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Chapter SixteenEquilibrium.Market EquilibriumuA market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.Market EquilibriumpD(p),S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*D(p*)=S(p*);the marketis in equilibrium.An ExampleAt the equilibrium price p*,D(p*)=S(p*).That is,which givesand.Market EquilibriumuCan we calculate the market equilibrium using the inverse market demand and supply curves?uYes,it is the same calculation.Market Equilibriumthe equation of the inverse marketdemand curve.Andthe equation of the inverse marketsupply curve.Market EquilibriumuTwo special cases:lquantity supplied is fixed,independent of the market price,andlquantity supplied is extremely sensitive to the market price.Market EquilibriumS(p)=c+dp,so d=0and S(p)c.pqq*=cD-1(q)=(a-q)/bMarketdemandMarket quantity supplied isfixed,independent of price.Market EquilibriumMarket quantity supplied isextremely sensitive to price.S-1(q)=p*.pqp*D-1(q)=(a-q)/bMarketdemand.Quantity TaxesuA quantity tax levied at a rate of$t is a tax of$t paid on each unit traded.uIf the tax is levied on sellers then it is an excise tax.uIf the tax is levied on buyers then it is a sales tax.Quantity TaxesuWhat is the effect of a quantity tax on a markets equilibrium?uHow are prices affected?uHow is the quantity traded affected?uWho pays the tax?uHow are gains-to-trade altered?.Quantity TaxesuA tax rate t makes the price paid by buyers,pb,higher by t from the price received by sellers,ps.Quantity TaxesuEven with a tax the market must clear.uI.e.quantity demanded by buyers at price pb must equal quantity supplied by sellers at price ps.Quantity Taxesanddescribe the markets equilibrium.Notice these conditions apply nomatter if the tax is levied on sellers or onbuyers.Quantity Taxesanddescribe the markets equilibrium.Notice that these two conditions apply nomatter if the tax is levied on sellers or onbuyers.Hence,a sales tax rate$t has thesame effect as an excise tax rate$t.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*No tax.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*$tAn excise taxraises the marketsupply curve by$t.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An excise taxraises the marketsupply curve by$t,raises the buyersprice and lowers thequantity traded.$tpbqt.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An excise taxraises the marketsupply curve by$t,raises the buyersprice and lowers thequantity traded.$tpbqtAnd sellers receive only ps=pb-t.ps.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An sales tax lowersthe market demandcurve by$t$t.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An sales tax lowersthe market demandcurve by$t,lowersthe sellers price andreduces the quantitytraded.$tqtps.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An sales tax lowersthe market demandcurve by$t,lowersthe sellers price andreduces the quantitytraded.$tpbpbqtpbAnd buyers pay pb=ps+t.ps.Quantity Taxes&Market EquilibriumuWho pays the tax of$t per unit traded?uThe division of the$t between buyers and sellers is the incidence of the tax.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*pbpbqtpbps.Quantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellers.Quantity Taxes&Market EquilibriumuE.g.suppose the market demand and supply curves are linear.Quantity Taxes&Market EquilibriumandWith the tax,the market equilibrium satisfiesandsoandSubstituting for pb gives.Quantity Taxes&Market EquilibriumandgiveThe quantity traded at equilibrium is.Quantity Taxes&Market EquilibriumAs t increases,ps falls,pb rises,andqt falls.Quantity Taxes&Market EquilibriumThe tax paid per unit by the buyer isThe tax paid per unit by the seller is.Quantity Taxes&Market EquilibriumThe total tax paid(by buyers and sellerscombined)is.What Determines Tax Incidence?.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtps.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to buyersprice is pb-p*.Change to quantitydemanded is D Dq.D Dq.Tax Incidence and Own-Price ElasticitiesAround p=p*the own-price elasticityof demand is approximately.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to sellersprice is ps-p*.Change to quantitydemanded is D Dq.D Dq.Tax Incidence and Own-Price ElasticitiesAround p=p*the own-price elasticityof supply is approximately.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersTax incidence=.Tax Incidence and Own-Price ElasticitiesTax incidence=So.Tax Incidence and Own-Price ElasticitiesTax incidence isThe fraction of a$t quantity tax paidby buyers rises as supply becomes moreown-price elastic or as demand becomesless own-price elastic.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyps=p*$tpbqt=q*As market demandbecomes less own-price elastic,taxincidence shifts moreto the buyers.When e eD=0,buyers pay the entire tax,even though it is levied on the sellers.Deadweight Loss and Own-Price ElasticitiesuA quantity tax imposed on a competitive market reduces the quantity traded and so reduces gains-to-trade(i.e.the sum of Consumers and Producers Surpluses).uThe lost total surplus is the taxs deadweight loss,or excess burden.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*No tax.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*No taxCSPS.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTax.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTax.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto government,and lowers total surplus.Tax.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSTaxDeadweight loss.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight loss fallsas market demandbecomes less own-price elastic.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight loss fallsas market demandbecomes less own-price elastic.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyps=p*$tpbqt=q*Deadweight loss fallsas market demandbecomes less own-price elastic.When e eD=0,the tax causes no deadweight loss.Deadweight Loss and Own-Price ElasticitiesuDeadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.uIf either e eD=0 or e eS=0 then the deadweight loss is zero.
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