AY 2018-2019
Microeconomics II Final Test 2nd part
7 June 2019
Prof. Nicola Dimitri
You can use the calculator if needed. Smartphones, lecture notes and books are not allowed. You have 1 hour and 30 minutes.
1. (11 points)
find first and second best contract (quantity and expenditure), in the buyer-seller model seen in class when
v (q )= q 1+q
.
2. (11 points)
Find first and second best contract in the principal-agent model seen in class when
U (w)= √ w
, andV (q−w)=q−w
3. (11 points)
Consider two agents, 1 and 2 . Agent 1 can be of just one type θ1 while player 2 can be of two types,
θ
2' andθ
2' ' . The two agents have the following preferences over three alternativesX = { x , y , z }
.Discuss if agent
2
has an incentive to reveal his true preferences with the following Social Choice Functions:a)
f ( θ
1, θ
2') =x , f ( θ1,θ
2'') = y
b)
f ( θ
1, θ
2' ') = y , f ( θ1,θ
'2
) = x
c)
f ( θ
1, θ
2') =z , f ( θ1,θ
2'') = y
d)
f ( θ
1, θ
2') = y , f ( θ1, θ
2' ') = z
e)
f ( θ
1, θ
2') =x , f ( θ1,θ
2'') = z
1
Name:_____________________
Surname:__________________
Matricola:__________________
θ1 θ2'
θ2' '
y y x
x z z
z x y
f)
f ( θ
1, θ
2') =z , f ( θ1,θ
2'') = x
2
