1、Chapter SixteenEquilibriumWhat Do We Do in This Chapter?uWe study the concept of equilibriumuWe will study external changes to equilibriumMarket 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)
2、MarketdemandMarketsupplyq=S(p)p*q*D(p*) = S(p*); the marketis in equilibrium.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
3、(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)/bMarketdemandQuantity TaxesuA quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.uIf the t
4、ax 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?Quantit
5、y 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 equal quantity supplied by sellers at price ps.D pS pbs()() Quantity Taxespptbs D
6、pS pbs()() anddescribe the markets equilibrium.Notice these conditions apply nomatter if the tax is levied on sellers or onbuyers.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
7、sales tax rate $t has thesame effect as an excise tax rate $t.Quantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*No taxQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*$tAn excise taxraises the marketsupply curve by $tQuantity Taxes & Market Equilibriu
8、mpD(p), S(p)MarketdemandMarketsupplyp*q*An excise taxraises the marketsupply 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 $t,raises the buyersprice and lo
9、wers thequantity traded.$tpbqtAnd sellers receive only ps = pb - t.psQuantity 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 market dema
10、ndcurve 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.psQuantity
11、Taxes & Market EquilibriumuWho pays the tax of $t per unit traded?uThe division of the $t between buyers and sellers is the incidence of the tax.Quantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsQuantity Taxes & Market EquilibriumpD(p), S(p)MarketdemandMarketsupplyp
12、*q*pbpbqtpbpsTax paid by buyersTax paid by sellersQuantity Taxes & Market EquilibriumuE.g. suppose the market demand and supply curves are linear.D pabpbb() S pcdpss() Quantity Taxes & Market EquilibriumD pabpbb() S pcdpss(). andWith the tax, the market equilibrium satisfiespptbs D pS pbs()() andsop
13、ptbs abpcdpbs .andSubstituting for pb givesab ptcdppacbtbdsss ().Quantity Taxes & Market Equilibriumpacbtbds andpptbs giveThe quantity traded at equilibrium isqD pS pabpadbcbdtbdtbsb ()().pacdtbdb Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt As t increases, ps falls,pb rises, and
14、qt falls.Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt The tax paid per unit by the buyer isppacdtbdacbddtbdb *.The tax paid per unit by the seller isppacbdacbtbdbtbds*. Quantity Taxes & Market Equilibriumpacbtbds pacdtbdb qadbcbdtbdt The total tax paid (by buyers and sellerscombi
15、ned) isTtqtadbcbdtbdt .Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsTax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to buyersprice is pb - p*.Change to quantitydemanded is D Dq.D DqTax Incidence and Own-Price Ela
16、sticitiesAround p = p* the own-price elasticityof demand is approximately DbbDqqpppppqpq D DD D*.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to sellersprice is ps - p*.Change to quantitydemanded is D Dq.D DqTax Incidence and Own-Price ElasticitiesAro
17、und p = p* the own-price elasticityof supply is approximately SssSqqpppppqpq D DD D*.Tax Incidence and Own-Price ElasticitiespD(p), S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersTax incidence = ppppbs *.Tax Incidence and Own-Price ElasticitiesTax incidence = ppppbs *
18、.ppqpqbD *.D D ppqpqsS *.D D SoppppbsSD *. Tax Incidence and Own-Price ElasticitiesppppbsSD *. Tax incidence isThe fraction of a $t quantity tax paidby buyers rises as supply becomes moreown-price elastic or as demand becomesless own-price elastic.Tax Incidence and Own-Price ElasticitiespD(p), S(p)M
19、arketdemandMarketsupplyps= p*$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.Deadweight Loss and Own-Price ElasticitiesuA quantity tax imposed on a competitive market redu
20、ces 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 taxDeadweight Loss and Own-Price Elastic
21、itiespD(p), S(p)MarketdemandMarketsupplyp*q*No taxCSPSDeadweight 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
22、SPSTaxDeadweight lossDeadweight 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 de
23、mandbecomes 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-Price 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.Summary: Key QuestionsuWhat is equilibrium?uWhat will happen if a tax is levied?
