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1、Lec 17 Chapter SixteenEquilibriumMarket EquilibriumA market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.Market EquilibriumpD(p)q=D(p)MarketdemandMarket EquilibriumpS(p)Marketsupplyq=S(p)Market EquilibriumpD(p),S(p)q=D(p)MarketdemandMarketsupplyq
2、=S(p)Market EquilibriumpD(p),S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*Market 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)MarketdemandMarketsupplyq=S(p)p*S(p)D(p)S(p);an excessof quantity supplied overquanti
3、ty 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)MarketdemandMarketsupplyq=S(p)p*D(p”)D(p”)S(p”);an excessof quantity demandedover quantity supplied.p”S(p”)Mar
4、ket price must rise towards p*.Market EquilibriumAn example of calculating a market equilibrium when the market demand and supply curves are linear.Market EquilibriumpD(p),S(p)D(p)=a-bpMarketdemandMarketsupplyS(p)=c+dpp*q*Market EquilibriumpD(p),S(p)D(p)=a-bpMarketdemandMarketsupplyS(p)=c+dpp*q*What
5、 are the valuesof p*and q*?Market EquilibriumAt the equilibrium price p*,D(p*)=S(p*).Market EquilibriumAt the equilibrium price p*,D(p*)=S(p*).That is,Market EquilibriumAt the equilibrium price p*,D(p*)=S(p*).That is,which givesMarket EquilibriumAt the equilibrium price p*,D(p*)=S(p*).That is,which
6、givesandMarket EquilibriumpD(p),S(p)D(p)=a-bpMarketdemandMarketsupplyS(p)=c+dpMarket EquilibriumCan we calculate the market equilibrium using the inverse market demand and supply curves?Market EquilibriumCan we calculate the market equilibrium using the inverse market demand and supply curves?Yes,it
7、 is the same calculation.Market Equilibriumthe equation of the inverse marketdemand curve.Andthe equation of the inverse marketsupply curve.Market EquilibriumqD-1(q),S-1(q)D-1(q)=(a-q)/bMarketinversedemandMarket inverse supplyS-1(q)=(-c+q)/dp*q*Market EquilibriumqD-1(q),S-1(q)D-1(q)=(a-q)/bMarketdem
8、andS-1(q)=(-c+q)/dp*q*At equilibrium,D-1(q*)=S-1(q*).Market inverse supplyMarket EquilibriumandAt the equilibrium quantity q*,D-1(p*)=S-1(p*).Market EquilibriumandAt the equilibrium quantity q*,D-1(p*)=S-1(p*).That is,Market EquilibriumandAt the equilibrium quantity q*,D-1(p*)=S-1(p*).That is,which
9、givesMarket EquilibriumandAt the equilibrium quantity q*,D-1(p*)=S-1(p*).That is,which givesandMarket EquilibriumqD-1(q),S-1(q)D-1(q)=(a-q)/bMarketdemandMarketsupplyS-1(q)=(-c+q)/dMarket EquilibriumTwo special cases:quantity supplied is fixed,independent of the market price,andquantity supplied is e
10、xtremely sensitive to the market price.Market EquilibriumMarket quantity supplied isfixed,independent of price.pqq*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.pqq*=cD-1(q)=(a-q)/bMarketdemandMarke
11、t 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(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.Ma
12、rket 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.p*=(a-c)/bMarket quantity supplied isfixed,independent of price.Market EquilibriumS(p)=c+dp,so d=0and S(p)c.pqD-1(q)=(a-q)/bMarketdemandq*=cp*
13、=D-1(q*);that is,p*=(a-c)/b.with d=0 give p*=(a-c)/bMarket quantity supplied isfixed,independent of price.Market EquilibriumTwo special cases arewhen quantity supplied is fixed,independent of the market price,andwhen quantity supplied is extremely sensitive to the market price.Market EquilibriumMark
14、et quantity supplied isextremely sensitive to price.pqMarket 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)/bMarketdemandMarket EquilibriumMarket quantity supplied i
15、sextremely sensitive to price.S-1(q)=p*.pqp*D-1(q)=(a-q)/bMarketdemandq*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*Quantity TaxesA quantity tax levied at a rate of$t is a tax of$t paid on eac
16、h 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.Quantity TaxesWhat is the effect of a quantity tax on a markets equilibrium?How are prices affected?How is the quantity traded affected?Who pays the tax?How are gains-to-trade
17、 altered?Quantity TaxesA tax rate t makes the price paid by buyers,pb,higher by t from the price received by sellers,ps.Quantity TaxesEven with a tax the market must clear.I.e.quantity demanded by buyers at price pb must equal quantity supplied by sellers at price ps.Quantity Taxesanddescribe the ma
18、rkets 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$t has thesame effect as an excise
19、tax rate$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 EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*An excise taxraises t
20、he 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$t,raises the buyersprice and lowers thequantity traded.$tpbqtAnd sellers receive only ps=pb-t.psQ
21、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 market dema
22、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 Taxes&Marke
23、t 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 EquilibriumWho pays the tax of$t per unit traded?The division of the$t between buyers and sellers is t
24、he incidence of the tax.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)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by sel
25、lersQuantity Taxes&Market EquilibriumpD(p),S(p)MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersQuantity Taxes&Market EquilibriumE.g.suppose the market demand and supply curves are linear.Quantity Taxes&Market EquilibriumandQuantity Taxes&Market EquilibriumandWith the tax,t
26、he market equilibrium satisfiesandsoandQuantity Taxes&Market EquilibriumandWith the tax,the market equilibrium satisfiesandsoandSubstituting for pb givesQuantity Taxes&Market EquilibriumandgiveThe quantity traded at equilibrium isQuantity Taxes&Market EquilibriumAs t 0,ps and pb theequilibrium price
27、 ifthere is no tax(t=0)and qt the quantity traded at equilibriumwhen there is no tax.Quantity Taxes&Market EquilibriumAs t increases,ps falls,pb rises,andqt falls.Quantity Taxes&Market EquilibriumThe tax paid per unit by the buyer isQuantity Taxes&Market EquilibriumThe tax paid per unit by the buyer
28、 isThe tax paid per unit by the seller isQuantity Taxes&Market EquilibriumThe total tax paid(by buyers and sellerscombined)isElasticity and Tax IncidenceWhat was the impact of tax?Taxes discourage market activity.When a good is taxed,the quantity sold is smaller.Buyers and sellers share the tax burd
29、en.Tax Incidence and Own-Price ElasticitiesThe incidence of a quantity tax depends upon the own-price elasticities of demand and supply.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsTax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*
30、$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 approximatelyTax Incidence and Own-Price ElasticitiesAround p=p*the own-price elasticityof demand is approximatelyTax Incidence and Ow
31、n-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsTax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsChange to sellersprice is ps-p*.Change to quantitydemanded is D Dq.D DqTax Incidence and Own-Price ElasticitiesAround p=p*the own-price elasticityof
32、 supply is approximatelyTax Incidence and Own-Price ElasticitiesAround p=p*the own-price elasticityof supply is approximatelyTax 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)
33、MarketdemandMarketsupplyp*q*pbpbqtpbpsTax paid by buyersTax paid by sellersTax incidence=Tax Incidence and Own-Price ElasticitiesTax incidence=Tax Incidence and Own-Price ElasticitiesTax incidence=SoTax Incidence and Own-Price ElasticitiesTax incidence isThe fraction of a$t quantity tax paidby buyer
34、s rises as supply becomes moreown-price elastic or as demand becomesless own-price elastic.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsAs market demandbecomes less own-price elastic,taxincidence shifts moreto the buyers.Tax Incidence and Own-Price Elasticiti
35、espD(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 moreto the b
36、uyers.Tax Incidence and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyps=p*$tpbqt=q*As market demandbecomes less own-price elastic,taxincidence shifts moreto the buyers.When e eD=0,buyers pay the entire tax,even though it is levied on the sellers.Tax Incidence and Own-Price ElasticitiesTax
37、 incidence isSimilarly,the fraction of a$t quantitytax paid by sellers rises as supplybecomes less own-price elastic or asdemand becomes more own-price elastic.Elasticity and Tax Incidence So,how is the burden of the tax divided?The burden of a tax falls more heavily on the side of the market that i
38、s less elastic.Deadweight Loss and Own-Price ElasticitiesA 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 taxs deadweight loss,or excess burden.Deadweight Loss and
39、Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*No taxDeadweight Loss and Own-Price ElasticitiespD(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)Market
40、demandMarketsupplyp*q*No taxCSPSDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*No taxCSPSDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PSDeadweight Loss and Own-Price ElasticitiespD(p),S(p)Marke
41、tdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p)
42、,S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto governmentTaxDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSThe tax reducesboth CS and PS,transfers surplusto government,and lowers total surplus.TaxDeadweight
43、Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsCSPSTaxDeadweight lossDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight lossDeadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight
44、 loss fallsas market demandbecomes less own-price elastic.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyp*q*$tpbqtpsDeadweight loss fallsas market demandbecomes less own-price elastic.Deadweight Loss and Own-Price ElasticitiespD(p),S(p)MarketdemandMarketsupplyps=p*$tpbq
45、t=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 ElasticitiesDeadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.If either eD=0 or eS=0 then the deadweight loss is zero.