INTMIC9.jpg Chapter 16 Equilibrium Market Equilibrium uA market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. Market Equilibrium p D(p) q=D(p) Market demand Market Equilibrium p S(p) Market supply q=S(p) Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) Market Equilibrium p D(p), S(p) q=D(p) Market demand Market supply q=S(p) p* q* 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. 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 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*. 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 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*. Market Equilibrium uAn example of calculating a market equilibrium when the market demand and supply curves are linear. Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp p* q* 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*? Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives Market Equilibrium At the equilibrium price p*, D(p*) = S(p*). That is, which gives and Market Equilibrium p D(p), S(p) D(p) = a-bp Market demand Market supply S(p) = c+dp Market Equilibrium uCan we calculate the market equilibrium using the inverse market demand and supply curves? Market Equilibrium uCan we calculate the market equilibrium using the inverse market demand and supply curves? uYes, it is the same calculation. Market Equilibrium the equation of the inverse market demand curve. And the equation of the inverse market supply curve. 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* 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 Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, which gives Market Equilibrium and At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is, which gives and 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 Market Equilibrium uTwo special cases: –quantity supplied is fixed, independent of the market price, and –quantity supplied is extremely sensitive to the market price. Market Equilibrium Market quantity supplied is fixed, independent of price. p q q* 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. 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. 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. 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. 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. 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. 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 Market Equilibrium Market quantity supplied is extremely sensitive to price. p q Market Equilibrium Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p q p* 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 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* 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* 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. 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? Quantity Taxes uA tax rate t makes the price paid by buyers, pb, higher by t from the price received by sellers, ps. 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. Quantity Taxes and describe the market’s equilibrium. Notice these conditions apply no matter if the tax is levied on sellers or on buyers. 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. Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax 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 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 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 Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* No tax 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 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 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 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 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. Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by buyers Quantity Taxes & Market Equilibrium p D(p), S(p) Market demand Market supply p* q* pb pb qt pb ps Tax paid by sellers 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 Quantity Taxes & Market Equilibrium uE.g. suppose the market demand and supply curves are linear. Quantity Taxes & Market Equilibrium and Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies and so and Quantity Taxes & Market Equilibrium and With the tax, the market equilibrium satisfies and so and Substituting for pb gives Quantity Taxes & Market Equilibrium and give The quantity traded at equilibrium is 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. ® Quantity Taxes & Market Equilibrium As t increases, ps falls, pb rises, and qt falls. Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is Quantity Taxes & Market Equilibrium The tax paid per unit by the buyer is The tax paid per unit by the seller is Quantity Taxes & Market Equilibrium The total tax paid (by buyers and sellers combined) is Tax Incidence and Own-Price Elasticities uThe incidence of a quantity tax depends upon the own-price elasticities of demand and supply. Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps 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 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of demand is approximately Tax Incidence and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps 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 Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately Tax Incidence and Own-Price Elasticities Around p = p* the own-price elasticity of supply is approximately 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 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 = Tax Incidence and Own-Price Elasticities Tax incidence = Tax Incidence and Own-Price Elasticities Tax incidence = So 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. 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. 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. 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. 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. 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. 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. Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax PS Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* No tax CS PS 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 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 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 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 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 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 Deadweight Loss and Own-Price Elasticities p D(p), S(p) Market demand Market supply p* q* $t pb qt ps Deadweight loss 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. 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. 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. 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.