Antitrust Policy: The Impact of Revenue Penalties on Price

Abstract

The paper examines the impact on a firm’s price when it faces the possibility of an antitrust investigation and associated potential revenue penalty. As well as presenting a general model of antitrust intervention, an illustrative example reflecting the provisions of the 1998 UK Competition Act is offered, the example being developed to explore the implications of the probability of antitrust intervention and punishment increasing non-linearly as a firm’s profit rises.

Appendix

Second order condition to be satisfied to ensure that profits are in fact maximized in Eq. 1:

$$ \begin{array}{*{20}l} {{\frac{{{\text{d}}^{2} \Pi }} {{{\text{d}}P^{2} }} = 2{\left( {\frac{{{\text{d}}q}} {{{\text{d}}P}}} \right)} + P\frac{{{\text{d}}^{2} q}} {{{\text{d}}P^{2} }} - \frac{{{\text{d}}^{2} C}} {{{\text{d}}q^{2} }}2{\left( {\frac{{{\text{d}}q}} {{{\text{d}}P}}} \right)} - \frac{{{\text{d}}C}} {{{\text{d}}q}}\frac{{{\text{d}}^{2} q}} {{{\text{d}}P^{2} }}} \hfill} \\ {{\quad \quad \quad - \frac{{{\text{d}}\gamma }} {{{\text{d}}\pi }}\frac{{{\text{d}}\pi }} {{{\text{d}}P}}\frac{{{\text{d}}R}} {{{\text{d}}\pi }}\frac{{{\text{d}}\pi }} {{{\text{d}}P}} - \gamma \frac{{{\text{d}}^{2} R}} {{{\text{d}}\pi ^{2} }}{\left( {\frac{{{\text{d}}\pi }} {{{\text{d}}P}}} \right)}^{2} - \gamma \frac{{{\text{d}}R}} {{{\text{d}}\pi }}\frac{{{\text{d}}^{2} \pi }} {{{\text{d}}P^{2} }}} \hfill} \\ {{\quad \quad \quad - \frac{{{\text{d}}R}} {{{\text{d}}\pi }}\frac{{{\text{d}}\pi }} {{{\text{d}}P}}\frac{{{\text{d}}\gamma }} {{{\text{d}}\pi }}\frac{{{\text{d}}\pi }} {{{\text{d}}P}} - R\frac{{{\text{d}}^{2} \gamma }} {{{\text{d}}\pi ^{2} }}{\left( {\frac{{{\text{d}}\pi }} {{{\text{d}}P}}} \right)}^{2} - R\frac{{{\text{d}}\gamma }} {{{\text{d}}\pi }}\frac{{{\text{d}}^{2} \pi }} {{{\text{d}}P^{2} }} < 0} \hfill} \\ \end{array} $$