License or entry with vertical differentiation in duopoly

We consider choice of options for a foreign innovating firm to license its technology for producing the high quality good to a domestic firm, or to enter the market of the domestic country with or without license. Under the assumption of uniform distribution about taste parameters of consumers; when cost functions are linear, if the low quality good’s quality is sufficiently high, license without entry strategy is optimum; if the low quality good’s quality is low, both of entry without license strategy and license without entry strategy are optimum; when cost functions are quadratic, if the high quality good’s quality is high, license without entry strategy is optimum; if the high quality good’s quality is low, entry with license strategy is optimum.