At a hotel in Munich in May 2007, Webasto, a German auto parts
maker, decided to license the rights to one of its best-selling products - a
roof-top solar panel for cars and trucks - to the highest bidder at a public
auction. (See International Herald Tribune, May 13, 2007). Firms com-
ing from di¤erent industries attended this public auction. From which
type of industry do you think the highest bidder for Webasto’s products
came from? From a concentrated (monopoly-like) industry? From a
much more competitive industry with numerous small players? Or from
some intermediate (oligopoly-like) industry? The following exercise will
help you answering these questions.
Assume that the demand for trucks is p = 100 ???? q (where q is the
quantity and p is the price), and that Webasto’s roof-top solar panel
allows truck manufacturers to reduce the constant marginal cost of pro-
duction from 70 to 60.
1. Con…rm that this is a nondrastic (or minor) innovation and that
marginal cost would have to be reduced to less than 40 for the
innovation to be drastic (or major).
2. Suppose that the industry is a monopoly (not threatened by entry).
How much is this …rm willing to pay (per period of time) to acquire
the innovation?
3. Suppose that the industry is a Bertrand oligopoly. That is, there
are n …rms (with n  2) that compete in price. Before the in-
novation, all …rms have the same marginal cost of 70. After the
innovation, one of them has a lower cost of 60. Compute how much
the latter …rm is willing to pay for the innovation.
4. Now assume that the market is served by Cournot duopolists who
have identical marginal costs of 70 before the innovation.
(a) Con…rm that the pre-innovation price is 80 and that at this
price each …rm has pro…ts per period of 100.
(b) Suppose that one of these …rms is granted use of the innova-
tion. Con…rm that the price falls to 76.67, and compute the
per period pro…ts of the two …rms.
(c) How much is any of these duopolists willing to pay to acquire
the innovation?
1
5. Suppose that the industry is a monopoly threatened by entry.
More precisely, with the existing technology, production at a mar-
ginal cost of 70 does not make entry pro…table. However, by low-
ering the marginal cost to 60, the new technology makes entry
pro…table. So, by acquiring the innovation, the incumbent …rms
precludes entry: it remains a monopolist and produces now at a
marginal cost of 60. On the other hand, if the monopolist does not
acquire the innovation, another …rm does, which allows it to enter
the market. The market structure becomes thus an asymmetric
Cournot duopoly in which the incumbent …rm has a marginal cost
of 70, while the entrant has a marginal cost of 60.
(a) How much is the incumbent …rm willing to pay for the inno-
vation?
(b) How much is the entrant willing to pay for the innovation?
(c) If the innovation goes to the highest bidder, what is the
inzuence of innovation on market structure? Discuss.
6. Finally, by collecting your answers to questions 1 to 5, rank the
various market structures according to the incentives to innovate
that they convey to …rms. Comment your ranking.
Exercise 2.
Consider the following duopoly. Each …rm i (i = 1; 2) incurs a con-
stant marginal cost equal to ci and produces a di¤erentiated product,
qi, sold at price pi. The demand system is obtained from the opti-
mization problem of a representative consumer. We assume a quadratic
utility function which generates the linear inverse demand schedule pi =
a ???? qi ???? qj in the region of quantities where prices are positive. The
parameter 2 [0; 1] is an inverse measure of the degree of product dif-
ferentiation: the lower the more products are di¤erentiated (if = 1,
products are perfect substitutes; if = 0, products are perfectly di¤er-
entiated). Firms compete à la Cournot on the product market. Initially,
both …rms produce at cost ci = c. A new process innovation allows …rms
to reduce the constant marginal cost of production from c to c0 = c ???? x
(with 0 < x < c). We assume that the innovation is nondrastic. That is
the cost reduction does not allow the innovator to behave like a monopo-
list. A su¢ cient condition is that the monopoly price corresponding to c0
is larger than the initial cost c; that is, (a + c ???? x) =2 > c. Equivalently,
assuming without loss of generality that the di¤erence a ???? c is equal to
unity, we assume: x < a ???? c = 1.
2
1. Compute how much a duopolist is willing to pay for acquiring the
innovation and being its single user (i.e., compute the di¤erence
between the pro…t a …rm makes when it is the sole user of the inno-
vation and the pro…t it makes when no …rm uses the innovation).
2. Suppose now that a product innovation allows …rms to increase
product di¤erentiation (i.e., to reduce the parameter ). Show
that if the initial degree of product substitution, , is larger than
2=3, then the adoption of this product innovation always reduces
the incentives to adopt the process innovation (computed at the
previous question).
Exercise 3.
Consider an innovative environment where independent or nearly si-
multaneous discoveries are possible. More speci…cally, we assume that
two …rms are engaged in R&D that results either in an innovation (with
probability ) or failure (with probability 1????). It is assumed that the
probability of success () is independent across …rms. Firms can protect
their innovation either by secrecy or by …ling for a patent.
 If the innovation is protected by secrecy, it leaks out with proba-
bility 1 ???? s, regardless of the number of successful …rms. When
this happens, the innovation is publicly available and production
is at the competitive level, driving the innovator’s pro…ts down to
zero.
 Patent protection is measured by the probability that a patent
holder can exclude competitors from using the innovation, which
is denoted p. Hence, with probability 1 ???? p, the innovation
becomes public, resulting again in zero pro…ts for the innovator.
If only one …rm succeeds in R&D and the innovation does not become
public, the …rm earns monopoly pro…t m. If both …rms succeed and
their innovation does not become public, each …rm earns duopoly pro…t
d < m. In the case where both …rms are successful and …le for the
patent, each …rm obtains it with probability 1=2. The two …rms have to
decide whether to …le for a patent (strategy noted P) or resort to secrecy
(strategy noted S). This decision has to be made before learning whether
the competitor has succeeded or not.
1. Using the above information, compute the …rms’expected pro…ts
for the four combinations of strategies. Denote (a1; aq2) the ex-
pected pro…t for a …rm when it chooses strategy a1 and its oppo-
nent chooses strategy a2, with a1 and a2 2 fP; Sg. You are thus
asked to compute (P; P), (P; S), (S; P), and (S; S).
3
2. Suppose that p = s. That is, the innovation has the same
probability of becoming public whether it is protected by secrecy
or by a patent (in other words, patent and secrecy o¤er the same
level of protection).
(a) Show that patenting is a dominant strategy. That is, show
that both (P; P)  (S; P) and (P; S)  (S; S) are
true.
(b) Show also that successful …rms prefer the situation where they
both …le for a patent over the situation where they both keep
the innovation secret. That is, show that (P; P)  (S; S)
is true.
3. Suppose now that p 6= s. To ease the computations, set m = 16,
d = 4, and  = 1=2
(a) Compute the values of (P; P), (P; S), (S; P), and  (S; S) under these assumptions.
(b) Characterize the Nash equilibrium (in pure strategies) of the
game for all p; s 2 [0; 1]. Represent graphically the charac-
terization of the equilibrium in the plane (p; s).
(c) Show that both …rms may choose to protect the innovation via
a patent even though patents o¤er a weaker protection than
secrecy. Explain the economic intuition behind this result.