zev
Uploaded by
15 SLIDES
309 VUES
150LIKES

Understanding the Excess Burden of a Unit Tax: Derivation of the Formula and Implications

DESCRIPTION

This chapter delves into the derivation of the excess burden (deadweight loss) caused by a unit tax, quantified by W = 1/2T × DQ. Here, T represents the tax, and DQ signifies the change in equilibrium quantity resulting from the tax imposition. The chapter guides readers through the steps of solving for DQ using definitions and elasticity considerations while analyzing compensated demand and supply curves. Additionally, it discusses the implications of perfect competition on welfare loss, providing a comprehensive understanding of taxation effects in economic theory.

1 / 15

Télécharger la présentation

Understanding the Excess Burden of a Unit Tax: Derivation of the Formula and Implications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 11Appendix

  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 owner’s 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 Compensated Demand Curve P1 Price Regular Demand Curve Q1 0 Gasoline per Year

  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 Substitution Effect of a Tax-Induced Price Increase ST S E2 PG E1 1.00 Price (Dollars) A PN DR DQS DC Q2 Q1 Gasoline per Year (Gallons) 0 DQ

  15. Figure 11A.3 A Compensated Supply Curve for an Input Compensated Labor Supply Curve W1 Wages Regular Labor Supply Curve Q1 0 Input Services per Year

More Related