Chapter 16: Equilibrium

Transcription

1 Econ 401 Price Theory Chapter 16: Equilibrium Instructor: Hiroki Watanabe Summer / 44 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 2 / 44

2 A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. 3 / 44 4 / 44

3 5 / 44 Figure: 6 / 44

4 In a competitive market, laissez-faire regime automatically adjusts price to realize maximum total surplus (first fundamental theorem of welfare economics. C.f. Ch31). 7 / 44 Two special cases: 1 quantity supplied is fixed, independent of the market price, and 2 quantity supplied is extremely sensitive to the market price. 8 / 44

5 9 / 44 Figure: 10 / 44

6 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 11 / 44 Change in Price 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 an excise tax. If the tax is levied on buyers then it is a sales tax. 12 / 44

7 Change in Price What is the effect of a quantity tax on a market s equilibrium? How are prices affected? How is the quantity traded affected? Who pays the tax? 13 / 44 Clearing Market with Tax A tax rate t makes the price paid by buyers, p b, higher by t from the price received by sellers, p s. p b p s = t. Even with a tax the market must clear. Quantity demanded by buyers at price p b must equal quantity supplied by sellers at price p s : D(p b ) = S(p s ). 14 / 44

8 Clearing Market with Tax Market clearing conditions: p b p s = t D(p b ) = S(p s ). Note that these two conditions apply no matter if the tax is levied on sellers or on buyers. A sales tax rate t has the same effect as an excise tax rate t 15 / 44 Clearing Market with Tax 16 / 44

9 Clearing Market with Tax In general, it s easier to use an excise tax. MC(y) = p is the supply function. MC(y) is the additional cost of producing one more unit of y. When a unit tax t is imposed, we can simply redefine MC as MC(y) ˆ := MC(y) + t and use this as a new supply function. 17 / 44 Who Pays the Tax Tax Incidence Who pays the tax of t per unit traded? The division of the t between buyers and sellers is the incidence of the tax. When the excise tax is imposed, it s just the sellers who take on the tax burden? Technically yes, but the buyers also have to face a higher price than before and share the tax burden as well. 18 / 44

10 Who Pays the Tax Tax Incidence 19 / 44 Who Pays the Tax Tax Incidence Figure: 20 / 44

11 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 21 / 44 The incidence of a quantity tax depends upon the own-price elasticities of demand and supply. 22 / 44

12 23 / 44 Figure: Recall the price elasticity of demand is the percentage change in q D divided by the percentage change in p: ε D (q ) = q/q (p b p )/p p b p = q p ε D (q ) q. 24 / 44

13 25 / 44 Figure: The price elasticity of supply is the percentage change in q S divided by the percentage change in p: ε S (q ) = q/q (p p s )/p p p s = q p ε S (q ) q. 26 / 44

14 27 / 44 Computing Tax Incidence Figure: Tax incidence: Tax Incidence := tax burden on buyers tax burden on sellers = (p b p )q t (p p s )q t = p b p p p s = q p /(ε D q ) q p /(ε S q ) = εs ε D. 28 / 44

15 Computing Tax Incidence Buyers take on more tax burden when: 1 supply becomes more own-price elastic, or 2 demand becomes less own-price elastic. 29 / 44 Example: Buyer s Burden Increases as Demand Becomes Elastic 30 / 44

16 Example: Buyer s Burden Increases as Demand Becomes Elastic 31 / 44 Figure: Example: Buyer s Burden Increases as Demand Becomes Elastic 32 / 44

17 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 33 / 44 A quantity tax imposed on a competitive market usually reduces the quantity traded. Reduction in total surplus (=CS + PS). Deadweight Loss (DWL) is the lost total surplus. Had it not been for tax, we wouldn t have DWL. 34 / 44

18 35 / 44 Figure: Deadweight loss due to a quantity tax rises as either aggregate demand or aggregate supply becomes more own-price elastic. If either ε D = 0 or ε S = 0 then the deadweight loss is zero. 36 / 44

19 37 / 44 Figure: 38 / 44

20 39 / 44 Figure: 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 40 / 44

21 Tax usually creates DWL. Fine. Then does subsidy produce an extra SEW? 41 / 44 $ $ Supply Supply CS Supply with subsidy CS PS Demand PS Demand q q O O $ $ SEW=CS+PS-Subsidy payment Supply Supply Supply with subsidy Supply with subsidy DWL Subsidy payment Demand Demand q q O O = SEW 42 / 44

22 1 Clearing Market 2 Tax Change in Price Clearing Market with Tax Who Pays the Tax Tax Incidence 3 Tax Incidence & Own-Price Elasticities Computing Tax Incidence Example: Buyer s Burden Increases as Demand Becomes Elastic 4 Deadweight Loss & Own-Price Elasticity 5 Deadweight Loss & Subsidy 6 Summary 43 / 44 Market equilibrium realizes maximum total surplus. Tax incidence and elasticity. 44 / 44