non-convexities of the kind considered in this paper are not necessary to account for the observed
pattern of production of new goods, and, hence, the patents are unnecessary. To the extent that
non-convexities of the kind considered here are important in actual innovations, the analysis of the
necessity of patents when markets signals can be manipulated is applicable.
2. Model
Consider an economy in which an innovator has an idea of quality F. This idea can be
transformed into a good of quality F if a fixed cost of K > 0 is incurred. If this cost is not incurred,
a good of quality θ = 0 is produced. We assume that the quality of the innovation θ ∈ [0, 0] and
is distributed according to the cumulative distribution function F (F). We assume that F is finite.
The social value of the innovation under competitive markets is given by S (F), where S' (∙) > 0,
S (0) = 0.
We normalize profits if a good is produced under the competitive markets to be equal to
zero. The good can also be produced by a monopoly. Let the monopoly profits be given by π(F),
where π'(∙) > 0, π(0) = 0. We assume that monopoly conveys deadweight costs. The social value
of the innovation under monopoly, Sm(θ), is smaller than the social value of the innovation under
competitive markets:
S (F) ≥ S m(F) ≥ 0.
We assume Sm' (∙) > 0, Sm (0) = 0.
One simple setup which generates the payoff functions S (∙), Sm (∙), π (∙) is the following.
Suppose that the inverse demand function for the single good produced in the marketplace is given
by p = D (q, F), where F is a shift parameter that affects the demand curve. Let cm ≥ 0 denote the
marginal cost of production. Here the social surplus is given by the area below the demand curve
and above the cost curve:
∕∙O
S(θ) = /
Jo
1(cm)
D(x, θ)dx.
The social surplus under monopoly is given by
S(0) = Γ°[D(x, F) + (pm - c)]dx,
Jpm
where pm is the price chosen by a profit-maximizing monopolist. This simple example easily maps
onto the general environment described above and generates the surplus function under the compet-