The freemium pricing model has become mainstream in the software industry. A large user base can induce positive network effects while expanding security risks associated with unpatched users. This study explores a two-stage decision problem faced by software vendors that involves a freemium...

We explore optimal health subsidies in a dynastic model with health externalities to productivity that cause low health spending, productivity, longevity, savings and labor but high fertility. Public or firms’ health subsidies increase health spending, longevity and productivity and decrease...