- price elastic.

92 Deadweight Loss and Own-Price Elasticities p q 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.

93 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  D = 0 or  S = 0 then the deadweight loss is zero.

94 END OF LECTURE  END OF LECTURE  The following slides are for self-study

95 Market Equilibrium  Can we calculate the market equilibrium using the inverse market demand and supply curves?

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

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

98 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*

99 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

100 Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*).

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

102 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

103 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.

104 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.


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