microlower.jpg © 2010 W. W. Norton & Company, Inc. microtitle.jpg microedition.jpg varianname.jpg 16 Equilibrium microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uA market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p) q=D(p) Market demand microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p S(p) Market supply q=S(p) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q* D(p*) = S(p*); the market is in equilibrium. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* S(p’) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. p’ D(p’) Market price must fall towards p*. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”) microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* D(p”) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. p” S(p”) Market price must rise towards p*. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uAn example of calculating a market equilibrium when the market demand and supply curves are linear. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp p* q* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp p* q* What are the values of p* and q*? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uCan we calculate the market equilibrium using the inverse market demand and supply curves? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uCan we calculate the market equilibrium using the inverse market demand and supply curves? uYes, it is the same calculation. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium the equation of the inverse market demand curve. And the equation of the inverse market supply curve. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium q D-1(q), S-1(q) D-1(q) = (a-q)/b Market inverse demand Market inverse supply S-1(q) = (-c+q)/d p* q* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium q D-1(q), S-1(q) D-1(q) = (a-q)/b Market demand S-1(q) = (-c+q)/d p* q* At equilibrium, D-1(q*) = S-1(q*). Market inverse supply microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, which gives microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, which gives and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium q D-1(q), S-1(q) D-1(q) = (a-q)/b Market demand Market supply S-1(q) = (-c+q)/d microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uTwo special cases: –quantity supplied is fixed, independent of the market price, and –quantity supplied is extremely sensitive to the market price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is fixed, independent of price. p q q* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q q* = c Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q q* = c D-1(q) = (a-q)/b Market demand Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q p* D-1(q) = (a-q)/b Market demand q* = c Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q p* = (a-c)/b D-1(q) = (a-q)/b Market demand q* = c p* = D-1(q*); that is, p* = (a-c)/b. Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q D-1(q) = (a-q)/b Market demand q* = c p* = D-1(q*); that is, p* = (a-c)/b. p* = (a-c)/b Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium S(p) = c+dp, so d=0 and S(p) º c. p q D-1(q) = (a-q)/b Market demand q* = c p* = D-1(q*); that is, p* = (a-c)/b. with d = 0 give p* = (a-c)/b Market quantity supplied is fixed, independent of price. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium uTwo special cases are –when quantity supplied is fixed, independent of the market price, and –when quantity supplied is extremely sensitive to the market price. ü microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is extremely sensitive to price. p q microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p q p* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p q p* D-1(q) = (a-q)/b Market demand microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p q p* D-1(q) = (a-q)/b Market demand q* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Market Equilibrium Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p q p* D-1(q) = (a-q)/b Market demand q* = a-bp* p* = D-1(q*) = (a-q*)/b so q* = a-bp* microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes uA 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes uWhat is the effect of a quantity tax on a market’s equilibrium? uHow are prices affected? uHow is the quantity traded affected? uWho pays the tax? uHow are gains-to-trade altered? microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes uA tax rate t makes the price paid by buyers, pb, higher by t from the price received by sellers, ps. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes uEven 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. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes and describe the market’s equilibrium. Notice these conditions apply no matter if the tax is levied on sellers or on buyers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes and describe the market’s equilibrium. Notice that these two conditions apply no matter if the tax is levied on sellers or on buyers. Hence, a sales tax rate $t has the same effect as an excise tax rate $t. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* $t An excise tax raises the market supply curve by $t microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An excise tax raises the market supply curve by $t, raises the buyers’ price and lowers the quantity traded. $t pb qt microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An excise tax raises the market supply curve by $t, raises the buyers’ price and lowers the quantity traded. $t pb qt And sellers receive only ps = pb - t. ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t $t microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. $t qt ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. $t pb pb qt pb And buyers pay pb = ps + t. ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* A sales tax levied at rate $t has the same effects on the market’s equilibrium as does an excise tax levied at rate $t. $t pb pb qt pb ps $t microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium uWho pays the tax of $t per unit traded? uThe division of the $t between buyers and sellers is the incidence of the tax. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by buyers microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by sellers microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by buyers Tax paid by sellers microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium uE.g. suppose the market demand and supply curves are linear. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies and so and microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies and so and Substituting for pb gives microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium and give The quantity traded at equilibrium is microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium As t ® 0, ps and pb ® the equilibrium price if there is no tax (t = 0) and qt the quantity traded at equilibrium when there is no tax. ® microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium As t increases, ps falls, pb rises, and qt falls. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is The tax paid per unit by the seller is microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Quantity Taxes & Market Equilibrium The total tax paid (by buyers and sellers combined) is microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities uThe incidence of a quantity tax depends upon the own-price elasticities of demand and supply. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Change to buyers’ price is pb - p*. Change to quantity demanded is Dq. Dq microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Change to sellers’ price is ps - p*. Change to quantity demanded is Dq. Dq microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by buyers Tax paid by sellers microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by buyers Tax paid by sellers Tax incidence = microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Tax incidence = microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Tax incidence = So microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Tax incidence is The fraction of a $t quantity tax paid by buyers rises as supply becomes more own-price elastic or as demand becomes less own-price elastic. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply ps= p* $t pb qt = q* As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply ps= p* $t pb qt = q* As market demand becomes less own- price elastic, tax incidence shifts more to the buyers. When eD = 0, buyers pay the entire tax, even though it is levied on the sellers. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Tax Incidence and Own-Price Elasticities Tax incidence is Similarly, the fraction of a $t quantity tax paid by sellers rises as supply becomes less own-price elastic or as demand becomes more own-price elastic. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities uA 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 tax’s deadweight loss, or excess burden. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS The tax reduces both CS and PS microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS The tax reduces both CS and PS, transfers surplus to government Tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS The tax reduces both CS and PS, transfers surplus to government Tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS The tax reduces both CS and PS, transfers surplus to government Tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS The tax reduces both CS and PS, transfers surplus to government, and lowers total surplus. Tax microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps CS PS Tax Deadweight loss microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Deadweight loss microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Deadweight loss falls as market demand becomes less own- price elastic. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Deadweight loss falls as market demand becomes less own- price elastic. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply ps= p* $t pb qt = q* Deadweight loss falls as market demand becomes less own- price elastic. When eD = 0, the tax causes no deadweight loss. microlower.jpg © 2010 W. W. Norton & Company, Inc. ‹#› Deadweight Loss and Own-Price Elasticities uDeadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic. uIf either eD = 0 or eS = 0 then the deadweight loss is zero.