Cost reduction, licensing and incentive to innovate: a note

In this Note we consider an economy composed by two firms; a leader and a follower, that invest in R&D for process innovations. Competition to innovate is usually modelled as a two stage game. In the first stage of the game both firms simultaneously reduces their production costs. In the second stage the firms compete à la Stackelberg and it is possible to prove that the profits of one of the two firms (and total profits) might decrease in a range of parameters. Then we consider the possibility of technology transfer from the leader that has the most productive technology to the follower under licensing by means of a fixed fee and of a royalty. It is possible to prove that under licensing total profits will increase in some range of parameters above mentioned in comparison to the pre-innovation case.