Modify the model presented in Section 14.4 such that followers can now use the innovation of the technological leader and immediately leapfrog the leader, but in this case they have to pay a license fee of ζ to the leader.
(a) Characterize the BGP in this case.
(b) Write the value functions.
(c) Explain why licensing can increase the growth rate of the economy in this case, and contrast this result to the one in Exercise
12.9, where licensing was never used in equilibrium. What is the source of the difference between the two sets of results?
Exercise 12.9
The discussion in the text presumed a particular form of patent policy, which provided ex post monopoly power to the innovator. An alternative intellectual property rights policy is licensing: firms that have made an innovation can license the rights to use this innovation to others. This exercise asks you to work through the implications of this type of licensing. Throughout, think of the licensing stage as follows: the innovator can make a take-it-or-leave-it-offer to one or many firms so that they can buy the rights to use the innovation (and produce as many units of the output as they like) in return for some licensing fee ν. Consider a competitive environment, and show that if firm 1 is allowed to license its innovation to others, this can never raise its profits and can never increase its incentives to undertake the innovation. Provide an intuition for this result. Now modify the model, so that each firm has a strictly convex and increasing cost of producing, ψ1(q), and also has to pay a fixed cost of ψ0 > 0 to be active (so that the average costs take the familiar inverted U shape). Show that licensing can be beneficial for firm 1 in this case and therefore increase innovation incentives. Explain why the results differ between the two cases.