Publisher Correction: Journal of Industry, Competition and Trade

https://doi.org/10.1007/s10842-020-00343-3

The Publisher would like to correct the introduced formatting errors and presentation of the mathematical expressions found on page 12 of the pdf version.

In the original publication, all signs (+) and (−) above the mathematical expressions are not properly aligned and displayed.

The Publisher apologizes for the oversight and for any confusion it may have caused.

The original article has been corrected and the updated equations are presented in this article.

$$ \frac{\partial {\pi}^U}{\partial k}=\overset{\left(-\right)}{\overset{\left(+\right)}{\frac{\partial {\pi}^U}{\partial c}}\overset{\left(-\right)}{\frac{\partial c}{\partial k}}}+\overset{\left(+\right)}{\frac{\overset{\left(+\right)}{\partial {\pi}^U}}{\partial q}\overset{\left(+\right)}{\frac{\partial q}{\partial k}}}=-\frac{k{\left(a-w\right)}^2}{4{\left[2\left(1+v\right)-k-r\right]}^3}<0,\kern1em k\in \left[0,1\right]. $$
$$ \frac{d{\pi}^D}{dr}=\overset{\left(-\right)}{\overset{\left(+\right)}{\frac{\partial {\pi}^D}{\partial p}}\overset{\left(-\right)}{\frac{\partial p}{\partial q}}\overset{\left(+\right)}{\frac{\partial q}{\partial r}}}+\overset{\left(+\right)}{\frac{\overset{\left(+\right)}{\partial {\pi}^D}}{\partial q}\overset{\left(+\right)}{\frac{\partial q}{\partial r}}}+\overset{\left(+\right)}{\frac{\overset{\left(-\right)}{\partial {\pi}^D}}{\partial c}\overset{\left(-\right)}{\frac{\partial c}{\partial r}}}=\frac{\left[2\left(1+v\right)-k-3r\right]{\left(a-w\right)}^2}{8{\left[2\left(1+v\right)-k-r\right]}^3}\frac{>}{<}0,\kern1em r\in \left[0,1\right]. $$