B d ² ² p a c dt b d b ² ² 10 quantity tax market

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b d ² ± ± ² p a c dt b d b ± ² ²
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10 Quantity Tax & Market Equilibrium p a c bt b d s ± ± ² p a c dt b d b ± ² ² q ad bc bdt b d t ² ± ² As t o 0, p s and p b o the equilibrium price if there is no tax (t = 0) and q t the quantity traded at equilibrium when there is no tax. o ad bc , b d ² ² *, p d b c a ² ± Quantity Tax & Market Equilibrium p a c bt b d s ± ± ² p a c dt b d b ± ² ² q ad bc bdt b d t ² ± ² As t increases, p s falls, p b rises, and q t falls. Quantity Tax & Market Equilibrium p a c bt b d s ± ± ² p a c dt b d b ± ² ² q ad bc bdt b d t ² ± ² The tax paid per unit by the buyer is p p a c dt b d a c b d dt b d b ± ± ² ² ± ± ² ² * . The tax paid per unit by the seller is p p a c b d a c bt b d bt b d s * . ± ± ² ± ± ± ² ²
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11 Quantity Tax & Market Equilibrium p a c bt b d s ± ± ² p a c dt b d b ± ² ² q ad bc bdt b d t ² ± ² The total tax paid (by buyers and sellers combined) is T tq t ad bc bdt b d t ² ± ² . Tax Incidence and Price Elasticities The incidence of a quantity tax depends upon the own-price elasticities of demand and supply. Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t p b q t p s Change to buyers’ price is p b - p*. Change to quantity demanded is ' q. ' q
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12 Tax Incidence and Price Elasticities Around p = p* the own-price elasticity of demand is approximately H D b q q p p p | ± ' * * * Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t p b q t p s Change to sellers’ price is p s - p*. Change to quantity demanded is ' q. ' q Tax Incidence and Price Elasticities Around p = p* the own-price elasticity of supply is approximately H S s q q p p p | ± ' * * *
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13 Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p* q* p b q t p s Tax paid by buyers Tax paid by sellers Tax incidence = p p p p b s ± ± * * . Tax Incidence and Price Elasticities Tax incidence = p p p p b s ± ± * * . p p q p q b D ± | u u * * * . ' H p p q p q s S ± | u u * * * . ' H So p p p p b s S D ± ± | ± * * . H H Tax Incidence and Price Elasticities p p p p b s S D ± ± | ± * * . H H 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.
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14 Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t p b q t p s As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t p b q t p s As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. Tax Incidence and Price Elasticities p D(p), S(p) Market demand Market supply p s = p* $t p b q t = q* As market demand becomes less own- price elastic, tax incidence shifts more to the buyers.
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