Revenue functions and Dupuit curves for indirect taxes with cross-border shopping

The partial revenue from each indirect tax and the total revenue from all indirect taxes on consumer goods are derived as functions of all commodity prices, the tax rates of each commodity, total expenditure and demographic variables using a complete demand system. Within this framework we define Dupuit curves, or Laffer curves, and analyze their existence and maximum points theoretically and empirically. The macro demand system is based on exact aggregation across all households in the economy, and on exact aggregation across commodities within a detailed non-homogeneous utility tree. An empirical application for Norway with 55 commodity groups is presented. For beer, wine, spirits and tobacco, consumers can choose among buying at home, cross-border shopping/ tax-free shopping and smuggling. These substitution possibilities increase substantially the price elasticities for these goods. The partial revenue from wine as function of the tax share on wine has a single maximum value close to the actual tax rate in Norway in 1999, conditioned on all the other exogenous variables. The total revenue as a function of the tax share on wine also has a single maximum value, larger than that for the partial revenue. The same results are valid for spirits. For beer and tobacco there is no revenue maximizing tax share.