1EquilibriumECON 370: Microeconomic TheorySummer 2004 – Rice UniversityStanley GilbertEcon 370 - Equilibrium 2Market EquilibriumpD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*D(p*) = S(p*); market is in equilibriumEcon 370 - Equilibrium 3D(p’) < S(p’); Market price must fall towards p*Excess SupplypD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*p’Econ 370 - Equilibrium 4D(p”) > S(p”); Market price must rise towards p*Excess DemandpD(p), S(p)q=D(p)MarketdemandMarketsupplyq=S(p)p*q*p’’2Econ 370 - Equilibrium 5Quantity Taxes: Introduction• Quantity tax - a tax of $t paid on each unit traded• What is the effect of quantity tax on equilibrium?• How are prices affected?• How is the quantity traded affected?• Who pays the tax?• How are gains-to-trade altered?Econ 370 - Equilibrium 6Quantity Taxes• A tax rate t makes price paid by buyers, pbhigher by t from the price received by sellers, ps• Consumers make their decisions based on what they actually pay (pb)• Producers make their decisions based on what they actually receive (ps)• But ps≠ pb, Rather: ps+ t = pb• Even with tax (different consumer and producer prices) the market must clear– That is: D(pb) = S(ps)Econ 370 - Equilibrium 7Mathematically• Market equilibrium is described by:– pb– ps= t and –D(pb) = S(ps)• So, we can solve for either–D(ps+ t) = S(ps) or–D(pb) = S(pb+ t)• Note that it doesn’t matter whether you tax producers or consumers• Prices, quantities, and tax collected are the sameEcon 370 - Equilibrium 8Quantity Taxes on ProducersNo taxpD(p), S(p)p*q*Mkt DMkt S3Econ 370 - Equilibrium 9A producer tax raises market supply curve by $tQuantity Taxes on ProducerspD(p), S(p)p*q*$tMkt DMkt SEcon 370 - Equilibrium 10A producer tax raises the buyers’ price, lowers qQuantity Taxes on ProducerspD(p), S(p)p*q*$tpbqtMkt DMkt SEcon 370 - Equilibrium 11pD(p), S(p)p*q*$tAnd sellers receive only ps= pb-tpbqtpsQuantity Taxes on ProducersMkt DMkt SEcon 370 - Equilibrium 12Quantity Taxes on ConsumersNo taxpD(p), S(p)p*q*Mkt DMkt S4Econ 370 - Equilibrium 13pD(p), S(p)p*q*$tA consumer tax lowers market demand by $tQuantity Taxes on ConsumersMkt DMkt SEcon 370 - Equilibrium 14pD(p), S(p)p*q*$tConsumer tax lowers sellers’ price, reduces qqtpsQuantity Taxes on ConsumersMkt DMkt SEcon 370 - Equilibrium 15pD(p), S(p)p*q*$tAnd buyers pay pb=ps+ tqtpsQuantity Taxes on ConsumersMkt DMkt SpbEcon 370 - Equilibrium 16Identical effects, whether quantity tax levied on sellers or producersQuantity Taxes on ConsumerspD(p), S(p)p*q*$tqtpsMkt DMkt Spb5Econ 370 - Equilibrium 17Tax Incidence• Who pays the tax of $t per unit traded?• Economic incidence (of a tax) – division of tax burden between buyers and sellers after all market adjustments– Not statutory incidenceEcon 370 - Equilibrium 18Tax Incidence GraphpD(p), S(p)p*q*qtpsMkt DMkt SpbSeller’s ShareBuyer’s ShareEcon 370 - Equilibrium 19Quantity Tax Example• Linear market demand and supply curves:•D(pb) = a – bpb•S(ps) = a – bps•We seek– Pretax equilibrium– Post-tax equilibrium– Tax Share• Where Tax shares are– Seller’s Share = p*– ps– Buyer’s Share = pb– p*Econ 370 - Equilibrium 20Tax Incidence and Own-Price Elasticities• The incidence of a quantity tax can be expressed in terms of own-price elasticities of demand and supply6Econ 370 - Equilibrium 21Tax Incidence and Own-Price ElasticitiesAround p = p* the own-price elasticityof demand is approximately***pppqqbD−∆≈ε***qpqppDb××∆≈−⇒εEcon 370 - Equilibrium 22Tax Incidence and Own-Price Elasticities***pppqqsS−∆≈εAround p = p* the own-price elasticityof supply is approximately***qpqppSs××∆≈−⇒εEcon 370 - Equilibrium 23Tax Incidence and Own-Price Elasticities***qpqppDb××∆≈−ε***qpqppSs××∆≈−εDSsbppppεε−≈−−**Tax incidence ratio = sbpppp−−**Econ 370 - Equilibrium 24Tax Incidence and Own-Price ElasticitiesDSsbppppεε−≈−−**Tax incidence ratio is:Consumer Share is:SDSεεε−−Producer Share is:SDDεεε−7Econ 370 - Equilibrium 25Tax Incidence and Own-Price Elasticities• Fraction of quantity tax paid by buyers rises as– supply becomes more own-price elastic– as demand becomes less own-price elastic•When εD= 0, buyers pay entire tax, even though it is levied on the sellers• The fraction of quantity tax paid by sellers rises as– supply becomes less own-price elastic or – as demand becomes more own-price elastic•When εs= 0, sellers pay entire tax, even though it is levied on the buyersEcon 370 - Equilibrium 26DWL and Own-Price Elasticities• A quantity tax imposed on a competitive market– reduces quantity traded– reduces gains-to-trade (i.e. the sum of Consumers’ and Producers’ Surpluses)• Deadweight loss - lost total surplus– Excess burden– Welfare cost– Efficiency costEcon 370 - Equilibrium 27CSPSDWL and Own-Price Elasticities: GraphpD(p), S(p)p*q*Mkt D Mkt SNo taxEcon 370 - Equilibrium 28TaxCSPSDWL and Own-Price Elasticities: GraphpD(p), S(p)p*q*Mkt D Mkt SqtpspbThe tax reduces both CS and PS, transfers some of this surplus to government as tax revenue8Econ 370 - Equilibrium 29TaxCSPSDWL and Own-Price Elasticities: GraphpD(p), S(p)p*q*Mkt D Mkt SqtpspbDead-weight Loss is surplus lost as a result of the taxDWLEcon 370 - Equilibrium 30pD(p), S(p)ps= p*$tpbqt = q*When εD= 0, the tax causes no deadweight lossDWL and Own-Price Elasticities: GraphMkt DMkt SEcon 370 - Equilibrium 31DWL and Own-Price Elasticities• DWL due to a quantity tax rises as either market demand/supply becomes more own-price elastic• If either εD= 0 or εs= 0 then the DWL is