the no money pump assumption by two constraints — one that requires that the sum of the payoffs
to the innovator and the competitor is non-negative, and the other that the sum of transfers to
them is non-positive. This formulation of the problem is identical to the social planner’s problem
in the environment with no market signals. To see that the formulations are identical, note that,
using (13) and (14), (15) can now be written as
У (θ) > max m (
θ,θc l v
θ) [(t(θ, θ ) + Tc(θ, θ )∏70) - -K + T(θ, θ ) + Tc(θ, θ
Repeating essentially the same steps as in Proposition 1, it is straightforward to see that the
solution to the relaxed problem must have a threshold θ* below which it is optimal not to innovate,
the patent length is nondecreasing in the quality of the good θ. And since social surplus is decreasing
in the length of the patent, having a constant patent length is optimal. Q.E.D. ■
Note that the proof of this proposition relies crucially on the preceding lemma. We have
argued that the lemma fails to hold if bribes are exogenously limited in size. It follows that the
proposition relies crucially on the assumption that the bribes can be made sufficiently large.
This proposition provides a very strong, perhaps overly strong, result. It implies that a variety
of ways of sustaining innovative activity, such as government subsidies for innovation, subsidies to
research and so on are ineffective in stimulating innovation. The observation that, in practice, such
mechanisms have been effective suggest that the idea that bribes can be made entirely in secret is
too strong an assumption. Nevertheless, it highlights the importance of monitoring side payments
in using prize-like mechanisms to provide innovation incentives and highlights the sense in which
innovators have incentives to abuse mechanisms which rely on market signals. Below, we discuss
other ways in which innovators could distort market signals.
One interpretation of bribes is that they are implicit payments sustained by a form of implicit
collusion. An example of such implicit collusion is as follows. Suppose that the economy has
two agents and lasts for an infinite number of periods. Agents discount the future at the rate β.
With probability 0.5, one of these agents is the innovator and the other is the competitor in each
period. Suppose that the planner chooses some mechanism. Fix an equilibrium of this infinitely
repeated mechanism. The bribe paid by the innovator to the competitor can now be thought as
the difference between the payoffs in this equilibrium and the best equilibrium. Suppose that the
payoffs in any equilibrium are bounded above and that the differences in the payoffs in the best
and the worst equilibria are given by B. Then the size of the payoffs is limited and Proposition 4.
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