Higher costs, higher profits: Stackelberg leadership under family decision-making

In this paper, the key argument put forward is that, due to the possibility of sharing, one unit of a product under examination may deliver higher gross utility to a two-person family than to one person acting independently. Based on this argument, we propose a family decision-making framework which is characterized by kinked demand functions, and offer a treatment of Stackelberg markets with one leader and one follower. Under symmetric low production costs, the profits of the follower can be higher than the profits of the leader. We call this the second-mover advantage. This occurs generically when families have relatively low willingness-to-pay for a second unit, or in other words when the sharing effect is quite strong. In the parameter region that supports the second-mover advantage, we explore the effects of a symmetric increase in production costs. The increase in the costs may turn the second-mover advantage into a first-mover advantage, and both the leader's profit and the consumer surplus may increase. These results have implications for the desirability of tax interventions by the government and process innovations by the firms.