Optimal Commodity Taxation Ramsey Rule Reinterpreted Recall the formula for excess burden for good X EB X Xt 2 X<X Planners optimization problem is to minimize total excess burden by choose taxes on goods X and Y, subject to a revenue constraint
11 Optimal Commodity Taxation: Ramsey Rule Reinterpreted • Recall the formula for excess burden for good X: EB P Xt X = X X 1 2 2 • Planner’s optimization problem is to minimize total excess burden by choose taxes on goods X and Y, subject to a revenue constraint
Optimal Commodity Taxation Ramsey Rule Reinterpreted Setting up the LaGrangian minL=olnxPx Xtx+an Yty+AR-Px Xtx-P Yt) 12
12 Optimal Commodity Taxation: Ramsey Rule Reinterpreted • Setting up the LaGrangian: min ( ) , , L P Xt P Yt R P Xt P Yt t t X X X Y Y Y X X Y Y X Y = + + − − 1 2 1 2 2 2