A monopoly that sells to brand-name loyal customers and to price-sensitive customers must decide whether to carry both name-brand and private-label products and how much to charge. The monopoly may charge either more or less for the brand name if it carries a private label, and the price differential between the products is sensitive to cost and taste parameters.
Perloff, J. M., LaFrance, J. T., & Chouinard, H. (2012). Brand name and private label price setting by a monopoly store. Economics Letters, 116(3), 508 - 511. https://doi.org/10.1016/j.econlet.2012.04.062