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

© 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.

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

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

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

© 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*

© 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.

© 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’)

© 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*.

© 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”)

© 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*.

© 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.

© 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*

© 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*?

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

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

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

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

© 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

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

© 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.

© 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.

© 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*

© 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

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

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

© 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

© 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

© 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

© 2010 W. W. Norton & Company, Inc. 30 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.

© 2010 W. W. Norton & Company, Inc. 31 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?

© 2010 W. W. Norton & Company, Inc. 32 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.

© 2010 W. W. Norton & Company, Inc. 33 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.

© 2010 W. W. Norton & Company, Inc. 34 Quantity Taxes and describe the market’s equilibrium. Notice these conditions apply no matter if the tax is levied on sellers or on buyers.

© 2010 W. W. Norton & Company, Inc. 35 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.

© 2010 W. W. Norton & Company, Inc. 36 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax

© 2010 W. W. Norton & Company, Inc. 37 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

© 2010 W. W. Norton & Company, Inc. 38 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

© 2010 W. W. Norton & Company, Inc. 39 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

© 2010 W. W. Norton & Company, Inc. 40 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax

© 2010 W. W. Norton & Company, Inc. 41 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

© 2010 W. W. Norton & Company, Inc. 42 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

© 2010 W. W. Norton & Company, Inc. 43 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

© 2010 W. W. Norton & Company, Inc. 44 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

© 2010 W. W. Norton & Company, Inc. 45 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.

© 2010 W. W. Norton & Company, Inc. 46 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps

© 2010 W. W. Norton & Company, Inc. 47 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers

© 2010 W. W. Norton & Company, Inc. 48 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by sellers

© 2010 W. W. Norton & Company, Inc. 49 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

© 2010 W. W. Norton & Company, Inc. 50 Tax Incidence and Own-Price Elasticities u The incidence of a quantity tax depends upon the own-price elasticities of demand and supply.

© 2010 W. W. Norton & Company, Inc. 51 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps

© 2010 W. W. Norton & Company, Inc. 52 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

© 2010 W. W. Norton & Company, Inc. 53 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately

© 2010 W. W. Norton & Company, Inc. 54 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately

© 2010 W. W. Norton & Company, Inc. 55 Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps

© 2010 W. W. Norton & Company, Inc. 56 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

© 2010 W. W. Norton & Company, Inc. 57 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately

© 2010 W. W. Norton & Company, Inc. 58 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately

© 2010 W. W. Norton & Company, Inc. 59 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

© 2010 W. W. Norton & Company, Inc. 60 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 =

© 2010 W. W. Norton & Company, Inc. 61 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.

© 2010 W. W. Norton & Company, Inc. 62 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.

© 2010 W. W. Norton & Company, Inc. 63 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.

© 2010 W. W. Norton & Company, Inc. 64 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.

© 2010 W. W. Norton & Company, Inc. 65 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.

© 2010 W. W. Norton & Company, Inc. 66 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.

© 2010 W. W. Norton & Company, Inc. 67 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax

© 2010 W. W. Norton & Company, Inc. 68 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS

© 2010 W. W. Norton & Company, Inc. 69 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax PS

© 2010 W. W. Norton & Company, Inc. 70 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS

© 2010 W. W. Norton & Company, Inc. 71 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS

© 2010 W. W. Norton & Company, Inc. 72 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

© 2010 W. W. Norton & Company, Inc. 73 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

© 2010 W. W. Norton & Company, Inc. 74 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

© 2010 W. W. Norton & Company, Inc. 75 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

© 2010 W. W. Norton & Company, Inc. 76 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

© 2010 W. W. Norton & Company, Inc. 77 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

© 2010 W. W. Norton & Company, Inc. 78 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss

© 2010 W. W. Norton & Company, Inc. 79 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.

© 2010 W. W. Norton & Company, Inc. 80 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.

© 2010 W. W. Norton & Company, Inc. 81 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.

© 2010 W. W. Norton & Company, Inc. 82 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.