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1、Chapter SixteenEquilibrium均衡均衡StructureuMarket equilibriumuQuantity tax and equilibriumuTax incidence （税收分担）税收分担）uDeadweight loss （额外净损失）额外净损失）Market EquilibriumuA market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.uAlso called “market is cleare
2、d”uSupply may not equal productionMarket EquilibriumpD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)Market SettinguCompetitive market Contestable marketMarket EquilibriumpD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*D(p*) = S(p*); the marketis in equilibrium.Market EquilibriumpD(p), S(p)q=D(p)Ma
3、rketdemandMarketsupplyq=S(p)p*S(p)D(p) S(p); an excessof quantity supplied overquantity demanded.pD(p)Market EquilibriumpD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*S(p)D(p) S(p”); an excessof quantity demandedover quantity supplied.p”S(p”)Market EquilibriumpD(p), S(p)q=D(p)MarketdemandMarketsup
4、plyq=S(p)p*D(p”)D(p”) S(p”); an excessof quantity demandedover quantity supplied.p”S(p”)Market price must rise towards p*.Market Equilibrium Linear D & SD pabp( ) S pcdp( ) At the equilibrium price p*, D(p*) = S(p*).That is,abpcdp *which givespacbd* andqD pS padbcbd*()(). Market EquilibriumpD(p), S(
5、p)D(p) = a-bpMarketdemandMarketsupplyS(p) = c+dppacbd* dbbcadq* Market EquilibriumuCan we calculate the market equilibrium using the inverse market demand and supply curves?uYes, it is the same calculation.Market EquilibriumqD pabppaqbDq ( )( ),1qS pcdppcqdSq ( )( ),1the equation of the inverse mark
6、etdemand curve. Andthe equation of the inverse marketsupply curve.Market EquilibriumqD-1(q),S-1(q)D-1(q) = (a-q)/bMarket inversedemandS-1(q) = (-c+q)/dp*q*At equilibrium,D-1(q*) = S-1(q*).Market inverse supplyMarket EquilibriumpDqaqb 1( )pSqcqd 1( ).andAt the equilibrium quantity q*, D-1(p*) = S-1(p
7、*).That is,aqbcqd *which givesqadbcbd* andpDqSqacbd*()(). 11Market EquilibriumqD-1(q),S-1(q)D-1(q) = (a-q)/bMarketdemandMarketsupplyS-1(q) = (-c+q)/dpacbd* dbbcadq* Market EquilibriumuTwo special cases:lquantity supplied is fixed, independent of the market price, andlquantity supplied is extremely s
8、ensitive to the market price.Market EquilibriumS(p) = c+dp, so d=0and S(p) c.pqq* = cMarket quantity supplied isfixed, independent of price.Market EquilibriumS(p) = c+dp, so d=0and S(p) c.pqp*D-1(q) = (a-q)/bMarketdemandq* = cMarket quantity supplied isfixed, independent of price.Market EquilibriumS
9、(p) = c+dp, so d=0and S(p) c.pq p* =(a-c)/bD-1(q) = (a-q)/bMarketdemandq* = cp* = D-1(q*); that is,p* = (a-c)/b.Market quantity supplied isfixed, independent of price.Market EquilibriumS(p) = c+dp, so d=0and S(p) c.pqD-1(q) = (a-q)/bMarketdemandq* = cp* = D-1(q*); that is,p* = (a-c)/b.pacbd* qadbcbd
10、* with d = 0 givepacb* qc*. p* =(a-c)/bMarket quantity supplied isfixed, independent of price.Market EquilibriumMarket quantity supplied isextremely sensitive to price.S-1(q) = p*.pqp*Market EquilibriumMarket quantity supplied isextremely sensitive to price.S-1(q) = p*.pqp*D-1(q) = (a-q)/bMarketdema
11、ndq*Market EquilibriumMarket quantity supplied isextremely sensitive to price.S-1(q) = p*.pqp*D-1(q) = (a-q)/bMarketdemandq* =a-bp*p* = D-1(q*) = (a-q*)/b soq* = a-bp*Comparative StaticsuShifting demand curves Income Price of other productsuShifting supply curves TechnologyuTaxesQuantity TaxesuA qua
12、ntity 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
13、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.pptbs Quantity TaxesuEven with a tax the market must clear.uI.e. quantity demanded by buyers at price pb must
14、equal quantity supplied by sellers at price ps.D pS pbs()() Quantity Taxespptbs D pS pbs()() anddescribe 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 $t.Quantity
15、 Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*No taxQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*$tAn excise taxraises the marketsupply curve by $tQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*An excise taxraises the market
16、supply curve by $t,raises the buyersprice and lowers thequantity traded.$tpbqtQuantity 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.psQ
17、uantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*No taxQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*An sales tax lowersthe market demandcurve by $t$tQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*An sales tax lowersthe m
18、arket demandcurve by $t, lowersthe sellers price andreduces the quantitytraded.$tqtpsQuantity 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.p
19、sQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*A sales tax levied atrate $t has the sameeffects on themarkets equilibriumas does an excise taxlevied at rate $t.$tpbpbqtpbps$tQuantity Taxes & Market EquilibriumuWho pays the tax of $t per unit traded?uThe division of the $t
20、 between buyers and sellers is the incidence of the tax (税收分担税收分担).Quantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersQuantity Taxes & Market EquilibriumpD(p), S(p)M
21、arketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by sellersQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersQuantity Taxes & Market EquilibriumuE.g. suppose the market demand and supply curves are linear.D pabpbb() S pcdpss() Quant
22、ity Taxes & Market EquilibriumandD pabpbb() S pcdpss(). Quantity Taxes & Market EquilibriumandWith the tax, the market equilibrium satisfiesandsoandD pabpbb() S pcdpss(). pptbs D pS pbs()() pptbs abpcdpbs .Quantity Taxes & Market EquilibriumD pabpbb() S pcdpss(). andWith the tax, the market equilibr
23、ium satisfiespptbs D pS pbs()() andsopptbs abpcdpbs .andSubstituting for pb givesab ptcdppacbtbdsss ().Quantity Taxes & Market Equilibriumpacbtbds andpptbs giveThe quantity traded at equilibrium isqD pS pabpadbcbdtbdtbsb ()().pacdtbdb Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt
24、As t 0, ps and pb theequilibrium price ifthere is no tax (t = 0) and qt the quantity traded at equilibriumwhen there is no tax.adb cbd ,*,pdbca Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt As t increases, ps falls,pb rises, andqt falls.Quantity Taxes & Market Equilibriumpacbtbds
25、pacdtbdb qadbcbdtbdt The tax paid per unit by the buyer isppacdtbdacbddtbdb *.Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt The tax paid per unit by the buyer isppacdtbdacbddtbdb *.The tax paid per unit by the seller isppacbdacbtbdbtbds*. Quantity Taxes & Market Equilibriumpacbtbd
26、s pacdtbdb qadbcbdtbdt The total tax paid (by buyers and sellerscombined) isTtqtadbcbdtbdt .Tax Incidence and Own-Price ElasticitiesuThe incidence of a quantity tax depends upon the own-price elasticities of demand and supply.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsuppl
27、yp*q*$tpbqtpsTax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to buyersprice is pb - p*.Change to quantitydemanded is D Dq.D DqTax Incidence and Own-Price ElasticitiesAround p = p* the own-price elasticityof demand is approximately Dbqqppp D D*Tax Inciden
28、ce and Own-Price ElasticitiesAround p = p* the own-price elasticityof demand is approximately DbbDqqpppppqpq D DD D*.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsTax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to
29、 sellersprice is ps - p*.Change to quantitydemanded is D Dq.D DqTax Incidence and Own-Price ElasticitiesAround p = p* the own-price elasticityof supply is approximately Ssqqppp D D*Tax Incidence and Own-Price ElasticitiesAround p = p* the own-price elasticityof supply is approximately SssSqqpppppqpq
30、 D DD D*.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersTax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersTax incidence = ppppbs *.Tax Incidence
31、and Own-Price ElasticitiesTax incidence = ppppbs *.ppqpqbD *.D D ppqpqsS *.D D Tax Incidence and Own-Price ElasticitiesTax incidence = ppppbs *.ppqpqbD *.D D ppqpqsS *.D D SoppppbsSD *. Tax Incidence and Own-Price ElasticitiesppppbsSD *. Tax incidence isThe fraction of a $t quantity tax paidby buyer
32、s rises as supply becomes moreown-price elastic or as demand becomesless own-price elastic.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsAs market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers. Tax Incidence and Own-Price Elastic
33、itiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsAs market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers. Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyps= p*$tpbqt = q*As market demandbecomes less own-price elastic, taxincidence shifts m
34、oreto the buyers. 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 D = 0, buyers pay the entire tax, even though it is levied on the sellers.Tax Incidence and Own-Pr
35、ice ElasticitiesppppbsSD *. Tax incidence isSimilarly, the fraction of a $t quantitytax paid by sellers rises as supplybecomes less own-price elastic or asdemand becomes more own-price elastic.Deadweight Loss and Own-Price ElasticitiesuA quantity tax imposed on a competitive market reduces the quant
36、ity traded and so reduces gains-to-trade (i.e. the sum of Consumers and Producers Surpluses).uThe lost total surplus is the taxs deadweight loss（额外净损失）额外净损失）, or excess burden.Deadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*No taxDeadweight Loss and Own-Price Elastic
37、itiespD(p), S(p)MarketdemandMarketsupplyp*q*No taxCSDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*No taxPSDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*No taxCSPSDeadweight Loss and Own-Price Elasticities$tqtCSThe tax reducesboth
38、CS and PSpD(p), S(p)MarketdemandMarketsupplyp*q*pbpsPSDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsC
39、SPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp
40、*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto government,and lowers total surplus.TaxDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight lossDeadweight Loss and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDea
41、dweight 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 D = 0, the tax causes no deadweight loss.Deadweight Loss and Own-Pri
42、ce ElasticitiesuDeadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.uIf either D = 0 or S = 0 then the deadweight loss is zero.Examples of Equilibrium AnalysisuPrice ceilinguMinimum pricelAgricultural price controllMinimum wagepD(p), S(
43、p)p*q*pmaxDABCEFqSPrice controlD DCS=C-ED DPS=-C-FDWL=-E-F +waiting in lineqDpD(p), S(p)p*q*pmaxDABCEFqmaxPrice control with rationingD DCS=C-ED DPS=-C-FDWL=-E-F +corruptionpD(p), S(p)p*q*psDABCEFqmaxPrice floor with acreage controlPayment=E+F+GD DCS=-B-ED DPS=B-F+paymentGovernment loss=paymentDWL=-E-FGMinimum WageuSingle sector single type of laboruCovered vs. uncovered sectoruSkilled vs. unskilled workers