Taxing a Commodity with and without Revenue Neutrality: A Calibrated Theoretical Consumer Equilibrium Model

Abstract

It has long been recognized that taxing a commodity that generates negative externalities can be used to reduce its consumption. One way to do this is to impose revenue neutrality but that may alter the tax rate required to meet a consumption reduction target. We explore the relationships among the commodity tax rate, the demand and supply elasticities, and the revenue offsets by calibrating a theoretical consumer equilibrium model and then recalibrating it with alternative parameter configurations. For each configuration we simulate equilibrium for three policy scenarios: no neutrality, neutrality achieved by subsidizing other commodities, and neutrality achieved by income transfer.

Appendix: Standard Parameter Values

Compensated price elasticities:

$$ \begin{array}{*{20}{c}} {{\varepsilon_{\text{aa}}} = - 0.{5}00} \hfill & {{\varepsilon_{\text{ab}}} = 0.{5}00} \hfill & {{\varepsilon_{\text{ba}}} = 0.{25}0} \hfill & {{\varepsilon_{\text{bb}}} = - 0.{25}0} \hfill \\ \end{array} $$

Expenditure elasticities:

$$ \begin{array}{*{20}{c}} {{\eta_{\text{a}}} = {1}.000} \hfill & {{\eta_{\text{b}}} = {1}.000} \hfill \\ \end{array} $$

Derived coefficients of demand equations:

$$ \begin{array}{*{20}{c}} {{\gamma_{\text{aa}}} = 0.0{56}} \hfill & {{\gamma_{\text{ab}}} = - 0.0{56}} \hfill & {{\gamma_{\text{ba}}} = - 0.0{56}} \hfill & {{\gamma_{\text{bb}}} = 0.0{56}} \hfill \\ {{\alpha_{\text{a}}} = 0.{333}} \hfill & {{\alpha_{\text{b}}} = 0.{667}} \hfill & {{\beta_{\text{a}}} = 0.000} \hfill & {{\beta_{\text{b}}} = 0.000} \hfill \\ \end{array} $$

Supply elasticities:

$$ {\lambda_{\text{a}}} = \infty {\lambda_{\text{b}}} = \infty $$

Saving rate:

φ = 0.050