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Chapter Sixteen Equilibrium Market Equilibrium A market clears or is in equilibrium when the total quantity demanded by buyers exactly equals the total quantity supplied by sellers. Market Equilibrium Market p demand Market supply q=S(p) D(p*) = S(p*); the market is in equilibrium. p* q=D(p) q* D(p), S(p) Market Equilibrium Market p demand Market supply q=S(p) D(p’) < S(p’); an excess of quantity supplied over quantity demanded. q=D(p) p’ p* D(p’) S(p’) D(p), S(p) Market price must fall towards p*. Market Equilibrium Market p demand Market supply q=S(p) D(p”) > S(p”); an excess of quantity demanded over quantity supplied. q=D(p) p* p” S(p”) D(p”) D(p), S(p) Market price must rise towards p*. Market Equilibrium An example of calculating a market equilibrium when the market demand and supply curves are linear. D(p) a bp S(p) c dp Market Equilibrium Market p demand Market supply S(p) = c+dp What are the values of p* and q*? p* D(p) = a-bp q* D(p), S(p) Market Equilibrium D(p) a bp S(p) c dp At the equilibrium price p*, D(p*) = S(p*). That is, a bp* c dp* which gives ac p bd * ad bc and q D(p ) S(p ) . bd * * * Market Equilibrium Market p demand * Market supply S(p) = c+dp p ac bd D(p) = a-bp ad bc q bd * D(p), S(p) Market Equilibrium Two special cases are when quantity supplied is fixed, independent of the market price, and when quantity supplied is extremely sensitive to the market price. Market Equilibrium Market p demand Market quantity supplied is fixed, independent of price. S(p) = c+dp, so d=0 and S(p) c. p* D-1(q) = (a-q)/b q* = c q Market Equilibrium Market p demand p* = (a-c)/b Market quantity supplied is fixed, independent of price. S(p) = c+dp, so d=0 and S(p) c. p* = D-1(q*); that is, p* = (a-c)/b. D-1(q) = (a-q)/b q* = c q Market Equilibrium Two special cases are when quantity supplied is fixed, independent of the market price, and when quantity supplied is extremely sensitive to the market price. Market Equilibrium p Market quantity supplied is extremely sensitive to price. q Market Equilibrium Market p demand Market quantity supplied is extremely sensitive to price. S-1(q) = p*. p* = D-1(q*) = (a-q*)/b so q* = a-bp* p* D-1(q) = (a-q)/b q* = a-bp* q Quantity Taxes A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded. If the tax is levied on sellers then it is called an excise tax. If the tax is levied on buyers then it is called a sales tax. Quantity Taxes What is the effect of a quantity tax on a market’s equilibrium? How are prices affected? How is the quantity traded affected? Who actually pays the tax? How is the market’s ability to generate gains-to-trade altered? Quantity Taxes A tax makes the price paid by buyers, pb, different from the price received by sellers, ps. In fact, the buyer and seller prices must differ by exactly the amount of the tax. pb ps t Quantity Taxes Even with a tax present the market must still clear, so the quantity demanded by buyers facing the price pb and the quantity supplied by sellers facing the price ps must be equal. D(pb ) S(ps ) Quantity Taxes D(pb ) S(ps ) pb ps t and describe the market’s equilibrium. Notice that these two conditions apply no matter if the tax is levied on sellers or on buyers. Quantity Taxes D(pb ) S(ps ) pb ps t 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 levied at a rate of $t has exactly the same effect on a competitive market’s equilibrium as an excise tax levied at a rate of $t. Quantity Taxes & Market Equilibrium Market p demand Market supply No tax p* q* D(p), S(p) Quantity Taxes & Market Equilibrium Market p demand Market supply $t pb p* ps qt q* An excise tax raises the market supply curve by $t, raises the buyers’ price and lowers the quantity traded. D(p), S(p) And sellers receive only ps = pb - t. Quantity Taxes & Market Equilibrium Market p demand Market supply No tax p* q* D(p), S(p) Quantity Taxes & Market Equilibrium Market p demand Market supply An sales tax lowers the market demand curve by $t p* $t q* D(p), S(p) Quantity Taxes & Market Equilibrium Market p demand p* ps Market supply $t qt q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. D(p), S(p) Quantity Taxes & Market Equilibrium Market p demand pb p* ps Market supply $t qt q* An sales tax lowers the market demand curve by $t, lowers the sellers’ price and reduces the quantity traded. D(p), S(p) And buyers pay pb = ps + t. Quantity Taxes & Market Equilibrium Market p demand Market supply $t pb p* ps $t qt 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. D(p), S(p) Quantity Taxes & Market Equilibrium Who pays the tax of $t per unit traded? The division of the $t between buyers and sellers is called the incidence of the tax. Quantity Taxes & Market Equilibrium Market Market p demand supply Tax paid by buyers pb p* ps Tax paid by sellers qt q* D(p), S(p) Quantity Taxes & Market Equilibrium An example of computing the effects of a quantity tax on a market equilibrium. Again suppose the market demand and supply curves are linear. D(pb ) a bpb S(ps ) c dps Quantity Taxes & Market Equilibrium D(pb ) a bpb and S(ps ) c dps . With the tax, the market equilibrium satisfies pb ps t and D(pb ) S(ps ) so pb ps t and a bpb c dps . Substituting for pb gives a c bt a b(ps t ) c dps ps . bd Quantity Taxes & Market Equilibrium a c bt ps and bd pb ps t give a c dt pb bd The quantity traded at equilibrium is qt D( pb ) S( ps ) ad bc bdt a bpb . bd Quantity Taxes & Market Equilibrium a c bt ps bd a c dt pb bd ad bc bdt q bd t The total tax paid (by buyers and sellers combined) is ad bc bdt T tq t . bd t Deadweight Loss and Own-Price Elasticities A quantity tax imposed on a competitive market reduces the quantity traded at equilibrium and so reduces the gains-to-trade; i.e. the sum of Consumers’ Surplus and Producers’ Surplus is reduced. The loss in total surplus is called the deadweight loss, or excess burden, of the tax. Deadweight Loss and Own-Price Elasticities Market p demand Market supply No tax p* q* D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply No tax p* CS PS q* D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply $t pb CS p* ps PS qt q* The tax reduces both CS and PS D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply $t pb CS p* Tax ps PS qt q* The tax reduces both CS and PS, transfers surplus to government, and lowers total surplus. D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply $t pb CS p* Tax ps PS Deadweight loss qt q* D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply $t pb p* ps qt q* Deadweight loss falls as market demand becomes less ownprice elastic. D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand Market supply $t pb p* ps qt q* Deadweight loss falls as market demand becomes less ownprice elastic. D(p), S(p) Deadweight Loss and Own-Price Elasticities Market p demand pb ps= p* Market supply $t Deadweight loss falls as market demand becomes less ownprice elastic. D(p), S(p) qt = q* When eD = 0, the tax causes no deadweight loss. Deadweight Loss and Own-Price Elasticities Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more ownprice elastic. If either eD = 0 or eS = 0 then the deadweight loss is zero.
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