An expert must train a novice. The novice initially has no cash, so he can only pay the expert with the accumulated surplus from his production. At any time, the novice can leave the relationship with his acquired knowledge and produce on his own. The sole reason he does not is the prospect of learning in future periods. The profit-maximizing relationship is structured as an apprenticeship, in which all production generated during training is used to compensate the expert. Knowledge transfer takes a simple form. In the first period, the expert gifts the novice a positive level of knowledge, which is independent of the players’ discount rate. After that, the novice’s total value of knowledge grows at the players’ discount rate until all knowledge has been transferred. The inefficiencies that arise from this contract are caused by the expert’s artificially slowing down the rate of knowledge transfer rather than by her reducing the total amount of knowledge eventually transferred. We show that these inefficiencies are larger the more patient the players are. Finally, we study the impact of knowledge externalities across players.
