文档介绍：1 Chapter 11 Appendix 2 Derivation of the Formula for Excess Burden of a Unit Tax W = 1/2 T ×Q Where: W = excess burden (Deadweight loss) T = tax Q = change in equilibrium quantity as a result of the tax 3 Solving for Q Step 1: Some Definitions T = P G–P N P G = P G –P* P N = P N–P*4 Solving for Q Step 2: es into play E D =(Q/Q* )/(P G/P*) =( Q/Q* ) × (P*/ P G) =( Q/Q* ) × [P* /(P G – P* )] E S =(Q/Q* )/(P N/P*) =( Q/Q* ) × (P*/ P N) = ( Q/Q* ) × [P* /(P N– P* )] 5 Solving for Q Step 3: Solving for P GE D = ( Q/Q* ) × [P* /(P G –P* )] (P G–P*) = ( Q/Q* ) × (P*/E D) P G = ( Q/Q* ) × (P*/E D ) + P*6 Solving for Q Step 4: Solving for P N E S = ( Q/Q* ) × (P* /(P N–P*) (P N–P*) = ( Q/Q* ) × (P*/E S) P N = ( Q/Q* ) × (P*/E S ) + P* 7 Solving for Q Step 5: Using the T = P G –P N definition T = P G –P N = ( Q/Q* ) × (P*/E D ) +P *– [( Q/Q* ) × (P*/E S ) +P*] = ( Q/Q* ) × (P*/E D ) – ( Q/Q* ) × (P*/E S ) = ( Q/Q* ) × (P* ) × [(1/ E D ) – (1/ E S )] = ( Q/Q* ) × (P* ) × [(E S–E D )/(E DE S )] 8 Solving for Q Step 6: Solving T = ( Q/Q* ) × (P* ) [( E S–E D )/(E DE S )] for Q T = ( Q/Q* ) × (P* ) [( E S–E D )/(E DE S )] So Q = T(P*/Q* ) × [(E DE S )/(E S–E D )] Plugging back into W = 1/2 TQ W = 1/2 T 2(P*/Q* ) × [(E DE S )/(E S–E D )] 9 Derivation for the Ad-Valorem Tax If the pre- and post-tax prices are close to one another, then W = 1/2 t 2(P*Q* ) × [(E DE S ) / ( E S–E D )] If LRAC is perfectly inelastic, then W = 1/2 t 2 (P*Q* ) × (E D ) × [(E S )/(E S– E D )] = 1/2 t 2 (P*Q* ) × (E D) because [( E S )/(E S–E D )] approaches 1. 10 Individual Losses in Welfare Under petition If there is petition, then E D is infinite from the firm owner ’s perspective. This implies that DWL = 1/2 t 2(P*Q*)E S