The Song Remains Not the Same: Correlated Intercept and Slope Uncertainties Matter to Prices versus Quantities

Richard D. Horan and James Shortle

Journal of the Association of Environmental and Resource Economists, 2021, vol. 8, issue 4, 691 - 719

Abstract: Weitzman’s “relative slope rule” (RSR) is a rule of thumb for determining the relative efficiency of quantity versus price instruments to regulate firms under asymmetric information. This rule identifies the more efficient instrument based on the relative slopes of the marginal benefit and cost functions. The RSR relies on three key assumptions: the unknown cost and benefit functions are well represented by second-order approximations, the regulator’s uncertainty is confined to the intercepts of the linearized marginal functions, and these intercepts are not correlated. Subsequent work has adopted these assumptions as the default case and found the RSR to be robust, although Malcomson showed the RSR may break down when the marginal cost function’s intercept and slope are both uncertain and correlated. We provide theoretical support for the presence of this correlated uncertainty and, using numerical examples, show the relative slope rule may be in error in this setting.

Date: 2021
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