ch11_补偿性需求曲线.ppt

1,Chapter 11 Appendix,2,Derivation of the Formula for Excess Burden of a Unit Tax,W = 1/2T DQ,Where: W = excess burden (Deadweight loss) T = tax DQ = change in equilibrium quantity as a result of the tax,3,Solving for DQ,Step 1: Some Definitions T = PG PN DPG = PG P* DPN = PN P*,4,Solving for DQ,Step 2: Elasticity comes into play ED =(DQ/Q*)/(DPG/P*) =(DQ/Q*) (P*/DPG) =(DQ/Q*) P*/(PG P*) ES =(DQ/Q*)/(DPN/P*) =(DQ/Q*) (P*/DPN) = (DQ/Q*) P*/(PN P*),5,Solving for DQ,Step 3: Solving for PG ED = (DQ/Q*) P*/(PG P*) (PG P*) = (DQ/Q*) (P*/ED) PG = (DQ/Q*) (P*/ED) + P*,6,Solving for DQ,Step 4: Solving for PN ES = (DQ/Q*) (P*/(PN P*) (PN P*) = (DQ/Q*) (P*/ES) PN = (DQ/Q*) (P*/ES) +P*,7,Solving for DQ,Step 5: Using the T = PG PN definition T = PG PN = (DQ/Q*) (P*/ED) +P* (DQ/Q*) (P*/ES) +P* = (DQ/Q*) (P*/ED) (DQ/Q*) (P*/ES) = (DQ/Q*) (P*) (1/ED) (1/ES) = (DQ/Q*) (P*) (ES ED)/(EDES),8,Solving for DQ,Step 6: Solving T = (DQ/Q*) (P*) (ES ED)/(EDES) for DQ T = (DQ/Q*) (P*) (ES ED)/(EDES) So DQ = T(P*/Q*) (EDES)/(ES ED) Plugging back into W = 1/2TDQ W = 1/2T2(P*/Q*) (EDES)/(ES ED),9,Derivation for the Ad-Valorem Tax,If the pre- and post-tax prices are close to one another, then W = 1/2t2(P*Q*) (EDES) / (ES ED) If LRAC is perfectly inelastic, then W = 1/2t2 (P*Q*) (ED) (ES)/(ES ED) = 1/2t2 (P*Q*) (ED) because (ES)/(ES ED) approaches 1.,10,Individual Losses in Welfare Under Perfect Competition,If there is perfect competition, then ED is infinite from the firm owners perspective. This implies that DWL = 1/2t2(P*Q*)ES,11,Compensated Demand Curves,Recall that compensated demand curves show the relationship between price and quantity demanded, excluding the income effect. It only looks at the substitution away from the taxed good.,12,Figure 11A.1 Regular and Compensated Demand Curves For a Normal Good,13,Compensated Supply Curves,Recall that compensated supply curves show the relationship between price and quantity supplied excluding the income effect. It only looks at the substitution away from the taxed good.,14,Figure 11A.2 Using A Compensated Demand Curve to Isolate The