where T (0) represents the prize. Since a prize is a lump sum transfer financed by lump sum taxes
on consumers, it does not affect the social surplus. The solution of the problem with prizes is then
to set the patent length τ = 0 and reward innovators with prizes above the critical threshold value
where the voluntary participation constraint binds. Thus, if the planner has as much information
as the innovator, patents are never optimal. This reasoning leads us to consider the environments
in which the planner has less information than private agents.
4. Benchmark with private information
Consider a benchmark model in which the quality of the idea 0 is private information to the
innovator. No other agent can observe θ. The planner only observes whether the good has been
produced or not. Since the innovator can always incur no cost and produce a good of type 0, the
instruments available to the planner are, without loss of generality, the length of the patent τ and
the lump-sum prize or transfer T.
We now define a mechanism design problem of the social planner as follows. From the
revelation principle we can restrict attention to direct mechanisms which consist of a reported type
0 ∈ [0, 0] for the innovator to the planner and the outcome functions 5(0), τ(0), T(0). The function
5 (0): [0, 0] → {0,1} is an instruction from the planner to the innovator recommending whether or
not to incur the fixed cost K. The patent length function is given by τ (0) : [0,0] → [0,1]. The
prize function is given by T (0) : [0, 0] → (-∞, ∞).
These outcome functions induce the following payoffs for the innovator. Let V(0, 0, 7) denote
the profits of the innovator who has an idea of quality 0 and reports an idea of quality 0 to the
planner, where 7 = 1 denotes that type 0 > 0 good is produced, and 7 = 0 denotes that 0 = 0 good
is produced. The innovator’s payoffs are given by
V(0, 0, 7) = 5(0) ∣τ(0)π(γ0) — 7K + T(0)1 .
The social surplus for the planner under truth telling is given by
W = I {5(0) [τ(0)Sm(0) + (1 — τ(0))S(0) — K]} W (0). (3)
The above equation states that for the period of length τ (0) , the good is produced under
monopoly so that the planner receives the surplus of Sm"(0), for the period of (1 — τ(0)) the good is
produced by the competitive markets and the surplus of S(0) is received.