Economics, Organization, and Management
Examination Set (July 10th, 2015)
(Paolo Bertoletti)
Time: 90 minutes.
1.
Suppose that two firms form a joint venture to perform a common project. An
investment y with total revenue R(y) = 9y – y2 has a cost of v1(y) = y for the first firm and of
v2(y) = 2y, to the second firm. Which is the efficient level of investment? Which is the
minimum share of the revenue that will be accepted by firm 2?
Total value is given by TV(y) = R(y) – v1(y) – v2(y) = 6y – y2. The FOC TV’(y) = 6 – 2y = 0 shows
that the efficient level is y* = 3. Accordingly, R(y*) = 18: since v2(y*) = 6 the minimum share that
firm 2 will accept is given by 1/3.
2. A potential buyer can have either a willingness to pay of 4 (with probability 1/3) or of 2
(with probability 2/3). A potential seller has either a cost of 2 (with probability 1/2) or a cost
of 3 (with probability 1/2). Will they be able to exchange efficiently? Why or why not?
The situation is described in the following matrix:
B\S
2 (Prob = 1/2)
3 (Prob = 1/2)
2 (Prob = 2/3)
p22
/
4 (Prob = 1/3)
p42
p43
Standard considerations (the need to reduce the incentive to overevaluate her cost for the seller and
to underestimate his willingness to pay for the buyer) suggest that a mediator should choose p22 = 2
and p43 = 3. Moreover, the incentive compatible constraints (for the sake of simplicity we write p
for p42) also require that:
B(4): (4 - p)/2 + (4 - 3)/2 = 5/2 – p/2  (4 - 2)/2 = 1,
i.e., 3  p,
S(1): (p - 2)/3  (3 - 2)/3 = 1/3,
i.e., p  3.
Accordingly, they should be able to exchange efficiently, for instance by using the indicated set of
contingent prices.
3. Discuss how the difficulties of “Performance Measurement” in a transaction can affect the
way it is organized.
When the performances required in a transaction cannot be measured with accuracy, arrangements
are made to tackle the problem. For example, in situation involving moral hazard by the insured
person, incomplete coverage is used, or single worker instead of a team are used to perform specific
job (e.g., taxi driving), with a loss of efficiency with respect to the case of full observation of the
performances.