"We show that the effects of tariff changes on welfare and import volume can be fully characterized by their effects on the generalized mean and variance of the tariff distribution. Using these tools, we derive new results for welfare- and market-access-improving tariff changes, which imply two 'cones of liberalization' in price space. Because welfare is negatively but import volume positively related to the generalized variance, the cones do not intersect, which poses a dilemma for trade policy reform. Finally, we show that generalized and trade-weighted moments are mutually proportional when the trade expenditure function is CES"--National Bureau of Economic Research web site.