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Chapter Sixteen Equilibrium
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Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.
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Market Equilibrium p q q d =D(p) Market demand
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Market Equilibrium p q Market supply q s =S(p)
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Market Equilibrium p q q d =D(p) Market demand Market supply q s =S(p)
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Market Equilibrium p q q d =D(p) Market demand Market supply q s =S(p) p* q*
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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
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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’)
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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*.
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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”)
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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*.
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Market Equilibrium: linear case An example of calculating a market equilibrium when the market demand and supply curves are linear.
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Market Equilibrium: linear case p q D(p) = a-bp Market demand Market supply S(p) = c+dp p* q*
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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*?
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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*)
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Market Equilibrium: linear case At the equilibrium price p*, D(p*) = S(p*). That is,
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Market Equilibrium: linear case At the equilibrium price p*, D(p*) = S(p*). That is, which gives
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Market Equilibrium: linear case At the equilibrium price p*, D(p*) = S(p*). That is, which gives and
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Market Equilibrium: linear case p q D(p) = a-bp Market demand Market supply S(p) = c+dp
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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)
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Market Equilibrium Perfectly inelastic supply Supply is fixed at q=q* p qq*
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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
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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?
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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
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Market Equilibrium p qq* = c D -1 (q) = (a-q)/b Market demand Inverse demand function expresses p as a function of q
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Market Equilibrium p q p* D -1 (q) = (a-q)/b Market demand q* = c p* = ( a - q*)/b
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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
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Market Equilibrium Market quantity supplied is extremely sensitive to price. p q
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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?
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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
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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*
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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*
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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
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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?
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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
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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.
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Quantity Taxes and describe the market equilibrium Notice that these conditions apply no matter whether the tax is levied on sellers or on buyers
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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).
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Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* No tax
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Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* $t An excise tax raises the market supply curve by $t
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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
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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
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Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax
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Quantity Taxes & Market Equilibrium p q Market demand Market supply p* q* An sales tax lowers the market demand curve by $t $t
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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
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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
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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
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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.
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Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps
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Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by buyers
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Quantity Taxes & Market Equilibrium p q Pre-tax demand Pre-tax supply p* q* pbpb pbpb qtqt pbpb psps Tax paid by sellers
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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
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Quantity Taxes & Market Equilibrium Example: suppose the market demand and supply curves are linear.
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Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and
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Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies andso and Substituting for p b gives
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Quantity Taxes & Market Equilibrium and give The quantity traded at equilibrium is
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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
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Quantity Taxes & Market Equilibrium As t increases, p s falls, p b rises, andq t falls.
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Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is
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Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is The tax paid per unit by the seller is
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Quantity Taxes & Market Equilibrium The total tax paid (by buyers and sellers combined) is
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Tax Incidence and Own-Price Elasticities The incidence of a quantity tax depends upon the own-price elasticities of demand and supply
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Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps
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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. qq
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Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately
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Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately
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Tax Incidence and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps
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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. qq
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Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately
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Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately
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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
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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 =
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Tax Incidence and Own-Price Elasticities Tax incidence =
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Tax Incidence and Own-Price Elasticities Tax incidence = So
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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
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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.
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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.
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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
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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.
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Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax
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Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax CS PS
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Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* No tax CS PS
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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
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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
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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
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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
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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
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Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps CS PS Tax Deadweight loss
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Deadweight Loss and Own-Price Elasticities p q Market demand Market supply p* q* $t pbpb qtqt psps Deadweight loss
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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.
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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.
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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.
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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.
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END OF LECTURE END OF LECTURE The following slides are for self-study
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Market Equilibrium Can we calculate the market equilibrium using the inverse market demand and supply curves?
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Market Equilibrium Can we calculate the market equilibrium using the inverse market demand and supply curves? Yes, it is the same calculation.
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Market Equilibrium the equation of the inverse market demand curve. And the equation of the inverse market supply curve.
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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*
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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
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Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*).
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Market Equilibrium and At the equilibrium quantity q*, D -1 (p*) = S -1 (p*). That is, which gives
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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
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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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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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